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
A delayed mathematical model of Dengue dynamical transmission between vector mosquitoes and human, incorporating a control strategy of perfect pediatric vaccination is proposed in this paper. By some analytical skills...A delayed mathematical model of Dengue dynamical transmission between vector mosquitoes and human, incorporating a control strategy of perfect pediatric vaccination is proposed in this paper. By some analytical skills, we obtain the existence of disease-free equilibria and endemic equilibrium, the necessary conditions of global asymptotical stability about two disease-free equilibria. Further, by Pontryagin’s maximum principle, we obtain the optimal control of the disease. Finally, numerical simulations are carried out to verify the correctness of the theoretical results and feasibility of the control measure.展开更多
In this work, we present results of an investigation of environmental precursors of infectious epidemic of dengue fever in the Metropolitan Area of Rio de Janeiro, RJ, Brazil, obtained by a numerical model with repres...In this work, we present results of an investigation of environmental precursors of infectious epidemic of dengue fever in the Metropolitan Area of Rio de Janeiro, RJ, Brazil, obtained by a numerical model with representation of infection and reinfection of the population. The period considered extend between 2000 and 2011, in which it was possible to pair meteorological data and the reporting of dengue patients worsening. These data should also be considered in the numerical model, by assimilation, to obtain simulations of Dengue epidemics. The model contains compartments for the human population, for the vector Aedes aegypti and four virus serotypes. The results provide consistent evidence that worsening infection and disease outbreaks are due to the occurrence of environmental precursors, as the dynamics of the accumulation of water in the breeding and energy availability in the form of metabolic activation enthalpy during pre-epidemic periods.展开更多
Considering the impact of environmental white noise on the quantity and behavior ofvector of disease,a stochastic differential model describing the transmission of Denguefever between mosquitoes and humans,in this pap...Considering the impact of environmental white noise on the quantity and behavior ofvector of disease,a stochastic differential model describing the transmission of Denguefever between mosquitoes and humans,in this paper,is proposed.By using Lyapunovmethods and Ito's formula,we first prove the existence and uniqueness of a globalpositive solution for this model.Further,some sufficient conditions for the extinction andpersistence in the mean of this stochastic model are obtained by using the techniquesof a series of stochastic inequalities.In addition,we also discuss the existence of aunique stationary distribution which leads to the stochastic persistence of this disease.Finally,several numerical simulations are carried to illustrate the main results of thiscontribution.展开更多
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A delayed mathematical model of Dengue dynamical transmission between vector mosquitoes and human, incorporating a control strategy of perfect pediatric vaccination is proposed in this paper. By some analytical skills, we obtain the existence of disease-free equilibria and endemic equilibrium, the necessary conditions of global asymptotical stability about two disease-free equilibria. Further, by Pontryagin’s maximum principle, we obtain the optimal control of the disease. Finally, numerical simulations are carried out to verify the correctness of the theoretical results and feasibility of the control measure.
文摘In this work, we present results of an investigation of environmental precursors of infectious epidemic of dengue fever in the Metropolitan Area of Rio de Janeiro, RJ, Brazil, obtained by a numerical model with representation of infection and reinfection of the population. The period considered extend between 2000 and 2011, in which it was possible to pair meteorological data and the reporting of dengue patients worsening. These data should also be considered in the numerical model, by assimilation, to obtain simulations of Dengue epidemics. The model contains compartments for the human population, for the vector Aedes aegypti and four virus serotypes. The results provide consistent evidence that worsening infection and disease outbreaks are due to the occurrence of environmental precursors, as the dynamics of the accumulation of water in the breeding and energy availability in the form of metabolic activation enthalpy during pre-epidemic periods.
基金This research is partially supported by the National Natural Science Foundation of China(Grant nos.11961066 and 11771373)the Scientific Research Program of Colleges in Xinjiang(Grant no.X.JEDU2018I001).
文摘Considering the impact of environmental white noise on the quantity and behavior ofvector of disease,a stochastic differential model describing the transmission of Denguefever between mosquitoes and humans,in this paper,is proposed.By using Lyapunovmethods and Ito's formula,we first prove the existence and uniqueness of a globalpositive solution for this model.Further,some sufficient conditions for the extinction andpersistence in the mean of this stochastic model are obtained by using the techniquesof a series of stochastic inequalities.In addition,we also discuss the existence of aunique stationary distribution which leads to the stochastic persistence of this disease.Finally,several numerical simulations are carried to illustrate the main results of thiscontribution.
