Stochastic and deterministic mathematical model of cholera disease dynamics with direct transmission

Advances in Difference Equations

article

Tilahun, Getachew Teshome¹  Woldegerima, Woldegebriel Assefa²  Wondifraw, Aychew¹ 

[1]Department of Mathematics, Haramaya University

[2]Department of Mathematics and Applied Mathematics, University of Pretoria

[3]Department of Mathematics, Mekelle University

关键词: Stochastic modeling;    Cholera;    Numerical simulation;   

DOI  :  10.1186/s13662-020-03130-w

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this paper we develop a stochastic mathematical model of cholera disease dynamics by considering direct contact transmission pathway. The model considers four compartments, namely susceptible humans, infectious humans, treated humans, and recovered humans. Firstly, we develop a deterministic mathematical model of cholera. Since the deterministic model does not consider the randomness process or environmental factors, we converted it to a stochastic model. Then, for both types of models, the qualitative behaviors, such as the invariant region, the existence of a positive invariant solution, the two equilibrium points (disease-free and endemic equilibrium), and their stabilities (local as well as global stability) of the model are studied. Moreover, the basic reproduction numbers are obtained for both models and compared. From the comparison, we obtained that the basic reproduction number of the stochastic model is much smaller than that of the deterministic one, which means that the stochastic approach is more realistic. Finally, we performed sensitivity analysis and numerical simulations. The numerical simulation results show that reducing contact rate, improving treatment rate, and environmental sanitation are the most crucial activities to eradicate cholera disease from the community.

【 授权许可】

CC BY