A wide range of infectious diseases are both vertically and horizontally transmitted. Such diseases are spatially transmitted via multiple species in heterogeneous environments, typically described by complex meta-population models. The reproduction number, R0, is a critical metric predicting whether the disease can invade the meta-population system. This paper presents the reproduction number ...

In this paper, we introduce a malaria model with an asymptomatic class in human population and exposed classes in both human and vector populations. The model assumes that asymptomatic individuals can get re-infected and move to the symptomatic class. In the case of an incomplete treatment, symptomatic individuals move to the asymptomatic class. If successfully treated, the symptomatic individu...

A multi-strain model of a vector-borne disease with distributed delay in the vector and the host is investigated. It is shown that if the reproduction number of the model R0 < 1, the unique disease-free equilibrium is globally asymptotically stable.Without loss of generality, strain one is assumed to have the largest reproduction number. In this case, the dominance equilibrium of strain one is ...