A diffusive model of Ebola transmission

Abstract

Ebola Virus Disease (EVD) first appeared in 1976 with two concurrent outbreaks. Human mobility greatly facilitated the spread of the disease in every successive outbreak as was the case in 2014 west African EVD outbreak. The role of movement of infected individuals in the transmission dynamics of EVD has been investigated by non diffusion-type models. However this movement across a large geographical area is modeled as diffusion. In this study, a diffusive model is developed and analyzed to describe the transmission dynamics of Ebola virus as a result of human mobility. Positivity and boundedness of solutions of themodelwith zero flux boundary conditions are shown. The basic reproduction numberis computed using the next generation matrix approach. The Routh-Hurwitzcriterion is applied to analyze the local stability of Disease-Free Equilibrium(DFE) and the Gersgorin argument is used to show that Endemic Equilibrium (EE) is locally asymptotically stable provided that basic reproduction number is greater than one. Model analysis shows that DFE point is both locallyandgloballyasymptomatically stable providedthat basic reproduction number is less than one, which implies that the disease would not invade the populationunderstudy. The existence of traveling wave solutions of diffusive model is shown. These waves propagate at a speed of h meters per second, connectingthe DFE and Endemic Equilibrium (EE), which is the speed at which the diseasespread when basic reproduction number is greater than one. Sensitivity analysis with respect to the basic reproduction number indicates that, contact rate and probability of transmission are the most significant parameters for the disease to invade the population. Therefore control strategies such as screening and quarantineshould target reduction of contact rate between the susceptible and theinfected individuals. Numerical simulation carried out revealed that the higherthe diffusion rate the higher the number of infectives as a result of increasedcontact. From the sensitivity analysis and numerical simulation in this study,control strategies such as screening and quarantine of the infected individual are deduced. The control strategies deduced in this study when effectively implementedwould greatly reduce EVD transmission.