Dynamics of a partially degenerate reaction-diffusion cholera model with horizontal transmission and phage-bacteria interaction
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Date
2023-01-24
Authors
Hu, Zhenxiang
Wang, Shengfu
Nie, Linfei
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We propose a cholera model with coupled reaction-diffusion equations and ordinary differential equations for discussing the effects of spatial heterogeneity, horizontal transmission, environmental viruses and phages on the spread of vibrio cholerae. We establish the well-posedness of this model which includes the existence of unique global positive solution, asymptotic smoothness of semiflow, and existence of a global attractor. The basic reproduction number R0 is obtained to describe the persistence and extinction of the disease. That is, the disease-free steady state is globally asymptotically stable for R0≤1, while it is unstable for R0>1. And, the disease is persistence and the model has the phage-free and phage-present endemic steady states in this case. Further, the global asymptotic stability of phage-free and phage-present endemic steady states are discussed for spatially homogeneous model. Finally, some numerical examples are displayed in order to illustrate the main theoretical results and our opening questions.
Description
Keywords
Cholera model, Environmental and horizontal transmission, Spatial heterogeneity and phages, Basic reproduction number, Global asymptotic stability
Citation
Hu, Z., Wang, S., & Nie, L. (2023). Dynamics of a partially degenerate reaction-diffusion cholera model with horizontal transmission and phage-bacteria interaction. Electronic Journal of Differential Equations, 2023(08), pp. 1-38.
Rights
Attribution 4.0 International