Essential Features Preserving Dynamics of Stochastic Dengue Model

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.

A Model of Perfect Pediatric Vaccination of Dengue with Delay and Optimal Control

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.

Dynamic Modelling of Dengue Epidemics in Function of Available Enthalpy and Rainfall

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.

Dynamics of a dengue epidemic model with class-age structure

We introduce the class-age-dependent rates of the infected and vaccinated class in the compartmental model of dengue transmission. An age-structured host-vector interac- tion model incorporating vaccination effects is formulated and analyzed for the spread of dengue. Moreover, the basic reproduction number is derived, which serves as a thresh- old value determining the stability of the equilibrium points. By constructing suitable Lyapunov functional, the global asymptotic stability of the equilibria of the model is established in terms of the basic reproduction number. In particular, the disease-free equilibrium of the model is globally asymptotically stable if the basic reproduction num- ber is less than one, while the disease persists and the unique endemic equilibrium is globally asymptotically stable if the basic reproduction number is greater than one. The analysis of our model indicates that our model is realistic to give a hint to control the transmission of dengue. Furthermore, it follows from the formulation of the infection-free equilibrium of susceptible humans So and the basic reproduction number R0 that both of them are decreasing with respect to the vaccination parameter ~bh, which indicates that appropriate vaccinating program may contribute to prevent the transmission of Dengue disease.

Stochastic dynamics of the transmission of Dengue fever virus bet ween mosquit oes aiul humans

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.