A Spatiotemporal Model on the Transmission Dynamics of Zika Virus Disease

Despite the preventive and control strategies in place, ZikV disease still persists especially in the Western countries and the Pacific islands. In this study, a spatiotemporal model is developed and analyzed to describe the transmission dynamics of ZikV disease and deduce potential control strategies. Positivity and boundedness of solutions of the model with zero flux boundary conditions are shown. The basic reproduction number, R0, is computed using the next generation matrix approach. Model analysis shows that the disease-free equilibrium (DFE) point is both locally and globally asymptotically stable provided that R0 < 1, which implies that the disease would not invade the population under study. The endemic equilibrium (EE) is locally asymptotically stable when R0 > 1, which implies that the disease would persist in the population, at manageable levels. Existence of travelling wave solutions of the spatiotemporal model is shown. These waves propagate at a speed v, connecting the DFE and EE, which is the speed at which the disease spreads if R0 > 1. Sensitivity analysis with respect to key parameters of, R0, indicates that control strategies should target reduction of the vector biting rate. Numerical simulations are carried out to graphically illustrate the long term behaviour of the model solutions.