Narrow Results

In this paper, two mathematical models are proposed and analyzed. The first one deals with the interaction of uninfected cells, infected cells, viruses and immune response within humans. The second one deals with the effects of environmental toxicant on the first model. In each case, sufficient conditions for local stability and global stability of the equilibria are obtained, computer simulations are performed and the result is biologically interpreted. It has been seen that the environmental toxicant has detrimental effects on healthy cells, infected cells as well as on the immune response of the body.

Ebola outbreaks in Africa have occurred mostly in the Central and West Africa regions that are politically identified as the Economic Community of Central African States (ECCAS) and Economic Community of Western African States (ECOWAS), respectively. In the ECOWAS region, people and goods are allowed to travel freely across national borders of all the 15 member countries, but in the ECCAS region such regional travel across the national borders of its 10 member countries is limited. In this paper, we use parameterized mathematical models of Ebola to investigate the effects of free international travel, and the timing of border closings, on the high number of Ebola infection cases and deaths of the recent 2014–2016 Ebola outbreaks in Guinea, Liberia and Sierra Leone (ECOWAS); as compared to previous and current outbreaks in Democratic Republic of Congo (ECCAS, 1976–2018). Simulations of our single-patch Ebola model without movement of humans across international borders are shown to capture the recorded numbers of Ebola infections and deaths in the ECCAS region, and simulations of our 3-patch model with interpatch movements capture that of the ECOWAS region. We obtain that international travel restrictions and timing of border closings can play important roles in mitigating against the spread of future fatal infectious disease outbreaks.