Stability analysis of SEISEIR-SEI modelling on the dynamics of spread dengue fever with vaccination and insecticide

Abstract

Abstract This article focuses on analysing an SEISEIR-SEI model. This model is a development of SEIR-SEI which studies the spread of dengue fever in human and mosquito. This model considers the exposed compartment for vaccinated, non-vaccinated human and also for mosquito. Fogging strategy is also carried out as an effort to inhibit mosquito breeding. Existence and stability of non-endemic and endemic equilibrium points are investigated and analysed using linearization and eigenvalue methods. From the analyses we found a threshold value for stability of non-endemic equilibrium point. Increasing the rate of mosquito bites can reduce the threshold value and even change non-endemic condition becomes endemic. Vaccination strategy does not change the non-endemic condition, it only speeds up the convergence to the non-endemic condition. Fogging strategy only affects position of the endemic and non-endemic equilibrium points. Reducing the rate of mosquito bites can prevent endemic condition. Several numerical simulations were carried out to confirm the analytical results obtained. From simulations we know that reducing the value of threshold may switch stability of non-endemic equilibrium point from unstable to asymptotically stable.

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