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A delay differential equation model of a vector borne disease with direct transmission

Abid Ali Lashari, Khalid Hattaf, Gul Zaman


We formulate and systematically study the dynamics of a simple vector host epidemic model in terms of delay differential equations. The model is analyzed using stability theory of delay differential equations. Both the disease-free and the endemic equilibria are found and their stability is investigated. It is shown that the introduction of time delay in the model has a destabilizing effect on the system and periodic solutions can arise by Hopf bifurcation. Using the theory of differential and integral equation, we show that the infection free equilibrium is globally asymptotically stable if the reproductive number R0 less than 1, and the endemic equilibrium is locally asymptotically stable if R0 greater than 1.


Vector-host model, Time delay, Stability, Hopf bifurcation.

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