Modeling the transmission dynamics of a two-strain dengue disease with infection age

Abstract

In this paper, we introduce a partial differential equation (PDE) model to describe the transmission dynamics of dengue with two viral strains and possible secondary infection for humans. The model features the variable infectiousness during the infectious period, which we call the infection age of the infectious host. We define two thresholds [Formula: see text] and [Formula: see text], and show that the strain [Formula: see text] can not invade the system if [Formula: see text]. Further, the disease-free equilibrium of the system is globally asymptotically stable if [Formula: see text]. When [Formula: see text], strain [Formula: see text] dominance equilibrium [Formula: see text] exists, and is locally asymptotically stable when [Formula: see text], [Formula: see text], [Formula: see text]. Then, by applying Lyapunov–LaSalle techniques, we establish the global asymptotical stability of the dominance equilibrium corresponding to some strain [Formula: see text]. This implies strain [Formula: see text] eliminates the other strain as long as [Formula: see text], where [Formula: see text] denotes the probability of a given susceptible mosquito being transmitted by a primarily infected human with strain [Formula: see text]. Finally, we study the existence of the coexistence equilibria under some conditions.