Journal of Applied Mathematics & Bioinformatics

Effects of Migratory Population and Control Strategies on the Transmission Dynamics of Dengue Virus

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  •                                                     Abstract

    In this Paper we formulate a mathematical model of dengue virus transmission in the human body to monitor the effects of migratory population and some control strategies at aquatic and adult stages of vector (mosquito). The model has a locally asymptotically stable disease-free equilibrium (DFE) whenever a certain epidemiological threshold, known as the basic reproduction number (R0), is less than unity. It is also shown, using a Lyapunov function and Lasalle Invariance Principle that the DFE of the dengue model is globally-asymptotically stable (GAS) whenever the reproduction number (R0) is less than unity. The model has a locally-asymptotically stable endemic equilibrium point (EEP) whenever R0>1. With the help of Lyapunov function and Lasalle Principle (Goh-Volterra type), by considering special case, the EEP of the model is shown to be GAS whenever R0>1. The model simulations reveals that the migratory infected individuals increases the burden of the dengue disease and also precautionary measures at the aquatic and adult stages decrease the number of new cases of dengue virus. Numerical simulation indicates that if we take the precautionary measures effectively then it would be more effective then even giving the treatment to the infected individuals.