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Dengue is one of the important infectious diseases in the world. In Malaysia, dengue occurs nationally and has been endemic for more than a decade. Hence, the modeling of dengue transmission is of great importance to help us understand the dynamical behavior of the disease. In this paper, we developed a compartmental model of the dengue transmission using the fractional order differential equation. It consists of six compartments representing the human and mosquito dynamics. The disease-free and the positive endemic equilibrium point are obtained. The stability analysis of the equilibria is presented. A sensitivity analysis of the model is performed to determine the relative importance of the model parameters to the transmission. Numerical simulations are given for different parameter settings. A case study, using the outbreak dengue data in the state of Selangor, Malaysia, in 2012, is presented.

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.

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