Mathematical Modelling of the Transmission of Ebola Virus in Human Populations in Uganda. - Nkamuhabwa, Jolly (Kabale University, 2024)
This research report aims at the Mathematical modeling of the transmission of the Ebola virus in human populations in Uganda. The Ebola virus is a Filo virus which belongs to the Filovirudae family of viruses. It causes the disease known as Ebola virus disease in humans, primates, and other animals. The research proposal is guided by some objectives which include developing and analyzing a mathematical model for the transmission of the Ebola virus in human populations of Uganda, formulating a modified SIER model for the Ebola virus disease transmission dynamics, determining disease-free equilibrium points and the basic reproduction number, to determine the endemic equilibrium points and to investigate the local stability of both the disease-free and endemic equilibrium points. The researcher investigates and proposes the generalized model called the SEIR model that describes the transmission strategies of Ebola virus disease caused through close contact, with organs and other bodily fluids in humans. It is identified that at a time, t, if the product of the population growth rate, r =[/, the sum of the natural death rate and the number of infected people is greater than the product of the basic reproduction number (Ro), the number of the susceptible populations, then the endemic equilibrium point will be stable and the disease will remain in the population. The research will show that if the product of the infection rate a, the exposure rate [, population rate r, is therefore less than the product of the sum a+µ, and 0+y+ the disease-free equilibrium will be stable. This indicator shows that the disease can be reduced to zero in the population. Individuals are born susceptible to Ebora disease in such a way that everybody in the population is capable of contracting it.