Abstract

Mathematical Modelling of Dengue Fever Incorporating Vaccination as Control

1Mohammed, Abdullahi,2Abdulfatai, AtteMomoh,3Abimbola, N. G. A. and 4Ali, I. M.

---

Abstract This paper proposes a mathematical model of dengue fever incorporating vaccination. The proposed model is governed by system of first-order differential equations. The model is divided into eight (8) compartments namely; Vaccinated humans, Susceptible humans, exposed humans, Infected humans, Recovered humans. Susceptible vectors, Exposed vectors and Infected vectors. The positivity of the solution is established. We derived the disease-free equilibrium and endemic equilibrium states of the model and carried out stability on the disease-free equilibrium. The results show that the model is both locally and globally asymptotically stable when 0 R ? 1 and unstable otherwise. Finally, we numerically solved the model equations to examine the impact of some variables of the model. The graph shows that vaccination and treatment reduce the disease in the population. Keywords: Dengue fever, Vaccination, Loss of immunity, Local stability, Global stability, Reproduction number.

PDF