Deterministic compartment models(CMs)and stochastic models,including stochastic CMs and agent-based models,are widely utilized in epidemic modeling.However,the relationship between CMs and their corresponding stochast...Deterministic compartment models(CMs)and stochastic models,including stochastic CMs and agent-based models,are widely utilized in epidemic modeling.However,the relationship between CMs and their corresponding stochastic models is not well understood.The present study aimed to address this gap by conducting a comparative study using the susceptible,exposed,infectious,and recovered(SEIR)model and its extended CMs from the coronavirus disease 2019 modeling literature.We demonstrated the equivalence of the numerical solution of CMs using the Euler scheme and their stochastic counterparts through theoretical analysis and simulations.Based on this equivalence,we proposed an efficient model calibration method that could replicate the exact solution of CMs in the corresponding stochastic models through parameter adjustment.The advancement in calibration techniques enhanced the accuracy of stochastic modeling in capturing the dynamics of epidemics.However,it should be noted that discrete-time stochastic models cannot perfectly reproduce the exact solution of continuous-time CMs.Additionally,we proposed a new stochastic compartment and agent mixed model as an alternative to agent-based models for large-scale population simulations with a limited number of agents.This model offered a balance between computational efficiency and accuracy.The results of this research contributed to the comparison and unification of deterministic CMs and stochastic models in epidemic modeling.Furthermore,the results had implications for the development of hybrid models that integrated the strengths of both frameworks.Overall,the present study has provided valuable epidemic modeling techniques and their practical applications for understanding and controlling the spread of infectious diseases.展开更多
Pharmacokinetic compartment models are the only models that can extract pharmacokinetic parameters from data collected in clinical studies but their estimates lack accuracy, explanations and physiological significance...Pharmacokinetic compartment models are the only models that can extract pharmacokinetic parameters from data collected in clinical studies but their estimates lack accuracy, explanations and physiological significance. The objective of this work was to develop particular solutions to drug concentration and AUC in the form of mathematical series and Heaviside functions for repetitive intermittent infusions in the one- and two-compartment models, as a function of dose number and total time using differential calculus. It was demonstrated that the central and peripheral compartment volumes determined from regression analysis of the aminoglycoside antibiotic Sisomicin concentration in plasma represent the actual physiological body fluid volumes accessible by the drug. The drug peak time and peak concentration in the peripheral compartment were also calculated as a function of dose number. It is also shown that the time of intercompartmental momentary distribution equilibrium can be used to determine the drug’s apparent volume of distribution within any dosing interval in multi-compartment models. These estimates were used to carry out simulations of plasma drug concentration with time in the one-compartment model. In conclusion, the two-compartment open mammillary pharmacokinetic model was fully explained for the aminoglycoside antibiotic sisomicin through the new concept of the apparent volume of distribution.展开更多
The first biphasic open one-compartment pharmacokinetic model is described. Its analytical solutions to drug concentration were developed from parameters of an open two-compartment pharmacokinetic model. The model is ...The first biphasic open one-compartment pharmacokinetic model is described. Its analytical solutions to drug concentration were developed from parameters of an open two-compartment pharmacokinetic model. The model is used to explain the unusually large compartment volumes and apparent volumes of distribution of lipophilic drugs, as well as to identify which of the pharmacokinetic parameters of the classical compartment models are biologically relevant.展开更多
Purpose: To review some of the basic models, differential equations and solutions, both analytic and numerical, which produce time courses for the fractions of Susceptible (S), Infectious (I) and Recovered (R) fractio...Purpose: To review some of the basic models, differential equations and solutions, both analytic and numerical, which produce time courses for the fractions of Susceptible (S), Infectious (I) and Recovered (R) fractions of the population during the epidemic and/or endemic conditions. Methods: Two and three-compartment models with analytic solutions to the proposed linear differential equations as well as models based on the non-linear differential equations first proposed by Kermack and McKendrick (KM) [1] a century ago are considered. The equations reviewed include the ability to slide between so-called Susceptible-Infected-Recovered (SIR), Susceptible-Infectious-Susceptible (SIS), Susceptible-Infectious (SI) and Susceptible-Infectious-Recovered-Susceptible (SIRS) models, effectively moving from epidemic to endemic characterizations of infectious disease. Results: Both the linear and KM model yield typical “curves” of the infected fraction being sought “to flatten” with the effects of social distancing/masking efforts and/or pharmaceutical interventions. Demonstrative applications of the solutions to fit real COVID-19 data, including linear and KM SIR fit data from the first 100 days following “lockdown” in the authors’ locale and to the total number of cases in the USA over the course of 1 year with SI and SIS models are provided. Conclusions: COVID-19 took us all by surprise, all wondering how to help. Spreading a basic understanding of some of the mathematics used by epidemiologists to model infectious diseases seemed like a good place to start and served as the primary purpose for this tutorial.展开更多
The two compartment model with variable extracellular volume is presented and solved by using both perturbation and analytical method. The computation for both creatinine and urea show that the perturbation solution ...The two compartment model with variable extracellular volume is presented and solved by using both perturbation and analytical method. The computation for both creatinine and urea show that the perturbation solution is not only simple but also accurate enough and is a good substitute for the more exact analytical solution.展开更多
Published clinical data of Prazosin were reevaluated pharmacokinetically using explicit solutions to drug concentration as a function of total time for IV bolus injection, intermittent intravenous infusion and oral ro...Published clinical data of Prazosin were reevaluated pharmacokinetically using explicit solutions to drug concentration as a function of total time for IV bolus injection, intermittent intravenous infusion and oral routes of administration in an open two-compartment model. In a novel way, the apparent volume of distribution was estimated from a two-compartment model and found to be close to the total body water suggesting that Prazosin is distributed in all tissues both extracellularly and intracellularly. In addition, extracting the value of the apparent volume of distribution from a two-compartment model allowed comparative simulations in the one-compartment model. It is shown that dosage calculations of Prazosin intermittent infusion can be safely performed using the simpler one-compartment model equations. Lastly, several additional time-dependent pharmacokinetic parameters e.g., the peak time in the central and peripheral compartment and non-steady state and steady state peak concentration and AUC were determined using series equations for all three routes of administration, as a function of dose number and total time upon multiple drug administrations in the two-compartment model. It is also the first time that steady-state plasma drug concentration equations were derived in a two-compartment mammillary model.展开更多
Nowadays, isotope environmental technique tends to be used as a reconnaissance tool , both qualitative and quantitative, to calculate the aquifer parameters particularly in carbonate rock aquifers. But, the hetero...Nowadays, isotope environmental technique tends to be used as a reconnaissance tool , both qualitative and quantitative, to calculate the aquifer parameters particularly in carbonate rock aquifers. But, the heterogeneous flow is still problematic when Lumped parameter Models are usually used to calculate the residence times and hydraulic parameters. However, Discrete State Compartment Model can provide a powerful model to heterogeneous medium. One such study was carried on in Dazha valley, where the environmental tritium was used as a tracer for determining hydrogeological parameters based on a discrete state compartment model展开更多
The residence-time distribution （RTD） and the compartment model were applied to characterizing the flow regions in red mud separation thickener’s feedwells. Combined with the experimental work, validated mathematic...The residence-time distribution （RTD） and the compartment model were applied to characterizing the flow regions in red mud separation thickener’s feedwells. Combined with the experimental work, validated mathematical model as well as three-dimensional computational fluid dynamics （CFD） model was established to analyze the flow regions of feedwells on an industrial scale. The concept of RTD, although a well-known method for the characterization of mixing behavior in conventional mixers and reactors, is still a novel measure for the characterization of mixing in feedwells. Numerical simulation results show that the inlet feed rate and the aspect ratio of feedwells are the most critical parameters which affect the RTD of feedwell. Further simulation experiments were then carried out. Under the optimal operation conditions, the volume fraction of dead zone can reduce by10.8% and an increasement of mixing flow volume fraction by 6.5% is also observed. There is an optimum feed inlet rate depending on the feedwell design. The CFD model in conjunction with the RTD analysis then can be used as an effective tool in the design, evaluation and optimization of thickener feedwell in the red mud separation.展开更多
The clinical pharmacokinetics of ribavirin after a single oral dose of 600 mg ribavirin tablets in healthy Chinese volunteers was studied. A rapid and simple high performance liquid chromatography （HPLC） method was ...The clinical pharmacokinetics of ribavirin after a single oral dose of 600 mg ribavirin tablets in healthy Chinese volunteers was studied. A rapid and simple high performance liquid chromatography （HPLC） method was developed to determine the ribavirin concentration in human plasma. C18 column was used for separation with a column temperature of 25℃, the mobile phase was ultrapure water adjusted to pH 3 with acetic acid at the flow rate of 1 mL/min, and the detection wavelength was set at 207 rim. The linear range of the standard curves was 50.4-2016.0 ng/mL and the lower limit of quantification （LLOQ） was 50.4 ng/mL. The relative recoveries of ribavirin were more than 90% in plasma. The RSD of the intra-day precision was less than 10% and that of inter-day was less than 15%. The pharmacokinetic parameters of ribavirin were calculated by WinNonlin. Results indicated that the two-compartment model was a better model for describing the pharmacokinetics profile of ribavirin than one-compartment model. The AUC0-t was 10807.8 h.ng/mL, the CL/F was 64879.5 mL, and the Cmax was 525.1 ng/mL. These results provided the experimental data for the development of ribavirin dosage form.展开更多
In this paper, we analyze the quasi-stationary distribution of the stochastic <em>SVIR</em> (Susceptible, Vaccinated, Infected, Recovered) model for the measles. The quasi-stationary distributions, as disc...In this paper, we analyze the quasi-stationary distribution of the stochastic <em>SVIR</em> (Susceptible, Vaccinated, Infected, Recovered) model for the measles. The quasi-stationary distributions, as discussed by Danoch and Seneta, have been used in biology to describe the steady state behaviour of population models which exhibit discernible stationarity before to become extinct. The stochastic <em>SVIR</em> model is a stochastic <em>SIR</em> (Susceptible, Infected, Recovered) model with vaccination and recruitment where the disease-free equilibrium is reached, regardless of the magnitude of the basic reproduction number. But the mean time until the absorption (the disease-free) can be very long. If we assume the effective reproduction number <em>R</em><em><sub>p</sub></em> < 1 or <img src="Edit_67da0b97-83f9-42ef-8a00-a13da2d59963.bmp" alt="" />, the quasi-stationary distribution can be closely approximated by geometric distribution. <em>β</em> and <em>δ</em> stands respectively, for the disease transmission coefficient and the natural rate.展开更多
The nitrogen （N） distribution and cycling of atmosphere-plant-soil system in the typical meadow Calamagrostis angustifolia wetland （TMCW） and marsh meadow Calamagrostis angustifolia wetland （MMCW） in the Sanjian...The nitrogen （N） distribution and cycling of atmosphere-plant-soil system in the typical meadow Calamagrostis angustifolia wetland （TMCW） and marsh meadow Calamagrostis angustifolia wetland （MMCW） in the Sanjiang plain were studied by a compartment model. The results showed that the N wet deposition amount was 0.757 gN/（m^2·a）, and total inorganic N （TIN） was the main body （0.640 gN/（m^2·a））. The ammonia volatilization amounts of TMCW and MMCW soils in growing season were 0.635 and 0.687 gN/m^2, and the denitrification gaseous lost amounts were 0.617 and 0.405 gN/m^2, respectively. In plant subsystem, the N was mainly stored in root and litter. Soil organic N was the main N storage of the two plant-soil systems and the proportions of it were 93.98% and 92.16%, respectively. The calculation results of N turnovers among compartments of TMCW and MMCW showed that the uptake amounts of root were 23.02 and 28.18 gN/（m^2·a） and the values of aboveground were 11.31 and 6.08 gN/（m^2·a）, the re-translocation amounts from aboveground to root were 5.96 and 2.70 gN/（m^2·a）, the translocation amounts from aboveground living body to litter were 5.35 and 3.38 gN/（m^2·a）, the translocation amounts from litter to soil were larger than 1.55 and 3.01 gN/（m^2·a）, the translocation amounts from root to soil were 14.90 and 13.17 gN/（m^2·a）, and the soil （0-15 cm） N net mineralization amounts were 1.94 and 0.55 gN/（m^2·a）, respectively. The study of N balance indicated that the two plant-soil systems might be situated in the status of lacking N, and the status might induce the degradation of C. angustifolia wetland.展开更多
The nitrogen（N） biological cycle of the Suaeda salsa marsh ecosystem in the Yellow River estuary was studied during 2008 to 2009.Results showed that soil N had significant seasonal fluctuations and vertical distribu...The nitrogen（N） biological cycle of the Suaeda salsa marsh ecosystem in the Yellow River estuary was studied during 2008 to 2009.Results showed that soil N had significant seasonal fluctuations and vertical distribution.The N/P ratio（15.73±1.77） of S.salsa was less than 16,indicating that plant growth was limited by both N and P.The N absorption coefficient of S.salsa was very low（0.007）,while the N utilization and cycle coefficients were high（0.824 and 0.331,respectively）.The N turnover among compartments of S.salsa marsh showed that N uptake from aboveground parts and roots were 2.539 and 0.622 g/m2,respectively.The N translocation from aboveground parts to roots and from roots to soil were 2.042 and 0.076 g/m2,respectively.The N translocation from aboveground living bodies to litter was 0.497 g/m2,the annual N return from litter to soil was far less than 0.368 g/m2,and the net N mineralization in topsoil during the growing season was 0.033 g/m2.N was an important limiting factor in S.salsa marsh,and the ecosystem was classified as unstable and vulnerable.S.salsa was seemingly well adapted to the low-nutrient status and vulnerable habitat,and the nutrient enrichment due to N import from the Yellow River estuary would be a potential threat to the S.salsa marsh.Excessive nutrient loading might favor invasive species and induce severe long-term degradation of the ecosystem if human intervention measures were not taken.The N quantitative relationships determined in our study might provide a scientific basis for the establishment of effective measures.展开更多
Teak （Tectona grandis Linn. f.） ranks among the top five tropical hardwood species and is being promoted for use in plantations in its non-native range due to its high economic value. However, there is a general lac...Teak （Tectona grandis Linn. f.） ranks among the top five tropical hardwood species and is being promoted for use in plantations in its non-native range due to its high economic value. However, there is a general lack of data on ecosystem functioning of teak plantations. We aimed at understanding storage and flux of nutrients related to young plantations of teak. Cycling of nitrogen （N） and phosphorus （P） in a chronosequence of plantations （1, 5, 11, 18, 24 and 30 years） was studied in the Moist Deciduous Forest Region of North India with the objective of investigating the nutrient cycling pattern at younger age since the current trend of harvesting age of the species in several tropical countries is being drastically reduced for quick return from this high value crop. Standing state, nutrient uptake, nutrient return and nutrient retransloca-tion in these plantations were estimated by tree harvesting and chemical analysis methods. The range of total standing nutrient across all these plantations was 20.3 to 586.6 kg？ha-1 for N and 5.3 to 208.8 kg？ha-1 for P. Net uptake of N ranged from 19.4 to 88.9 kg？ha-1？a-1 and P from 3.8 to 18.1 kg？ha-1？a-1. Retranslocation of N and P among all the stands ranged from 8.7 to 48.0 kg？ha-1？a-1 and 0.01 to 3.5 kg？ha-1？a-1, respectively. Range of total nutrient return was 25.8 to 91.3 kg？ha-1？a-1 for N and 2.7 to 10.1 kg？ha-1？a-1 for P. N and P use efficiency was between 107.4 and 192.5 g dry organic matter （OM） g-1N, and 551.9 and 841.1 g OM g-1P, respec-tively. The turnover time ranged from 2.04-13.17 years for N and be-tween 2.40-22.66 years for P. Quantity of N and P in the soil nutrient pool ranged from 2566.8 to 4426.8 kg？ha-1 and 372 to 520 kg？ha-1, re-spectively. Storage and flux of components in different plant parts of different aged plantations were assessed and depicted in compartment models. Percentage storage in soil, litter and vegetation ranged from 82% to 99%, 0.6% to 2.4% and 0.5% to 15% for N, respectively, and from 63% to 98%, 0.5% to 2% and 1% to 35% for P, respectively. This infor-mation could be useful in managing external nutrient manipulation to crops of different ages for optimum biomass production or carbon se-questration.展开更多
The main characteristics of energy environment, energy products, primary productivity and basic process ofenergy flow for three-hardwood forest(Juglans mandshurica, Fraxinus mandshurica, and Phellodendron amurense) we...The main characteristics of energy environment, energy products, primary productivity and basic process ofenergy flow for three-hardwood forest(Juglans mandshurica, Fraxinus mandshurica, and Phellodendron amurense) werestudied. The research was mainly hased on the thcory and method of community energetics, dealing with fixed position,quantitative test and expcrimental analysis. The time-space dynamics of sun-radiation in three-hardwood forest were measured and the energy compartment model was set up. his rescarch work provided a scientitic basis for the exploitation, utilization and management of three-hardtwood forest.展开更多
A new method for parameter optimization of pharmacokinetics based on an artificial immune network named PKAIN is proposed. To improve local searching ability of the artificial immune network, a partition-based concurr...A new method for parameter optimization of pharmacokinetics based on an artificial immune network named PKAIN is proposed. To improve local searching ability of the artificial immune network, a partition-based concurrent simplex mutation is developed. By means of evolution of network cells in the PKAIN artificial immune network, an optimal set of parameters of a given pharmacokinetic model is obtained. The Laplace transform is applied to the pharmacokinetic differential equations of remifentanil and its major metabolite, remifentanil acid. The PKAIN method is used to optimize parameters of the derived compartment models. Experimental results show that the twocompartment model is sufficient for the pharmacokinetic study of remifentanil acid for patients with mild degree of renal impairment.展开更多
The sorption and desorption kinetics of dimethyl phthalate (DMP), diethyl phthalate (DEP), dibutyl phthalate (DBP) and phenol on water and sediment interface were studied using two compartment model in this paper. ...The sorption and desorption kinetics of dimethyl phthalate (DMP), diethyl phthalate (DEP), dibutyl phthalate (DBP) and phenol on water and sediment interface were studied using two compartment model in this paper. The results showed that the sorption coefficients of DMP, DEP, DBP and phenol measured by batch equilibrium method were 16.79, 24.55, 132 and 0.65μg 1-1/n · g -1 · ml -1/n , the sorption and desorption kinetic constants of DMP, DEP, DBP, phenol were 0.0248, 0.0357, 0.0727, 0.014ml·cm -2 ·h -1 and 0.000512, 0.000754, 0.00127, 0 000899h -1 at static condition respectively; and the sorption and desorption kinetics constants of above chemicals were 0 279, 0.382, 0.496, 0.0904ml·cm -2 ·h -1 and 0.0442, 0.0031, 0.00116, 0.00247h -1 at flow water condition respectively.展开更多
Taking the Chinese city of Xiamen as an example,simulation and quantitative analysis were performed on the transmissions of the Coronavirus Disease 2019(COVID-19)and the influence of intervention combinations to assis...Taking the Chinese city of Xiamen as an example,simulation and quantitative analysis were performed on the transmissions of the Coronavirus Disease 2019(COVID-19)and the influence of intervention combinations to assist policymakers in the preparation of targeted response measures.A machine learning model was built to estimate the effectiveness of interventions and simulate transmission in different scenarios.The comparison was conducted between simulated and real cases in Xiamen.A web interface with adjustable parameters,including choice of intervention measures,intervention weights,vaccination,and viral variants,was designed for users to run the simulation.The total case number was set as the outcome.The cumulative number was 4,614,641 without restrictions and 78 under the strictest intervention set.Simulation with the parameters closest to the real situation of the Xiamen outbreak was performed to verify the accuracy and reliability of the model.The simulation model generated a duration of 52 days before the daily cases dropped to zero and the final cumulative case number of 200,which were 25 more days and 36 fewer cases than the real situation,respectively.Targeted interventions could benefit the prevention and control of COVID-19 outbreak while safeguarding public health and mitigating impacts on people’s livelihood.展开更多
The apparent volume of distribution was defined for the first time as the phase volume that can hold the total amount of a substance at the measured phase substance concentration, in a system composed of two immiscibl...The apparent volume of distribution was defined for the first time as the phase volume that can hold the total amount of a substance at the measured phase substance concentration, in a system composed of two immiscible media that are in contact under conditions of constant phase volumes, at equilibrium. Its value is not affected by the total system solute mass and it only depends on the total system volume, the phase volumes and the affinity of the solute for the two phases in the system. Using this new concept of the apparent volume of distribution, we were able to demonstrate that under certain conditions compartment volumes in multi-compartment and multi-phasic pharmacokinetic models represent the actual physiological volumes of body fluids accessible by drugs. The classical pharmacokinetic models are now fully explained and can be used to provide accurate estimation of the pharmacokinetic parameters for hydrophilic drugs. In contrast, in the absence of tissue-plasma partition coefficients, lipophilic drugs that do not follow a one-compartment model are unlikely to be adequately described with classical multi-compartment pharmacokinetic models.展开更多
In this article, we consider the construction of a SVIR (Susceptible, Vaccinated, Infected, Recovered) stochastic compartmental model of measles. We prove that the deterministic solution is asymptotically the average ...In this article, we consider the construction of a SVIR (Susceptible, Vaccinated, Infected, Recovered) stochastic compartmental model of measles. We prove that the deterministic solution is asymptotically the average of the stochastic solution in the case of small population size. The choice of this model takes into account the random fluctuations inherent to the epidemiological characteristics of rural populations of Niger, notably a high prevalence of measles in children under 5, coupled with a very low immunization coverage.展开更多
This paper presents a new modified SIR model which incorporates appropriate delay parameters leading to a more precise prediction of COVID-19 real time data. The efficacy of the newly developed SIR model is proven by ...This paper presents a new modified SIR model which incorporates appropriate delay parameters leading to a more precise prediction of COVID-19 real time data. The efficacy of the newly developed SIR model is proven by comparing its predictions to real data obtained from four counties namely Germany, Italy, Kuwait, and Oman. Two included delay periods for incubation and recovery within the SIR model produce a sensible and more accurate representation of the real time data. In the absence of the two-delay period (<img src="Edit_8ce6d5c5-9b59-4640-9c0e-334e3948d11c.png" width="67" height="20" alt="" /><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">)</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> the dynamical behavior of the model will not correspond to today’s picture and lag the detection of the epidemic peak. The reproductive number <i></i></span></span></span><i><span><span><i><span style="font-family:Verdana;">R</span></i></span></span><span><span><span style="font-family:;" "=""><i><span style="font-family:Verdana;"><sub>0</sub></span></i><span style="font-family:Verdana;"></span></span></span></span></i> <span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">is defined for the model for values of recovery time delay <i></i></span></span></span><i><span style="font-family:Verdana;"><span style="font-family:Verdana;"><i><span style="font-family:Verdana;"><img src="Edit_882b068a-f7fa-478e-9fb9-4d78388010f3.png" width="25" height="20" alt="" /></span></i></span></span></i><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><sub></sub></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> of the infective case. The effect of recovery time <img src="Edit_882b068a-f7fa-478e-9fb9-4d78388010f3.png" width="25" height="20" alt="" /></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">may produce second wave, and/or an oscillation which could destabilize the behavior of the system and a periodic oscillation can arise due to Hopf bifurcation phenomenon.</span></span></span>展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.82173620 to Yang Zhao and 82041024 to Feng Chen)partially supported by the Bill&Melinda Gates Foundation(Grant No.INV-006371 to Feng Chen)Priority Academic Program Development of Jiangsu Higher Education Institutions.
文摘Deterministic compartment models(CMs)and stochastic models,including stochastic CMs and agent-based models,are widely utilized in epidemic modeling.However,the relationship between CMs and their corresponding stochastic models is not well understood.The present study aimed to address this gap by conducting a comparative study using the susceptible,exposed,infectious,and recovered(SEIR)model and its extended CMs from the coronavirus disease 2019 modeling literature.We demonstrated the equivalence of the numerical solution of CMs using the Euler scheme and their stochastic counterparts through theoretical analysis and simulations.Based on this equivalence,we proposed an efficient model calibration method that could replicate the exact solution of CMs in the corresponding stochastic models through parameter adjustment.The advancement in calibration techniques enhanced the accuracy of stochastic modeling in capturing the dynamics of epidemics.However,it should be noted that discrete-time stochastic models cannot perfectly reproduce the exact solution of continuous-time CMs.Additionally,we proposed a new stochastic compartment and agent mixed model as an alternative to agent-based models for large-scale population simulations with a limited number of agents.This model offered a balance between computational efficiency and accuracy.The results of this research contributed to the comparison and unification of deterministic CMs and stochastic models in epidemic modeling.Furthermore,the results had implications for the development of hybrid models that integrated the strengths of both frameworks.Overall,the present study has provided valuable epidemic modeling techniques and their practical applications for understanding and controlling the spread of infectious diseases.
文摘Pharmacokinetic compartment models are the only models that can extract pharmacokinetic parameters from data collected in clinical studies but their estimates lack accuracy, explanations and physiological significance. The objective of this work was to develop particular solutions to drug concentration and AUC in the form of mathematical series and Heaviside functions for repetitive intermittent infusions in the one- and two-compartment models, as a function of dose number and total time using differential calculus. It was demonstrated that the central and peripheral compartment volumes determined from regression analysis of the aminoglycoside antibiotic Sisomicin concentration in plasma represent the actual physiological body fluid volumes accessible by the drug. The drug peak time and peak concentration in the peripheral compartment were also calculated as a function of dose number. It is also shown that the time of intercompartmental momentary distribution equilibrium can be used to determine the drug’s apparent volume of distribution within any dosing interval in multi-compartment models. These estimates were used to carry out simulations of plasma drug concentration with time in the one-compartment model. In conclusion, the two-compartment open mammillary pharmacokinetic model was fully explained for the aminoglycoside antibiotic sisomicin through the new concept of the apparent volume of distribution.
文摘The first biphasic open one-compartment pharmacokinetic model is described. Its analytical solutions to drug concentration were developed from parameters of an open two-compartment pharmacokinetic model. The model is used to explain the unusually large compartment volumes and apparent volumes of distribution of lipophilic drugs, as well as to identify which of the pharmacokinetic parameters of the classical compartment models are biologically relevant.
文摘Purpose: To review some of the basic models, differential equations and solutions, both analytic and numerical, which produce time courses for the fractions of Susceptible (S), Infectious (I) and Recovered (R) fractions of the population during the epidemic and/or endemic conditions. Methods: Two and three-compartment models with analytic solutions to the proposed linear differential equations as well as models based on the non-linear differential equations first proposed by Kermack and McKendrick (KM) [1] a century ago are considered. The equations reviewed include the ability to slide between so-called Susceptible-Infected-Recovered (SIR), Susceptible-Infectious-Susceptible (SIS), Susceptible-Infectious (SI) and Susceptible-Infectious-Recovered-Susceptible (SIRS) models, effectively moving from epidemic to endemic characterizations of infectious disease. Results: Both the linear and KM model yield typical “curves” of the infected fraction being sought “to flatten” with the effects of social distancing/masking efforts and/or pharmaceutical interventions. Demonstrative applications of the solutions to fit real COVID-19 data, including linear and KM SIR fit data from the first 100 days following “lockdown” in the authors’ locale and to the total number of cases in the USA over the course of 1 year with SI and SIS models are provided. Conclusions: COVID-19 took us all by surprise, all wondering how to help. Spreading a basic understanding of some of the mathematics used by epidemiologists to model infectious diseases seemed like a good place to start and served as the primary purpose for this tutorial.
文摘The two compartment model with variable extracellular volume is presented and solved by using both perturbation and analytical method. The computation for both creatinine and urea show that the perturbation solution is not only simple but also accurate enough and is a good substitute for the more exact analytical solution.
文摘Published clinical data of Prazosin were reevaluated pharmacokinetically using explicit solutions to drug concentration as a function of total time for IV bolus injection, intermittent intravenous infusion and oral routes of administration in an open two-compartment model. In a novel way, the apparent volume of distribution was estimated from a two-compartment model and found to be close to the total body water suggesting that Prazosin is distributed in all tissues both extracellularly and intracellularly. In addition, extracting the value of the apparent volume of distribution from a two-compartment model allowed comparative simulations in the one-compartment model. It is shown that dosage calculations of Prazosin intermittent infusion can be safely performed using the simpler one-compartment model equations. Lastly, several additional time-dependent pharmacokinetic parameters e.g., the peak time in the central and peripheral compartment and non-steady state and steady state peak concentration and AUC were determined using series equations for all three routes of administration, as a function of dose number and total time upon multiple drug administrations in the two-compartment model. It is also the first time that steady-state plasma drug concentration equations were derived in a two-compartment mammillary model.
文摘Nowadays, isotope environmental technique tends to be used as a reconnaissance tool , both qualitative and quantitative, to calculate the aquifer parameters particularly in carbonate rock aquifers. But, the heterogeneous flow is still problematic when Lumped parameter Models are usually used to calculate the residence times and hydraulic parameters. However, Discrete State Compartment Model can provide a powerful model to heterogeneous medium. One such study was carried on in Dazha valley, where the environmental tritium was used as a tracer for determining hydrogeological parameters based on a discrete state compartment model
基金Project (50876116) supported by the National Natural Science Foundation of China
文摘The residence-time distribution （RTD） and the compartment model were applied to characterizing the flow regions in red mud separation thickener’s feedwells. Combined with the experimental work, validated mathematical model as well as three-dimensional computational fluid dynamics （CFD） model was established to analyze the flow regions of feedwells on an industrial scale. The concept of RTD, although a well-known method for the characterization of mixing behavior in conventional mixers and reactors, is still a novel measure for the characterization of mixing in feedwells. Numerical simulation results show that the inlet feed rate and the aspect ratio of feedwells are the most critical parameters which affect the RTD of feedwell. Further simulation experiments were then carried out. Under the optimal operation conditions, the volume fraction of dead zone can reduce by10.8% and an increasement of mixing flow volume fraction by 6.5% is also observed. There is an optimum feed inlet rate depending on the feedwell design. The CFD model in conjunction with the RTD analysis then can be used as an effective tool in the design, evaluation and optimization of thickener feedwell in the red mud separation.
文摘The clinical pharmacokinetics of ribavirin after a single oral dose of 600 mg ribavirin tablets in healthy Chinese volunteers was studied. A rapid and simple high performance liquid chromatography （HPLC） method was developed to determine the ribavirin concentration in human plasma. C18 column was used for separation with a column temperature of 25℃, the mobile phase was ultrapure water adjusted to pH 3 with acetic acid at the flow rate of 1 mL/min, and the detection wavelength was set at 207 rim. The linear range of the standard curves was 50.4-2016.0 ng/mL and the lower limit of quantification （LLOQ） was 50.4 ng/mL. The relative recoveries of ribavirin were more than 90% in plasma. The RSD of the intra-day precision was less than 10% and that of inter-day was less than 15%. The pharmacokinetic parameters of ribavirin were calculated by WinNonlin. Results indicated that the two-compartment model was a better model for describing the pharmacokinetics profile of ribavirin than one-compartment model. The AUC0-t was 10807.8 h.ng/mL, the CL/F was 64879.5 mL, and the Cmax was 525.1 ng/mL. These results provided the experimental data for the development of ribavirin dosage form.
文摘In this paper, we analyze the quasi-stationary distribution of the stochastic <em>SVIR</em> (Susceptible, Vaccinated, Infected, Recovered) model for the measles. The quasi-stationary distributions, as discussed by Danoch and Seneta, have been used in biology to describe the steady state behaviour of population models which exhibit discernible stationarity before to become extinct. The stochastic <em>SVIR</em> model is a stochastic <em>SIR</em> (Susceptible, Infected, Recovered) model with vaccination and recruitment where the disease-free equilibrium is reached, regardless of the magnitude of the basic reproduction number. But the mean time until the absorption (the disease-free) can be very long. If we assume the effective reproduction number <em>R</em><em><sub>p</sub></em> < 1 or <img src="Edit_67da0b97-83f9-42ef-8a00-a13da2d59963.bmp" alt="" />, the quasi-stationary distribution can be closely approximated by geometric distribution. <em>β</em> and <em>δ</em> stands respectively, for the disease transmission coefficient and the natural rate.
基金Project supported by the Knowledge Innovation Foundation of Chinese Academy of Sciences(KZCX2-YW-309,KZCX3-SW-332)the National Natural Science Foundation of China(No.920211003).
文摘The nitrogen （N） distribution and cycling of atmosphere-plant-soil system in the typical meadow Calamagrostis angustifolia wetland （TMCW） and marsh meadow Calamagrostis angustifolia wetland （MMCW） in the Sanjiang plain were studied by a compartment model. The results showed that the N wet deposition amount was 0.757 gN/（m^2·a）, and total inorganic N （TIN） was the main body （0.640 gN/（m^2·a））. The ammonia volatilization amounts of TMCW and MMCW soils in growing season were 0.635 and 0.687 gN/m^2, and the denitrification gaseous lost amounts were 0.617 and 0.405 gN/m^2, respectively. In plant subsystem, the N was mainly stored in root and litter. Soil organic N was the main N storage of the two plant-soil systems and the proportions of it were 93.98% and 92.16%, respectively. The calculation results of N turnovers among compartments of TMCW and MMCW showed that the uptake amounts of root were 23.02 and 28.18 gN/（m^2·a） and the values of aboveground were 11.31 and 6.08 gN/（m^2·a）, the re-translocation amounts from aboveground to root were 5.96 and 2.70 gN/（m^2·a）, the translocation amounts from aboveground living body to litter were 5.35 and 3.38 gN/（m^2·a）, the translocation amounts from litter to soil were larger than 1.55 and 3.01 gN/（m^2·a）, the translocation amounts from root to soil were 14.90 and 13.17 gN/（m^2·a）, and the soil （0-15 cm） N net mineralization amounts were 1.94 and 0.55 gN/（m^2·a）, respectively. The study of N balance indicated that the two plant-soil systems might be situated in the status of lacking N, and the status might induce the degradation of C. angustifolia wetland.
基金supported by the Innovation Program of the Chinese Academy of Sciences(No.KZCX2YW-223)the National Natural Science Foundation of China(No.40803023,40806048)+2 种基金the Key Program of Natural Science Foundation of Shandong Province(No. ZR2010DZ001)the Talents Foundation of the Chinese Academy of Sciences(No.AJ0809BX-036)the Open Research Foundation of Key Laboratory of China Oceanic Administration for Coast Ecology and Environment(No. 200906)
文摘The nitrogen（N） biological cycle of the Suaeda salsa marsh ecosystem in the Yellow River estuary was studied during 2008 to 2009.Results showed that soil N had significant seasonal fluctuations and vertical distribution.The N/P ratio（15.73±1.77） of S.salsa was less than 16,indicating that plant growth was limited by both N and P.The N absorption coefficient of S.salsa was very low（0.007）,while the N utilization and cycle coefficients were high（0.824 and 0.331,respectively）.The N turnover among compartments of S.salsa marsh showed that N uptake from aboveground parts and roots were 2.539 and 0.622 g/m2,respectively.The N translocation from aboveground parts to roots and from roots to soil were 2.042 and 0.076 g/m2,respectively.The N translocation from aboveground living bodies to litter was 0.497 g/m2,the annual N return from litter to soil was far less than 0.368 g/m2,and the net N mineralization in topsoil during the growing season was 0.033 g/m2.N was an important limiting factor in S.salsa marsh,and the ecosystem was classified as unstable and vulnerable.S.salsa was seemingly well adapted to the low-nutrient status and vulnerable habitat,and the nutrient enrichment due to N import from the Yellow River estuary would be a potential threat to the S.salsa marsh.Excessive nutrient loading might favor invasive species and induce severe long-term degradation of the ecosystem if human intervention measures were not taken.The N quantitative relationships determined in our study might provide a scientific basis for the establishment of effective measures.
文摘Teak （Tectona grandis Linn. f.） ranks among the top five tropical hardwood species and is being promoted for use in plantations in its non-native range due to its high economic value. However, there is a general lack of data on ecosystem functioning of teak plantations. We aimed at understanding storage and flux of nutrients related to young plantations of teak. Cycling of nitrogen （N） and phosphorus （P） in a chronosequence of plantations （1, 5, 11, 18, 24 and 30 years） was studied in the Moist Deciduous Forest Region of North India with the objective of investigating the nutrient cycling pattern at younger age since the current trend of harvesting age of the species in several tropical countries is being drastically reduced for quick return from this high value crop. Standing state, nutrient uptake, nutrient return and nutrient retransloca-tion in these plantations were estimated by tree harvesting and chemical analysis methods. The range of total standing nutrient across all these plantations was 20.3 to 586.6 kg？ha-1 for N and 5.3 to 208.8 kg？ha-1 for P. Net uptake of N ranged from 19.4 to 88.9 kg？ha-1？a-1 and P from 3.8 to 18.1 kg？ha-1？a-1. Retranslocation of N and P among all the stands ranged from 8.7 to 48.0 kg？ha-1？a-1 and 0.01 to 3.5 kg？ha-1？a-1, respectively. Range of total nutrient return was 25.8 to 91.3 kg？ha-1？a-1 for N and 2.7 to 10.1 kg？ha-1？a-1 for P. N and P use efficiency was between 107.4 and 192.5 g dry organic matter （OM） g-1N, and 551.9 and 841.1 g OM g-1P, respec-tively. The turnover time ranged from 2.04-13.17 years for N and be-tween 2.40-22.66 years for P. Quantity of N and P in the soil nutrient pool ranged from 2566.8 to 4426.8 kg？ha-1 and 372 to 520 kg？ha-1, re-spectively. Storage and flux of components in different plant parts of different aged plantations were assessed and depicted in compartment models. Percentage storage in soil, litter and vegetation ranged from 82% to 99%, 0.6% to 2.4% and 0.5% to 15% for N, respectively, and from 63% to 98%, 0.5% to 2% and 1% to 35% for P, respectively. This infor-mation could be useful in managing external nutrient manipulation to crops of different ages for optimum biomass production or carbon se-questration.
文摘The main characteristics of energy environment, energy products, primary productivity and basic process ofenergy flow for three-hardwood forest(Juglans mandshurica, Fraxinus mandshurica, and Phellodendron amurense) werestudied. The research was mainly hased on the thcory and method of community energetics, dealing with fixed position,quantitative test and expcrimental analysis. The time-space dynamics of sun-radiation in three-hardwood forest were measured and the energy compartment model was set up. his rescarch work provided a scientitic basis for the exploitation, utilization and management of three-hardtwood forest.
基金Project supported by Health Department of Jiangsu Province(No.P200512)
文摘A new method for parameter optimization of pharmacokinetics based on an artificial immune network named PKAIN is proposed. To improve local searching ability of the artificial immune network, a partition-based concurrent simplex mutation is developed. By means of evolution of network cells in the PKAIN artificial immune network, an optimal set of parameters of a given pharmacokinetic model is obtained. The Laplace transform is applied to the pharmacokinetic differential equations of remifentanil and its major metabolite, remifentanil acid. The PKAIN method is used to optimize parameters of the derived compartment models. Experimental results show that the twocompartment model is sufficient for the pharmacokinetic study of remifentanil acid for patients with mild degree of renal impairment.
文摘The sorption and desorption kinetics of dimethyl phthalate (DMP), diethyl phthalate (DEP), dibutyl phthalate (DBP) and phenol on water and sediment interface were studied using two compartment model in this paper. The results showed that the sorption coefficients of DMP, DEP, DBP and phenol measured by batch equilibrium method were 16.79, 24.55, 132 and 0.65μg 1-1/n · g -1 · ml -1/n , the sorption and desorption kinetic constants of DMP, DEP, DBP, phenol were 0.0248, 0.0357, 0.0727, 0.014ml·cm -2 ·h -1 and 0.000512, 0.000754, 0.00127, 0 000899h -1 at static condition respectively; and the sorption and desorption kinetics constants of above chemicals were 0 279, 0.382, 0.496, 0.0904ml·cm -2 ·h -1 and 0.0442, 0.0031, 0.00116, 0.00247h -1 at flow water condition respectively.
基金funded by Ministry of Science and Technology of the People’s Republic of China and the Beijing Organizing Committee for the 2022 Olympic and Paralympic Winter Games[2021YFF0306005]China-Africa Cooperation Program on Emerging and Re-emerging Infectious Diseases Control[No.2020C400032]
文摘Taking the Chinese city of Xiamen as an example,simulation and quantitative analysis were performed on the transmissions of the Coronavirus Disease 2019(COVID-19)and the influence of intervention combinations to assist policymakers in the preparation of targeted response measures.A machine learning model was built to estimate the effectiveness of interventions and simulate transmission in different scenarios.The comparison was conducted between simulated and real cases in Xiamen.A web interface with adjustable parameters,including choice of intervention measures,intervention weights,vaccination,and viral variants,was designed for users to run the simulation.The total case number was set as the outcome.The cumulative number was 4,614,641 without restrictions and 78 under the strictest intervention set.Simulation with the parameters closest to the real situation of the Xiamen outbreak was performed to verify the accuracy and reliability of the model.The simulation model generated a duration of 52 days before the daily cases dropped to zero and the final cumulative case number of 200,which were 25 more days and 36 fewer cases than the real situation,respectively.Targeted interventions could benefit the prevention and control of COVID-19 outbreak while safeguarding public health and mitigating impacts on people’s livelihood.
文摘The apparent volume of distribution was defined for the first time as the phase volume that can hold the total amount of a substance at the measured phase substance concentration, in a system composed of two immiscible media that are in contact under conditions of constant phase volumes, at equilibrium. Its value is not affected by the total system solute mass and it only depends on the total system volume, the phase volumes and the affinity of the solute for the two phases in the system. Using this new concept of the apparent volume of distribution, we were able to demonstrate that under certain conditions compartment volumes in multi-compartment and multi-phasic pharmacokinetic models represent the actual physiological volumes of body fluids accessible by drugs. The classical pharmacokinetic models are now fully explained and can be used to provide accurate estimation of the pharmacokinetic parameters for hydrophilic drugs. In contrast, in the absence of tissue-plasma partition coefficients, lipophilic drugs that do not follow a one-compartment model are unlikely to be adequately described with classical multi-compartment pharmacokinetic models.
文摘In this article, we consider the construction of a SVIR (Susceptible, Vaccinated, Infected, Recovered) stochastic compartmental model of measles. We prove that the deterministic solution is asymptotically the average of the stochastic solution in the case of small population size. The choice of this model takes into account the random fluctuations inherent to the epidemiological characteristics of rural populations of Niger, notably a high prevalence of measles in children under 5, coupled with a very low immunization coverage.
文摘This paper presents a new modified SIR model which incorporates appropriate delay parameters leading to a more precise prediction of COVID-19 real time data. The efficacy of the newly developed SIR model is proven by comparing its predictions to real data obtained from four counties namely Germany, Italy, Kuwait, and Oman. Two included delay periods for incubation and recovery within the SIR model produce a sensible and more accurate representation of the real time data. In the absence of the two-delay period (<img src="Edit_8ce6d5c5-9b59-4640-9c0e-334e3948d11c.png" width="67" height="20" alt="" /><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">)</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> the dynamical behavior of the model will not correspond to today’s picture and lag the detection of the epidemic peak. The reproductive number <i></i></span></span></span><i><span><span><i><span style="font-family:Verdana;">R</span></i></span></span><span><span><span style="font-family:;" "=""><i><span style="font-family:Verdana;"><sub>0</sub></span></i><span style="font-family:Verdana;"></span></span></span></span></i> <span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">is defined for the model for values of recovery time delay <i></i></span></span></span><i><span style="font-family:Verdana;"><span style="font-family:Verdana;"><i><span style="font-family:Verdana;"><img src="Edit_882b068a-f7fa-478e-9fb9-4d78388010f3.png" width="25" height="20" alt="" /></span></i></span></span></i><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><sub></sub></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> of the infective case. The effect of recovery time <img src="Edit_882b068a-f7fa-478e-9fb9-4d78388010f3.png" width="25" height="20" alt="" /></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">may produce second wave, and/or an oscillation which could destabilize the behavior of the system and a periodic oscillation can arise due to Hopf bifurcation phenomenon.</span></span></span>
