Communications of the
Korean Mathematical Society CKMS

This research is focused on a continuous epidemic model of transmission of {\it Plasmodium vivax} malaria with a time delay. The model is represented as a system of ordinary differential equations with delay. There are two equilibria, which are the disease-free state and the endemic equilibrium, depending on the basic reproduction number, $R_0$, which is calculated and decreases with the time delay. Moreover, the disease-free equilibrium is locally asymptotically stable if $R_0<1$. If $R_0>1$, a unique endemic steady state exists and is locally stable. Furthermore, Hopf bifurcation is applied to determine the conditions for periodic solutions.

Keywords: Plasmodium vivax malaria, basic reproduction number, locally stable, Hope bifurcation, time delay

MSC numbers: 00A71, 65L80, 92B05, 37C75