Abstract
This paper studies the global dynamics of a cholera model incorporating age structures and general infection rates. First, we explore the existence and point dissipativeness of the orbit and analyze the asymptotical smoothness. Then, we perform rigorous mathematical analysis on the existence and local stability of equilibria. Based on the uniform persistence, we further investigate the global behavior of the cholera infection model. The results of theoretical analysis are well confirmed by numerical simulations. This research generalizes some known results and provides deeper insights into the dynamics of cholera propagation.
Highlights
Cholera is a serious infectious disease that is caused by the bacterium Vibrio cholera
Due to the cholera toxin produced by the bacterium Vibrio cholera, it is characterized by severe symptoms, including acute diarrhea, vomiting, hypotension and a weak pulse
Global Stability of the Infection Equilibrium In this subsection, we focus on the global stability of the infection equilibrium E∗
Summary
Cholera is a serious infectious disease that is caused by the bacterium Vibrio cholera. Tien and Earn [2] established a water-borne infectious disease model including multiple propagation paths Control strategies, such as vaccination, were considered in cholera models in Posny et al [5] to inhibit the propagation of epidemics. A cholera model with bilinear incidence rates including two age structures was introduced and discussed in the work of Brauer et al [12] and was further investigated in the work of Wang and Zhang [13]. ∞ 0 k(a)i(t, a)da infectivity of infected individuals and pathogens at corresponding ages In this manuscript, we consider the following cholera model, taking general incidence rates into account, which is a generation of the model in Brauer et al [12].
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