Modelling and Simulation of the Spread of HBV Disease. - Niyirora, Ignatius (Kabale University, 2024)
The study was to model and simulation of the spread of HBV disease. It was guided by specific objectives that were to find out the disease-free equilibrium of the spread of Hepatitis B Virus, to determine sensitivity analysis on Ro to ascertain which parameter is most sensitive and that should be targeted by way of intervention and to examine the local stability of the model equation using the modified implicit function theorem. The first result of our simulations confirms that the disease-free equilibrium is globally asymptotically stable when Ro 1. On the other hand if R> there is a stable endemic solution. I presented a sample of the results obtained in these simulations. a sample of the effect of considering the transition rate between latent and susceptibles. Also, we give a bifurcation diagram of the infected population against the vaccination rate which shows that when Rn::'.'. I the values of the infected population /(I) tends to its disease-free equilibrium values. This model shows that when the vaccination fails to force the basic reproduction number to be less than one in value the disease fires up and approaches an endemic level. This result is obtained for the case that the vaccination rate p = 0.5.