Abstract

 In this work an SEIR model that described the dynamics of transmission of denque fever were proposed and analyzed. The standard method is used to analyze the behaviors of the proposed model. The results shown that there were two equilibrium points; disease free and endemic equilibrium point. The qualitative results are depended on a basic reproductive number . We obtained the basic reproductive number by using the next generation method and finding the spectral radius. Routh-Hurwitz criteria is used for determining the stabilities of the model. If , then the disease free equilibrium point is local asymptotically stable: that is the disease will died out, but if , then the endemic equilibrium is local asymptotically stable. After that the SEIR model is modified from the first model by adding optimal control functions that includes two time – dependent control functions with one minimizing the contract between the susceptible human and the infected vector and the other, minimizing the population of the infected human. The result from the numerical solutions of the models are shown and compared for supporting the analytic results.

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