Basic epidemic model of dengue transmission using the fractional order differential equations

Abstract

Dengue is normally emerging in tropical and subtropical countries and now has become a serious health problem. In Malaysia, dengue is considered endemic for the past few years. A reliable mathematical model of dengue epidemic is crucial to provide some means of interventions in controlling the spread of the disease. Many mathematical models have been proposed and analyzed in the literature, but very little of them used fractional order derivative in analyzing the dengue transmission. In this paper, a study on a basic fractional order epidemic model of dengue transmission is conducted using the SIR-SI model, including the aquatic phase of the vector. The population size of the human is assumed to be constant. The threshold quantity R0 is attained by the next generation matrix method. The preliminary result of the study is presented. It has shown that the disease-free equilibrium is locally asymptotically stable when R0 < 1, and unstable when R0 > 1. In other words, the dengue disease is eliminated if R0 < 1, and it approaches a positive endemic equilibrium if R0 > 1. Finally, some numerical results are presented based on the real data in Malaysia in 2016.