Narrow Results

In this paper, we study a system of differential equations that models the population dynamics of SEIR vector transmission of dengue fever. The model studied breeding value based on the number of reported cases of dengue fever in Selangor because the state had the highest case in Malaysia. The model explains that maximum level of human infection rate of dengue fever achieved in a very short period. It is also revealed that there existed suitability result between theoretical and empirical calculation using the model. The result of SEIR model will hopefully provide an insight into the spread of dengue fever in Selangor Malaysia and basic form for modeling this area.

A recent paper [W. D. Wang, Modeling adaptive behavior in influenza transmission, Math. Model. Nat. Phenom.7(3) (2012) 253–262] presented the local stability of the endemic equilibrium $E^{\ast }$ of an influenza transmission model incorporating human mobility behavior. In the present paper, we prove that $E^{\ast }$ is globally stable if the basic reproduction number ${{ℛ}}_0>1$.