Mathematical modeling of the recent spread of diseases in metapopulation systems : the case of Ebola virus in West Africa and Zika virus in South America

Abstract

In this time of global health issues, there are out there many viruses that are shaking the world, including the chikungunya virus, human immunodeficiency virus, corona virus, ebola virus and zika virus. A metapopulation model describing the spread of Ebola virus disease (EVD) between two patches is developed. Disease susceptible individuals moving from one patch into the other patch, with entries into each of the patch as population grow. Due to migration into the patch and birth, with assumption that birth rate and death rate constant. We also considered movement between the infected individual, amongst patches. Ebola Virus Disease (EVD), is a very contagious and highly infectious disease which spread is determined by the number of secondary contacts of an infectious individual moving from one community to another. We show that the metapopulation model is non-negative, providing condition for stability of the disease at disease free equilibrium (DFE). Which is said to be linearly stable if R0 < 1 and unstable if R0 > 1. We also developed and analyzed a metapopulation mathematical model of Zika Virus disease (ZVD) transmission dynamics in linked communities, with movement parameter related to the two patches. With assumption that Zika infected individuals do not migrate, we express the reproduction number representing the biological parameter involved in rate of secondary infection of Zika Virus Disease (ZVD) in both patches. Stability analysis is performed after which we consider four preventive measures such as personal protective measures, use of indoor residual spray, responsiveness to health guidelines and health awareness and the prevention of movement from one infected community to another. Numerical simulations are performed and show compartment dynamics that concur with the analysis.