The research on spatial epidemic models is a topic of considerable recent interest. In another hand, the advances in computer technology have stimulated the development of stochastic models. Metapopulation models are ...The research on spatial epidemic models is a topic of considerable recent interest. In another hand, the advances in computer technology have stimulated the development of stochastic models. Metapopulation models are spatial designs that involve movements of individuals between distinct subpopulations. The purpose of the present work has been to develop stochastic models in order to study the transmission dynamics and control of infectious diseases in metapopulations. The authors studied Susceptible-Infected-Susceptible （SIS） and Susceptible-lnfected-Recovered （SIR） epidemic schemes, using the Gillespie algorithm, Computational numerical simulations were carried in order to explore the models. The results obtained show how the dynamics of transmission and the application of control measures within each subpopulation may affect all subpopulations of the system. They also show how the distribution of control measures among subpopulations affects the efficacy of these strategies. The dynamics of the stochastic models developed in the current study follow the trends observed in the classic deterministic designs. Also, the present models exhibit fluctuating behavior. This work highlights the importance of the spatial distribution of the population in spread and control of infectious diseases. In addition, it shows how chance could play an important role in these scenarios.展开更多
India has been the latest global epicenter for COVID-19,a novel coronavirus disease that emerged in China in late 2019.We present a base mathematical model for the transmission dynamics of COVID-19 in India and its ne...India has been the latest global epicenter for COVID-19,a novel coronavirus disease that emerged in China in late 2019.We present a base mathematical model for the transmission dynamics of COVID-19 in India and its neighbor,Pakistan.The base model was rigorously analyzed and parameterized using cumulative COVID-19 mortality data from each of the two countries.The model was used to assess the population-level impact of the control and mitigation strategies implemented in the two countries(notably non-pharmaceutical interventions).Numerical simulations of the basic model indicate that,based on the current baseline levels of the control and mitigation strategies implemented,the pandemic trajectory in India is on a downward trend.This downward trend will be reversed,and India will be recording mild outbreaks,if the control and mitigation strategies are relaxed from their current levels.By early September 2021,our simulations suggest that India could record up to 460,000 cumulative deaths under baseline levels of the implemented control strategies,while Pakistan(where the pandemic is comparatively milder)could see over 24,000 cumulative deaths at current mitigation levels.The basic model was extended to assess the impact of back-and-forth mobility between the two countries.Simulations of the resulting metapopulation model show that the burden of the COVID-19 pandemic in Pakistan increases with increasing values of the average time residents of India spend in Pakistan,with daily mortality in Pakistan peaking in mid-August to mid-September of 2021.Under the respective baseline control scenarios,our simulations show that the backand-forth mobility between India and Pakistan could delay the time-to-elimination of the COVID-19 pandemic in India and Pakistan to November 2022 and July 2022,respectively.展开更多
The spread of methicillin-resistant strains of Staphylococcus aureus(MRSA)in health-care settings has become increasingly difficult to control and has since been able to spread in the general community.The prevalence ...The spread of methicillin-resistant strains of Staphylococcus aureus(MRSA)in health-care settings has become increasingly difficult to control and has since been able to spread in the general community.The prevalence of MRSA within the general public has caused outbreaks in groups of people in close quarters such as military barracks,gyms,daycare centres and correctional facilities.Correctional facilities are of particular importance for spreading MRSA,as inmates are often in close proximity and have limited access to hygienic products and clean clothing.Although these conditions are ideal for spreading MRSA,a recent study has suggested that recurrent epidemics are caused by the influx of colonized or infected individuals into the correctional facility.In this paper,we further investigate the effects of community dynamics on the spread of MRSA within the correctional facility and determine whether recidivism has a significant effect on disease dynamics.Using a simplified hotspot model ignoring disease dynamics within the correctional facility,as well as two metapopulation models,we demonstrate that outbreaks in correctional facilities can be driven by community dynamics even when spread between inmates is restricted.We also show that disease dynamics within the correctional facility and their effect on the outlying community may be ignored due to the smaller size of the incarcerated population.This will allow construction of simpler models that consider the effects of many MRSA hotspots interacting with the general community.It is suspected that the cumulative effects of hotspots for MRSA would have a stronger feedback effect in other community settings.展开更多
Emerging infectious diseases and climate change are two of the major challenges in 21st century.Although over the past decades,highly-resolved mathematical models have contributed in understanding dynamics of infectio...Emerging infectious diseases and climate change are two of the major challenges in 21st century.Although over the past decades,highly-resolved mathematical models have contributed in understanding dynamics of infectious diseases and are of great aid when it comes to finding suitable intervention measures,they may need substantial computational effort and produce significant CO_(2) emissions.Two popular modeling approaches for mitigating infectious disease dynamics are agent-based and population-based models.Agent-based models(ABMs)offer a microscopic view and are thus able to capture heterogeneous human contact behavior and mobility patterns.However,insights on individual-level dynamics come with high computational effort that scales with the number of agents.On the other hand,population-based models(PBMs)using e.g.ordinary differential equations(ODEs)are computationally efficient even for large populations due to their complexity being independent of the population size.Yet,population-based models are restricted in their granularity as they assume a(to some extent)homogeneous and well-mixed population.To manage the trade-off between computational complexity and level of detail,we propose spatial-and temporal-hybrid models that use ABMs only in an area or time frame of interest.To account for relevant influences to disease dynamics,e.g.,from outside,due to commuting activities,we use population-based models,only adding moderate computational costs.Our hybridization approach demonstrates significant reduction in computational effort by up to 98%–without losing the required depth in information in the focus frame.The hybrid models used in our numerical simulations are based on two recently proposed models,however,any suitable combination of ABM and PBM could be used,too.Concluding,hybrid epidemiological models can provide insights on the individual scale where necessary,using aggregated models where possible,thereby making a contribution to green computing.展开更多
Background Yellow Fever(YF)importation remains an active risk to Southeast Asia.This study aims to determine the effectiveness of vector control and ring vaccination as containment strategies.Methods We modelled a YF ...Background Yellow Fever(YF)importation remains an active risk to Southeast Asia.This study aims to determine the effectiveness of vector control and ring vaccination as containment strategies.Methods We modelled a YF outbreak in Singapore over 1 year using a metapopulation vector-host spatial model to explore the impact of a potential epidemic and intervention effectiveness.30 different scenarios were examined by varying the vector to human ratio m([1,3,6]),vaccination coverage([10%,50%,90%])and delay in vaccine rollout([7,14,30 days]),including three non-vaccination scenarios with the vector-to-human ratio m([1,3,6]).Results Vector control has a significant protective effect with an 89%reduction in the cumulative number of exposed cases at Day 365 when lowering m from 6 to 1 in the baseline scenario without ring vaccination.Vaccination coverage levels of 90%,50%,and 10%reduce the cumulative number of exposed cases by 88%,56%,and 12%,respectively,compared to baseline,when fixing m=3 and a 7-day rollout delay.A greater number of severe infections and deaths can be mitigated by decreasing the ratio m compared to ring vaccination strategies.The marginal gains in averting the number of infections and deaths are most significant when m is decreased,followed by increased vaccination coverage and reduced intervention delay as R0 is proportional to.This highlights the central role of vector control.Our findings suggested that ring vaccination is effective under lower mosquito-to-human ratios up to 1-week post-detection,with vaccination coverage of at least 50%.Under these settings,vaccine doses equal to 25%of the total population are needed to contain the initial outbreak,allowing time to monitor its progress and restock the supply.After that,further interventions where YF has not yet been declared endemic.Conclusion Our findings suggested that ring vaccination is effective under lower mosquito-to-human ratios up to 1-week post-detection,with vaccination coverage of at least 50%.After that,further interventions are required to bring the effective reproduction number Reff under 1,highlighting the need for rapid response and containment,preparation in the stockpiling of vaccines,and continual suppression of mosquito vector populations when faced with the risk of YF importation and outbreak.展开更多
In this work, we study a system of autonomous fractional differential equations. The differential operator is taken in the Caputo sense. Using the monotone iterative technique combined with the method of upper and low...In this work, we study a system of autonomous fractional differential equations. The differential operator is taken in the Caputo sense. Using the monotone iterative technique combined with the method of upper and lower solutions, we investigate the existence and uniqueness of solutions for coupled system which are nonlinear fractional differential equations, moreover, we obtain the dependence of the solution on the initial values. In addition, we give an important example that is a two-patch subdiffusive predator-prey metapopulation model, investigate the solvability and give the numerical results with this model. The numerical simulation indicates that the results of the suhdiffusive model approximate to the two-patch predator-prey metapopulation model with the order a approach to 1.展开更多
文摘The research on spatial epidemic models is a topic of considerable recent interest. In another hand, the advances in computer technology have stimulated the development of stochastic models. Metapopulation models are spatial designs that involve movements of individuals between distinct subpopulations. The purpose of the present work has been to develop stochastic models in order to study the transmission dynamics and control of infectious diseases in metapopulations. The authors studied Susceptible-Infected-Susceptible （SIS） and Susceptible-lnfected-Recovered （SIR） epidemic schemes, using the Gillespie algorithm, Computational numerical simulations were carried in order to explore the models. The results obtained show how the dynamics of transmission and the application of control measures within each subpopulation may affect all subpopulations of the system. They also show how the distribution of control measures among subpopulations affects the efficacy of these strategies. The dynamics of the stochastic models developed in the current study follow the trends observed in the classic deterministic designs. Also, the present models exhibit fluctuating behavior. This work highlights the importance of the spatial distribution of the population in spread and control of infectious diseases. In addition, it shows how chance could play an important role in these scenarios.
基金One of the authors(ABG)acknowledge the support,in part,of the Simons Foundation(Award#585022)the National Science Foundation(Grant Number:DMS-2052363)Another author(SS)acknowledges the support of the Fulbright Scholarship.
文摘India has been the latest global epicenter for COVID-19,a novel coronavirus disease that emerged in China in late 2019.We present a base mathematical model for the transmission dynamics of COVID-19 in India and its neighbor,Pakistan.The base model was rigorously analyzed and parameterized using cumulative COVID-19 mortality data from each of the two countries.The model was used to assess the population-level impact of the control and mitigation strategies implemented in the two countries(notably non-pharmaceutical interventions).Numerical simulations of the basic model indicate that,based on the current baseline levels of the control and mitigation strategies implemented,the pandemic trajectory in India is on a downward trend.This downward trend will be reversed,and India will be recording mild outbreaks,if the control and mitigation strategies are relaxed from their current levels.By early September 2021,our simulations suggest that India could record up to 460,000 cumulative deaths under baseline levels of the implemented control strategies,while Pakistan(where the pandemic is comparatively milder)could see over 24,000 cumulative deaths at current mitigation levels.The basic model was extended to assess the impact of back-and-forth mobility between the two countries.Simulations of the resulting metapopulation model show that the burden of the COVID-19 pandemic in Pakistan increases with increasing values of the average time residents of India spend in Pakistan,with daily mortality in Pakistan peaking in mid-August to mid-September of 2021.Under the respective baseline control scenarios,our simulations show that the backand-forth mobility between India and Pakistan could delay the time-to-elimination of the COVID-19 pandemic in India and Pakistan to November 2022 and July 2022,respectively.
文摘The spread of methicillin-resistant strains of Staphylococcus aureus(MRSA)in health-care settings has become increasingly difficult to control and has since been able to spread in the general community.The prevalence of MRSA within the general public has caused outbreaks in groups of people in close quarters such as military barracks,gyms,daycare centres and correctional facilities.Correctional facilities are of particular importance for spreading MRSA,as inmates are often in close proximity and have limited access to hygienic products and clean clothing.Although these conditions are ideal for spreading MRSA,a recent study has suggested that recurrent epidemics are caused by the influx of colonized or infected individuals into the correctional facility.In this paper,we further investigate the effects of community dynamics on the spread of MRSA within the correctional facility and determine whether recidivism has a significant effect on disease dynamics.Using a simplified hotspot model ignoring disease dynamics within the correctional facility,as well as two metapopulation models,we demonstrate that outbreaks in correctional facilities can be driven by community dynamics even when spread between inmates is restricted.We also show that disease dynamics within the correctional facility and their effect on the outlying community may be ignored due to the smaller size of the incarcerated population.This will allow construction of simpler models that consider the effects of many MRSA hotspots interacting with the general community.It is suspected that the cumulative effects of hotspots for MRSA would have a stronger feedback effect in other community settings.
基金Nataša Djurdjevac Conrad and Johannes Zonker for discussions on the models initially developed in(Winkelmann et al.,2021)funding by the German Federal Ministry of Education and Research under grant agreement 031L0297B(Project INSIDe)+2 种基金funding by the German Federal Ministry for Digital and Transport under grant agreement FKZ19F2211A(Project PANDEMOS)funding by the German Federal Ministry for Digital and Transport under grant agreement FKZ19F2211B(Project PANDEMOS)funding from the Initiative and Networking Fund of the Helmholtz Association(grant agreement number KA1-Co-08,Project LOKI-Pandemics).
文摘Emerging infectious diseases and climate change are two of the major challenges in 21st century.Although over the past decades,highly-resolved mathematical models have contributed in understanding dynamics of infectious diseases and are of great aid when it comes to finding suitable intervention measures,they may need substantial computational effort and produce significant CO_(2) emissions.Two popular modeling approaches for mitigating infectious disease dynamics are agent-based and population-based models.Agent-based models(ABMs)offer a microscopic view and are thus able to capture heterogeneous human contact behavior and mobility patterns.However,insights on individual-level dynamics come with high computational effort that scales with the number of agents.On the other hand,population-based models(PBMs)using e.g.ordinary differential equations(ODEs)are computationally efficient even for large populations due to their complexity being independent of the population size.Yet,population-based models are restricted in their granularity as they assume a(to some extent)homogeneous and well-mixed population.To manage the trade-off between computational complexity and level of detail,we propose spatial-and temporal-hybrid models that use ABMs only in an area or time frame of interest.To account for relevant influences to disease dynamics,e.g.,from outside,due to commuting activities,we use population-based models,only adding moderate computational costs.Our hybridization approach demonstrates significant reduction in computational effort by up to 98%–without losing the required depth in information in the focus frame.The hybrid models used in our numerical simulations are based on two recently proposed models,however,any suitable combination of ABM and PBM could be used,too.Concluding,hybrid epidemiological models can provide insights on the individual scale where necessary,using aggregated models where possible,thereby making a contribution to green computing.
基金supported by the Ministry of Health,Singapore,Population Health Metrics and Analysis(DEMOS)Grant E-608-0-0017-03 and PREPARE.
文摘Background Yellow Fever(YF)importation remains an active risk to Southeast Asia.This study aims to determine the effectiveness of vector control and ring vaccination as containment strategies.Methods We modelled a YF outbreak in Singapore over 1 year using a metapopulation vector-host spatial model to explore the impact of a potential epidemic and intervention effectiveness.30 different scenarios were examined by varying the vector to human ratio m([1,3,6]),vaccination coverage([10%,50%,90%])and delay in vaccine rollout([7,14,30 days]),including three non-vaccination scenarios with the vector-to-human ratio m([1,3,6]).Results Vector control has a significant protective effect with an 89%reduction in the cumulative number of exposed cases at Day 365 when lowering m from 6 to 1 in the baseline scenario without ring vaccination.Vaccination coverage levels of 90%,50%,and 10%reduce the cumulative number of exposed cases by 88%,56%,and 12%,respectively,compared to baseline,when fixing m=3 and a 7-day rollout delay.A greater number of severe infections and deaths can be mitigated by decreasing the ratio m compared to ring vaccination strategies.The marginal gains in averting the number of infections and deaths are most significant when m is decreased,followed by increased vaccination coverage and reduced intervention delay as R0 is proportional to.This highlights the central role of vector control.Our findings suggested that ring vaccination is effective under lower mosquito-to-human ratios up to 1-week post-detection,with vaccination coverage of at least 50%.Under these settings,vaccine doses equal to 25%of the total population are needed to contain the initial outbreak,allowing time to monitor its progress and restock the supply.After that,further interventions where YF has not yet been declared endemic.Conclusion Our findings suggested that ring vaccination is effective under lower mosquito-to-human ratios up to 1-week post-detection,with vaccination coverage of at least 50%.After that,further interventions are required to bring the effective reproduction number Reff under 1,highlighting the need for rapid response and containment,preparation in the stockpiling of vaccines,and continual suppression of mosquito vector populations when faced with the risk of YF importation and outbreak.
文摘In this work, we study a system of autonomous fractional differential equations. The differential operator is taken in the Caputo sense. Using the monotone iterative technique combined with the method of upper and lower solutions, we investigate the existence and uniqueness of solutions for coupled system which are nonlinear fractional differential equations, moreover, we obtain the dependence of the solution on the initial values. In addition, we give an important example that is a two-patch subdiffusive predator-prey metapopulation model, investigate the solvability and give the numerical results with this model. The numerical simulation indicates that the results of the suhdiffusive model approximate to the two-patch predator-prey metapopulation model with the order a approach to 1.
