A cholera model coupling within-host and between-host with age-dependent and asymptomatic infections

In this paper, a coupling cholera epidemic model is proposed, in which the pathogens could both spread within-host and between-host, meanwhile, there exist age-dependent infection between the asymptomatic and symptomatic infected people. For the fast-time subsystem, the infection-free and endemic equilibria are both globally asymptotically stable. For the slow-time subsystem, the basic reproduction number $R_0$ is determined, by which we observe that the disease-free equilibrium is globally asymptotically stable (the absence of pathogens in environment) if $R_0<1$, while the endemic equilibrium is globally asymptotically stable (the presence of pathogens in environment) when $R_0>1$. The theoretical results are illustrated by numerical simulations, by which we find that age-dependent and asymptomatic infections may further promote cholera spread. Besides, the linking of pathogen transmission at the individual level with infection at the population level could result in forward or backward bifurcation.