In 2022,Leukemia is the 13th most common diagnosis of cancer globally as per the source of the International Agency for Research on Cancer(IARC).Leukemia is still a threat and challenge for all regions because of 46.6...In 2022,Leukemia is the 13th most common diagnosis of cancer globally as per the source of the International Agency for Research on Cancer(IARC).Leukemia is still a threat and challenge for all regions because of 46.6%infection in Asia,and 22.1%and 14.7%infection rates in Europe and North America,respectively.To study the dynamics of Leukemia,the population of cells has been divided into three subpopulations of cells susceptible cells,infected cells,and immune cells.To investigate the memory effects and uncertainty in disease progression,leukemia modeling is developed using stochastic fractional delay differential equations(SFDDEs).The feasible properties of positivity,boundedness,and equilibria(i.e.,Leukemia Free Equilibrium(LFE)and Leukemia Present Equilibrium(LPE))of the model were studied rigorously.The local and global stabilities and sensitivity of the parameters around the equilibria under the assumption of reproduction numbers were investigated.To support the theoretical analysis of the model,the Grunwald Letnikov Nonstandard Finite Difference(GL-NSFD)method was used to simulate the results of each subpopulation with memory effect.Also,the positivity and boundedness of the proposed method were studied.Our results show how different methods can help control the cell population and give useful advice to decision-makers on ways to lower leukemia rates in communities.展开更多
This paper aims to perform a comparison of deterministic and stochastic models.The stochastic modelling is a more realistic way to study the dynamics of gonorrhoea infection as compared to its corresponding determinis...This paper aims to perform a comparison of deterministic and stochastic models.The stochastic modelling is a more realistic way to study the dynamics of gonorrhoea infection as compared to its corresponding deterministic model.Also,the deterministic solution is itself mean of the stochastic solution of the model.For numerical analysis,first,we developed some explicit stochastic methods,but unfortunately,they do not remain consistent in certain situations.Then we proposed an implicitly driven explicit method for stochastic heavy alcohol epidemic model.The proposed method is independent of the choice of parameters and behaves well in all scenarios.So,some theorems and simulations are presented in support of the article.展开更多
Nonlinear stochasticmodelling plays an important character in the different fields of sciences such as environmental,material,engineering,chemistry,physics,biomedical engineering,and many more.In the current study,we ...Nonlinear stochasticmodelling plays an important character in the different fields of sciences such as environmental,material,engineering,chemistry,physics,biomedical engineering,and many more.In the current study,we studied the computational dynamics of the stochastic dengue model with the real material of the model.Positivity,boundedness,and dynamical consistency are essential features of stochastic modelling.Our focus is to design the computational method which preserves essential features of the model.The stochastic non-standard finite difference technique is most efficient as compared to other techniques used in literature.Analysis and comparison were explored in favour of convergence.Also,we address the comparison between the stochastic and deterministic models.展开更多
Nonlinear modelling has a significant role in different disciplines of sciences such as behavioral,social,physical and biological sciences.The structural properties are also needed for such types of disciplines,as dyn...Nonlinear modelling has a significant role in different disciplines of sciences such as behavioral,social,physical and biological sciences.The structural properties are also needed for such types of disciplines,as dynamical consistency,positivity and boundedness are the major requirements of the models in these fields.One more thing,this type of nonlinear model has no explicit solutions.For the sake of comparison its computation will be done by using different computational techniques.Regrettably,the aforementioned structural properties have not been restored in the existing computational techniques in literature.Therefore,the construction of structural preserving computational techniques are needed.The nonlinearmodel for cervical cancer is constructed by parametric perturbation technique.Well-known computer methods are considered for the computation of cervical cancer dynamics.The well-known existing methods in literature are Euler Maruyama,Euler and Runge Kutta.Nonstandard finite difference method or Implicitly driven explicit method is first time considered for aforesaid model under the assumptions given byMickens in a stochastic way.Unfortunately,the aforementioned existing methods did not reinstate structural properties of cervical cancer dynamics in the human population.Our plannedmethod is structural preserving and a powerful tool for all nonlinear models of biomedical engineering problems.We have verified that existing computational methods do not preserve dynamical properties.But,the implicitly driven explicit method is a good device for dynamical properties.In the support of assertions,convergence analysis of implicitly driven explicit method is presented.展开更多
Pneumonia is a highly transmissible disease in children.According to the World Health Organization(WHO),the most affected regions include south Asia and sub-Saharan Africa.Worldwide,15%of pediatric deaths can be attri...Pneumonia is a highly transmissible disease in children.According to the World Health Organization(WHO),the most affected regions include south Asia and sub-Saharan Africa.Worldwide,15%of pediatric deaths can be attributed to pneumonia.Computing techniques have a significant role in science,engineering,and many other fields.In this study,we focused on the efficiency of numerical techniques via computer programs.We studied the dynamics of the pneumonia-like infections of epidemic models using numerical techniques.We discuss two types of analysis:dynamical and numerical.The dynamical analysis included positivity,boundedness,local stability,reproduction number,and equilibria of the model.We also discusswell-known computing techniques including Euler,Runge Kutta,and non-standard finite difference(NSFD)for the model.The non-standard finite difference(NSFD)technique shows convergence to the true equilibrium points of the model for any time step size.However,Euler and Runge Kutta do not work well over large time intervals.Computing techniques are the suitable tool for crosschecking the theoretical analysis of the model.展开更多
Pine wilt is a dramatic disease that kills infected trees within a few weeks to a few months.The cause is the pathogen Pinewood Nematode.Most plant-parasitic nematodes are attached to plant roots,but pinewood nematode...Pine wilt is a dramatic disease that kills infected trees within a few weeks to a few months.The cause is the pathogen Pinewood Nematode.Most plant-parasitic nematodes are attached to plant roots,but pinewood nematodes are found in the tops of trees.Nematodes kill the tree by feeding the cells around the resin ducts.The modeling of a pine wilt disease is based on six compartments,including three for plants(susceptible trees,exposed trees,and infected trees)and the other for the beetles(susceptible beetles,exposed beetles,and infected beetles).The deterministic modeling,along with subpopulations,is based on Law of mass action.The stability of the model along with equilibria is studied rigorously.The authentication of analytical results is examined through well-known computer methods like Non-standard finite difference(NSFD)and the model’s feasible properties(positivity,boundedness,and dynamical consistency).In the end,comparison analysis shows the effectiveness of the NSFD algorithm.展开更多
Most developing countries such as Afghanistan,Pakistan,India,Bangladesh,and many more are still fighting against poliovirus.According to the World Health Organization,approximately eighteen million people have been in...Most developing countries such as Afghanistan,Pakistan,India,Bangladesh,and many more are still fighting against poliovirus.According to the World Health Organization,approximately eighteen million people have been infected with poliovirus in the last two decades.In Asia,still,some countries are suffering from the virus.The stochastic behavior of the poliovirus through the transition probabilities and non-parametric perturbation with fundamental properties are studied.Some basic properties of the deterministic model are studied,equilibria,local stability around the stead states,and reproduction number.Euler Maruyama,stochastic Euler,and stochastic Runge-Kutta study the behavior of complex stochastic differential equations.The main target of this study is to develop a nonstandard computational method that restores dynamical features like positivity,boundedness,and dynamical consistency.Unfortunately,the existing methods failed to fix the actual behavior of the disease.The comparison of the proposed approach with existing methods is investigated.展开更多
Purpose: The triazole nucleus is an important part of the therapeutically interesting drug candidate as antimicrobial, analgesic, anticancer, anticonvulsant and anti-inflammatory agents. Methods: Therefore, in this st...Purpose: The triazole nucleus is an important part of the therapeutically interesting drug candidate as antimicrobial, analgesic, anticancer, anticonvulsant and anti-inflammatory agents. Methods: Therefore, in this study, twelve 4,5-disubstituted-1,2,4-triazole-3-thiols were synthesized by the reaction of substituted isothiocyanates and hydrazides using the common method of base catalysed intramolecular dehydrative cyclization of substituted thiosemicarbazides 3(a-f) and 4(a-f). The structures of these compounds were characterized by means of FT-IR, 1H-NMR, and elemental analysis data. All these compounds were screened for antibacterial, antioxidant, antitumor and cytotoxic activities. Results: Among these compounds: 5c, 5f and 6f were found active against gram positive cocci, the compounds 5a, 5b, 5d, 6a and 6f showed 85% free radical scavenging effect at 3 ppm when tested for antioxidant activity, 75% tumors inhibition was recorded using 5c, 5d and 6a and brine shrimps lethality assay declared 5a, 5b and 6d was 129.62 μg/ml, 161.577 μg/ml and 81.56 μg/ml respectively. Conclusion: Compounds carrying significant bioactivity can be further studied using animal models to establish their safety profile prior to initiating clinical trials.展开更多
In 2021,most of the developing countries are fighting polio,and parents are concerned with the disabling of their children.Poliovirus transmits from person to person,which can infect the spinal cord,and paralyzes the ...In 2021,most of the developing countries are fighting polio,and parents are concerned with the disabling of their children.Poliovirus transmits from person to person,which can infect the spinal cord,and paralyzes the parts of the body within a matter of hours.According to the World Health Organization(WHO),18 million currently healthy people could have been paralyzed by the virus during 1988–2020.Almost all countries but Pakistan,Afghanistan,and a fewmore have been declared polio-free.The mathematical modeling of poliovirus is studied in the population by categorizing it as susceptible individuals(S),exposed individuals(E),infected individuals(I),and recovered individuals(R).In this study,we study the fundamental properties such as positivity and boundedness of the model.We also rigorously study the model’s stability and equilibria with or without poliovirus.For numerical study,we design the Euler,Runge–Kutta,and nonstandard finite difference method.However,the standard techniques are time-dependent and fail to present the results for an extended period.The nonstandard finite difference method works well to study disease dynamics for a long time without any constraints.Finally,the results of different methods are compared to prove their effectiveness.展开更多
基金supported by the Fundacao para a Ciencia e Tecnologia,FCT,under the project https://doi.org/10.54499/UIDB/04674/2020(accessed on 1 January 2025).
文摘In 2022,Leukemia is the 13th most common diagnosis of cancer globally as per the source of the International Agency for Research on Cancer(IARC).Leukemia is still a threat and challenge for all regions because of 46.6%infection in Asia,and 22.1%and 14.7%infection rates in Europe and North America,respectively.To study the dynamics of Leukemia,the population of cells has been divided into three subpopulations of cells susceptible cells,infected cells,and immune cells.To investigate the memory effects and uncertainty in disease progression,leukemia modeling is developed using stochastic fractional delay differential equations(SFDDEs).The feasible properties of positivity,boundedness,and equilibria(i.e.,Leukemia Free Equilibrium(LFE)and Leukemia Present Equilibrium(LPE))of the model were studied rigorously.The local and global stabilities and sensitivity of the parameters around the equilibria under the assumption of reproduction numbers were investigated.To support the theoretical analysis of the model,the Grunwald Letnikov Nonstandard Finite Difference(GL-NSFD)method was used to simulate the results of each subpopulation with memory effect.Also,the positivity and boundedness of the proposed method were studied.Our results show how different methods can help control the cell population and give useful advice to decision-makers on ways to lower leukemia rates in communities.
基金The first author also thanks Prince Sultan University for funding this work through research-group number RG-DES2017-01-17.
文摘This paper aims to perform a comparison of deterministic and stochastic models.The stochastic modelling is a more realistic way to study the dynamics of gonorrhoea infection as compared to its corresponding deterministic model.Also,the deterministic solution is itself mean of the stochastic solution of the model.For numerical analysis,first,we developed some explicit stochastic methods,but unfortunately,they do not remain consistent in certain situations.Then we proposed an implicitly driven explicit method for stochastic heavy alcohol epidemic model.The proposed method is independent of the choice of parameters and behaves well in all scenarios.So,some theorems and simulations are presented in support of the article.
基金funded by the Research and initiative centre RGDES2017-01-17,Prince Sultan University.
文摘Nonlinear stochasticmodelling plays an important character in the different fields of sciences such as environmental,material,engineering,chemistry,physics,biomedical engineering,and many more.In the current study,we studied the computational dynamics of the stochastic dengue model with the real material of the model.Positivity,boundedness,and dynamical consistency are essential features of stochastic modelling.Our focus is to design the computational method which preserves essential features of the model.The stochastic non-standard finite difference technique is most efficient as compared to other techniques used in literature.Analysis and comparison were explored in favour of convergence.Also,we address the comparison between the stochastic and deterministic models.
文摘Nonlinear modelling has a significant role in different disciplines of sciences such as behavioral,social,physical and biological sciences.The structural properties are also needed for such types of disciplines,as dynamical consistency,positivity and boundedness are the major requirements of the models in these fields.One more thing,this type of nonlinear model has no explicit solutions.For the sake of comparison its computation will be done by using different computational techniques.Regrettably,the aforementioned structural properties have not been restored in the existing computational techniques in literature.Therefore,the construction of structural preserving computational techniques are needed.The nonlinearmodel for cervical cancer is constructed by parametric perturbation technique.Well-known computer methods are considered for the computation of cervical cancer dynamics.The well-known existing methods in literature are Euler Maruyama,Euler and Runge Kutta.Nonstandard finite difference method or Implicitly driven explicit method is first time considered for aforesaid model under the assumptions given byMickens in a stochastic way.Unfortunately,the aforementioned existing methods did not reinstate structural properties of cervical cancer dynamics in the human population.Our plannedmethod is structural preserving and a powerful tool for all nonlinear models of biomedical engineering problems.We have verified that existing computational methods do not preserve dynamical properties.But,the implicitly driven explicit method is a good device for dynamical properties.In the support of assertions,convergence analysis of implicitly driven explicit method is presented.
文摘Pneumonia is a highly transmissible disease in children.According to the World Health Organization(WHO),the most affected regions include south Asia and sub-Saharan Africa.Worldwide,15%of pediatric deaths can be attributed to pneumonia.Computing techniques have a significant role in science,engineering,and many other fields.In this study,we focused on the efficiency of numerical techniques via computer programs.We studied the dynamics of the pneumonia-like infections of epidemic models using numerical techniques.We discuss two types of analysis:dynamical and numerical.The dynamical analysis included positivity,boundedness,local stability,reproduction number,and equilibria of the model.We also discusswell-known computing techniques including Euler,Runge Kutta,and non-standard finite difference(NSFD)for the model.The non-standard finite difference(NSFD)technique shows convergence to the true equilibrium points of the model for any time step size.However,Euler and Runge Kutta do not work well over large time intervals.Computing techniques are the suitable tool for crosschecking the theoretical analysis of the model.
文摘Pine wilt is a dramatic disease that kills infected trees within a few weeks to a few months.The cause is the pathogen Pinewood Nematode.Most plant-parasitic nematodes are attached to plant roots,but pinewood nematodes are found in the tops of trees.Nematodes kill the tree by feeding the cells around the resin ducts.The modeling of a pine wilt disease is based on six compartments,including three for plants(susceptible trees,exposed trees,and infected trees)and the other for the beetles(susceptible beetles,exposed beetles,and infected beetles).The deterministic modeling,along with subpopulations,is based on Law of mass action.The stability of the model along with equilibria is studied rigorously.The authentication of analytical results is examined through well-known computer methods like Non-standard finite difference(NSFD)and the model’s feasible properties(positivity,boundedness,and dynamical consistency).In the end,comparison analysis shows the effectiveness of the NSFD algorithm.
文摘Most developing countries such as Afghanistan,Pakistan,India,Bangladesh,and many more are still fighting against poliovirus.According to the World Health Organization,approximately eighteen million people have been infected with poliovirus in the last two decades.In Asia,still,some countries are suffering from the virus.The stochastic behavior of the poliovirus through the transition probabilities and non-parametric perturbation with fundamental properties are studied.Some basic properties of the deterministic model are studied,equilibria,local stability around the stead states,and reproduction number.Euler Maruyama,stochastic Euler,and stochastic Runge-Kutta study the behavior of complex stochastic differential equations.The main target of this study is to develop a nonstandard computational method that restores dynamical features like positivity,boundedness,and dynamical consistency.Unfortunately,the existing methods failed to fix the actual behavior of the disease.The comparison of the proposed approach with existing methods is investigated.
文摘Purpose: The triazole nucleus is an important part of the therapeutically interesting drug candidate as antimicrobial, analgesic, anticancer, anticonvulsant and anti-inflammatory agents. Methods: Therefore, in this study, twelve 4,5-disubstituted-1,2,4-triazole-3-thiols were synthesized by the reaction of substituted isothiocyanates and hydrazides using the common method of base catalysed intramolecular dehydrative cyclization of substituted thiosemicarbazides 3(a-f) and 4(a-f). The structures of these compounds were characterized by means of FT-IR, 1H-NMR, and elemental analysis data. All these compounds were screened for antibacterial, antioxidant, antitumor and cytotoxic activities. Results: Among these compounds: 5c, 5f and 6f were found active against gram positive cocci, the compounds 5a, 5b, 5d, 6a and 6f showed 85% free radical scavenging effect at 3 ppm when tested for antioxidant activity, 75% tumors inhibition was recorded using 5c, 5d and 6a and brine shrimps lethality assay declared 5a, 5b and 6d was 129.62 μg/ml, 161.577 μg/ml and 81.56 μg/ml respectively. Conclusion: Compounds carrying significant bioactivity can be further studied using animal models to establish their safety profile prior to initiating clinical trials.
基金The authors express their gratitude to Princess Nourah bint Abdulrahman University Researchers Supporting Project(Grant No.PNURSP2022R61),Princess Nourah bint Abdulrahman University,Riyadh,Saudi Arabia.
文摘In 2021,most of the developing countries are fighting polio,and parents are concerned with the disabling of their children.Poliovirus transmits from person to person,which can infect the spinal cord,and paralyzes the parts of the body within a matter of hours.According to the World Health Organization(WHO),18 million currently healthy people could have been paralyzed by the virus during 1988–2020.Almost all countries but Pakistan,Afghanistan,and a fewmore have been declared polio-free.The mathematical modeling of poliovirus is studied in the population by categorizing it as susceptible individuals(S),exposed individuals(E),infected individuals(I),and recovered individuals(R).In this study,we study the fundamental properties such as positivity and boundedness of the model.We also rigorously study the model’s stability and equilibria with or without poliovirus.For numerical study,we design the Euler,Runge–Kutta,and nonstandard finite difference method.However,the standard techniques are time-dependent and fail to present the results for an extended period.The nonstandard finite difference method works well to study disease dynamics for a long time without any constraints.Finally,the results of different methods are compared to prove their effectiveness.
