Stability and control in a stochastic model of malaria population dynamics

IF 3.1 3区数学 Q1 MATHEMATICS

Advances in Difference Equations Pub Date : 2023-11-15 DOI:10.1186/s13662-023-03791-3

Peter J. Witbooi, Sibaliwe Maku Vyambwera, Garth J. van Schalkwyk, Grant E. Muller

引用次数: 0

Abstract

This article proves a stability theorem for the disease-free equilibrium of a stochastic differential equations model of malaria disease dynamics. The theorem is formulated in terms of an invariant which is similar to the basic reproduction number of a related deterministic model. Compared to the deterministic model, stability of the disease-free equilibrium holds more generally for the stochastic model. The optimal control theory is applied to the stochastic model, revealing some important new insights. Theoretical results are illustrated by way of simulations.

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疟疾种群动态随机模型的稳定性和控制

本文证明了疟疾疾病动力学随机微分方程模型的无病平衡的稳定性定理。该定理是用一个类似于相关确定性模型的基本再现数的不变量来表述的。与确定性模型相比，无病平衡的稳定性在随机模型中更为普遍。将最优控制理论应用于随机模型，揭示了一些重要的新见解。通过仿真对理论结果进行了说明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Advances in Difference Equations MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

8.60

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： The theory of difference equations, the methods used, and their wide applications have advanced beyond their adolescent stage to occupy a central position in applicable analysis. In fact, in the last 15 years, the proliferation of the subject has been witnessed by hundreds of research articles, several monographs, many international conferences, and numerous special sessions. The theory of differential and difference equations forms two extreme representations of real world problems. For example, a simple population model when represented as a differential equation shows the good behavior of solutions whereas the corresponding discrete analogue shows the chaotic behavior. The actual behavior of the population is somewhere in between. The aim of Advances in Difference Equations is to report mainly the new developments in the field of difference equations, and their applications in all fields. We will also consider research articles emphasizing the qualitative behavior of solutions of ordinary, partial, delay, fractional, abstract, stochastic, fuzzy, and set-valued differential equations. Advances in Difference Equations will accept high-quality articles containing original research results and survey articles of exceptional merit.