Mathematical models of Ebola virus disease with socio-economic dynamics

[摘要] ENGLISH ABSTRACT : West Africa hosted the deadliest Ebola virus disease epidemic from 2013 to 2016and one of the common characteristics of the affected countries is their statusof being developing countries. Poor economic and social living conditions is areality in these countries and they have deeply affected the fight against Ebolavirus disease. In this work, we focus on the potential impact of socio-economicfactors on Ebola virus disease dynamics. First, we use a compartmental modelto study the dynamics of Ebola virus disease when there is a limited numberof beds for patients. We use a non linear hospitalisation rate and formulate therate at which the time dependent number of available beds evolves. The resultssuggest that a timely supply of sufficient beds to Ebola treatment units, limits thespread of the disease by keeping the infectious in one place, during their infectiousperiod. Second, we formulate a mathematical model of Ebola virus disease thatconsiders human behaviour through an exponential non linear incidence rate.Suitable Lyapunov functions are built and the proofs of the global stability ofequilibria are presented. The results advocate for an immediate and efficaciousbehaviour change, as a control measure to rapidly control an Ebola virus diseaseepidemic. Third, we build a mathematical model of Ebola virus disease dynamics,that describes the introduction of a new strain of Ebola virus, through continuousor impulsive immigration of infectives. The results suggest controlled movementsof people between countries that have had Ebola outbreaks. Finally, we develop amodel of Ebola virus disease that considers two patches with different economicstatuses represented by the respective gross-national incomes of these patches.We assume that susceptible, exposed and recovered individuals from the poorerpatch move to the rich patch. The results indicate a decrease of the number ofinfected individuals in the rich patch when movements of populations are limitedthrough the improvement of the economy in the poor patch. We conclude thatthe improvement of the economy of poorer countries may be critical in avoidingpotential outbreaks of Ebola virus disease. The results in this thesis point to theneed to consider socio-economic factors in Ebola virus disease epidemic models.

[发布机构] Stellenbosch University