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Asymptotic Analysis of a Stochastic Model of Mosquito-Borne Disease with the Use of Insecticides and Bet Nets

Journal of Applied Mathematics and Physics 2024年第1期12卷 305-329页

作者： Boubacar Sidiki Kouyaté Modeste N’zi Department of Mathematics and Computer Science University of Science Technical and Technologies of Bamako Bamako Mali Laboratory of Applied Mathematics and Computer Science University Felix Houphouet-Boigny Abidjan C&#244te d’Ivoire

Ross’ epidemic model describing the transmission of malaria uses two classes of infection, one for humans and one for mosquitoes. This paper presents a stochastic extension of a deterministic vector-borne epidemic model based only on the class of human infectious. The consistency of the model is established by proving that the stochastic delay differential equation describing the model has a unique positive global solution. The extinction of the disease is studied through the analysis of the stability of the disease-free equilibrium state and the persistence of the model. Finally, we introduce some numerical simulations to illustrate the obtained results.

关键词： Vector-Borne Disease Epidemic Model Stochastic Delay Differential Equations Stochastic Stability lyapunov functional technique

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The stationary distribution and stochastic persistence for a class of disease models:Case study of malarial

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International Journal of Biomathematics 2020年第4期13卷 49-107页

作者： Divine Wanduku Georgia Avenue Room 3042StatesboroGA30460USA

This paper presents a nonlinear family of stochastic SEIRS models for diseases such as malaria in a highly random environment with noises from the disease transmission and natural death rates,and also from the random delays of the incubation and immunity *** analytical methods and local martingale characterizations are applied to find conditions for the disease to persist near an endemic steady state,and also for the disease to remain permanently in the system over ***,the ergodic stationary distribution for the stochastic process describing the disease dynamics is defined,and the statistical characteristics of the distribution are given *** results of this study show that the disease will persist and become permanent in the system,regardless of(1)whether the noises are from the discase transmission rate and/or from the natural death rates or(2)whether the delays in the system are constant or random for individuals in the ***,it is shown that"weak"noise is associated with the existence of an endemic stationary distribution for the disease,while"strong"noise is associated with extinction of the population over *** simulation examples for Plasnodiurr vitar malaria are given.

关键词： Basic reproduction number permanence in the mean local martingale lyapunov functional technique white noise intensity stationary distribution

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