Global Dynamic Behavior of a Multigroup Cholera Model with Indirect Transmission

Abstract

For a multigroup cholera model with indirect transmission, the infection for a susceptible person is almost invariably transmitted by drinking contaminated water in which pathogens,V. cholerae, are present. The basic reproduction numberℛ0is identified and global dynamics are completely determined byℛ0. It shows thatℛ0is a globally threshold parameter in the sense that if it is less than one, the disease-free equilibrium is globally asymptotically stable; whereas if it is larger than one, there is a unique endemic equilibrium which is global asymptotically stable. For the proof of global stability with the disease-free equilibrium, we use the comparison principle; and for the endemic equilibrium we use the classical method of Lyapunov function and the graph-theoretic approach.

Modeling Transmission Dynamics ofStreptococcus suiswith Stage Structure and Sensitivity Analysis

“…In the following, we will prove the global stability of the disease-free equilibrium and endemic equilibrium of system (13) by using a Lyapunov function. The Lyapunov function is a powerful tool for the stability analysis of autonomous differential system; it has been used for some epidemiological models with constant inflow and bilinear incidences or nonlinear incidences [19][20][21][22][23].…”

Global Dynamics of a Multi-group SEIR Epidemic Model with Infection Age

“…To include irregularity of infectiousness of the disease agent, we divide the host population into various groups according to their epidemiological characteristics. In the existing literature of epidemiological modelling, the multi-group epidemic models have been used to investigate the transmission pattern and to describe the transmission dynamics of many infectious diseases in heterogenous population such as Cholera (see [19]), Measles, HIV/ADIS (see [20]) and Gonorrhea (see [18]). In particular, to study the impact of variations in infectiousness of HIV, Hyman et al [20] proposed two simple models.…”

Mathematical modelling of cholera disease with seasonality and human behavior change

“…In June 2019, there was also a cholera outbreak in Ethiopia, and 6789 people were infected [51]. Outbreaks of cholera occur cyclically, usually twice per year in endemic areas [22]. It is reported that industrialized countries have not had significant cholera outbreaks thanks to their advanced water treatment infrastructure [1].…”