Malaria dynamics with long incubation period in hosts

Motivated by the empirical observation of the bimodal distribution of the incubation time of P. vivax   in Korea, we analyze a mathematical model for malaria transmission dynamics that features two distinct exposed classes in the human population. The short-term incubation period is modeled by exponential distribution, while it is assumed that the long-term incubation period has fixed length. Then we formulate the model as a system of delay differential equations. We identify the basic reproduction number R0R0 and show that it is a threshold parameter for the global dynamics of the model. If R0≤1R0≤1, the disease-free equilibrium is globally attractive, while the disease uniformly persists in the human and mosquito populations when R0>1R0>1. Furthermore, for the special case of lifelong immunity, we prove that the endemic equilibrium is globally asymptotically stable.