The SEIR Dynamical Transmission Model of Dengue Disease with and Without the Vertical Transmission of the Virus

Abstract

The transmission of dengue disease when there is a possibility of Vertical Transmission (VT) is studied using mathematical modeling. In the normal case, the mosquito is infected by the dengue virus when it bites an infectious human being. Evidence is gathering that the mosquitoes can also be infected through sexual contact with infected male mosquito. To see the possible consequence of having this addition mode of transmission, a SEIR, Susceptible-Exposed-Infected-Recovery, model is constructed. The Routh – Hurwitz criteria are applied to the model in order to establish the stability of the infection. It is seen that the model without the VT model has 2 equilibrium points, a disease free equilibrium point and an endemic equilibrium point, while the model with the VT has only an endemic equilibrium point. The numerical solutions of differential equations of the model without the VT mode exhibit dynamical behaviors that converges to the disease free equilibrium state when basic reproduction time R₀ is less than 1 and converges to endemic equilibrium state when R₀>1. The trajectories of the numerical solutions for all possibilities (with and without VT mode) projected onto various 2D planes and 3D spaces are presented.