Modelling the potential influence of human migration and two strains on Ebola virus disease dynamics

Migration of infected animals and humans, and mutation are considered as the source of the introduction of new pathogens and strains into a country. In this paper, we formulate a mathematical model of Ebola virus disease dynamics, that describes the introduction of a new strain of ebolavirus, through either mutation or immigration (which can be continuous or impulsive) of infectives. The mathematical analysis of the model shows that when the immigration of infectives is continuous, the new strain invades a country if its invasion reproduction number is greater than one. When the immigration is impulsive, a newly introduced strain is controllable when its reproduction number is less than the ratio of mortality to the population inflow and only locally stable equilibria exist. This ratio is one if the population size is constant. In case of mutation of the resident strain of ebolavirus, the coexistence of the resident and mutated strains is possible at least if their respective reproduction numbers are greater than one. Results indicate that the competition for the susceptible population is the immediate consequence of the coexistence of two different strains of ebolavirus in a country and this competition is favourable to the most infectious strain. Results also indicate that impulsive immigration of infectives when compared with continuous immigration of infectives gives time for the implementation of control measures. Our model results suggest controlled movements of people between countries that have had Ebola outbreaks despite the fact that closing boundaries is impossible.