Mathematical Analysis of an Ebola Model with Carriers, Relapse and Re-infection

Ebola virus disease (EVD) is a zoonotic filovirus caused by an RNA virus of the family filoviridae and genus Ebolavirus. It is transmitted by direct human to human contact via body fluids or indirect contact with contaminated surfaces. Due to its transmission mode the disease spreads so fast. The previous outbreaks have caused high mortality rates of up to 90%. Currently African countries like Democratic Republic of Congo and Uganda are experiencing a re-occurrence of EVD oubreak. The porous borders between African countries has always been an issue of concern with relevant authorities not taking meaningful measures to control cross border movement of persons. This poses a challenge to health systems especially in Kenya which is at a close proximity to Uganda. Ebola virus is known to persist in the immune-sites like the testicles, inside the eye and the central nervous system in people who have recovered from the disease. In women who get infected while pregnant the virus persists in the placenta, amniotic uid and the foetus whereas for lactating mothers the virus may persist in breast milk. In this paper, an ordinary differential equation that incorporates a carrier class after disease recovery, relapse and re-infection is formulated. The model is locally asymptotically stable when the reproduction number is less than one. The models endemic equilibrium indicate that the rate of change of infection with respect to time is zero, indicating that the disease is at a constant rate in the population regulated by deaths and recoveries. Simulation results show that Ebola disease carriers can contribute greatly to the disease burden.