[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.c180166

A MATHEMATICAL MODEL OF TRANSMISSION OF PLASMODIUM VIVAX MALARIA WITH A CONSTANT TIME DELAY FROM INFECTION TO INFECTIOUS

Kammanee, Athassawat (Applied Analysis Research Unit Department of Mathematics and Statistics Faculty of Science Prince of Songkla University)
Tansuiy, Orawan (Department of Mathematics and Statistics Faculty of Science Prince of Songkla University)

Publication Information

Communications of the Korean Mathematical Society / v.34, no.2, 2019 , pp. 685-699 More about this Journal

Abstract

This research is focused on a continuous epidemic model of transmission of 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;

Citations & Related Records

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