Mathematical Modeling Of The Effects Of Vaccination On Rotavirus And Malaria Co-infection Dynamics And Effects Of Public Health Education On The Spread Of Tungiasis

Rotavirus and malaria co-infection,and tungiasis continue to pose considerable public health emergencies worldwide,and are endemic in many nations in the developing world.This dissertation presents two studies;a mathematical model for the transmission dynamics of rotavirus and malaria co-infection in the context of rotavirus vaccination,and a tungiasis epidemic model with public health education effect.The first study proposes an 8-dimension dynamical model for rotavirus and malaria spread with an aim to explore their synergistic relationship in the presence of rotavirus vaccination.The main objective of this study is to investigate whether rotavirus vaccination has a positive effect on the transmission dynamics of rotavirus and malaria co-infection in children in the developing countries,especially among resource-poor communities in the sub-Saharan Africa where rotavirus-malaria coexistence is endemic.The model allows us to explore multiple dynamical aspects of rotavirus and malaria co-infections and vacci-nation using systems of ordinary differential equations.We first study the sub-models of rotavirus-only and malaria-only in order to gain insights into how vaccination impacts on transmission dynamics of each disease separately,thereafter we study the full model.We then determine the basic reproduction numbers of the sub-models and use them to estab-lish the existence and analyze the stability of equilibria.Using center manifold theory and Lyapunov stability theory,we prove the local and global stability of the disease-endemic equilibria,respectively,of the full model.We extend the model to investigate the effects of rotavirus vaccination on the co-infection dynamics of rotavirus and malaria.Results of the study show that the disease-free equilibria of the sub-models are globally asymptoti-cally stable as their basic reproduction numbers decrease through Rr=Rm=1,while the co-infection model is found to exhibit a backward bifurcation.Further analysis indicate ro-tavirus vaccination would effectively reduce co-infections with malaria,and consequently alter population dynamics in children in the endemic regions at large.The second study,on the other hand,presents a mathematical model derived using sys-tems of ordinary differential equations to study the dynamics of jigger infestation with pub-lic health education campaigns involved.Applying the method of next generation matrix,the basic reproduction number,RE is obtained and used to establish whether jigger infes-tation breaks out in the population and results in a jigger-present equilibrium or dies out eventually corresponding to a jigger-free equilibrium.By constructing suitable Lyapunov function as well as using geometric approach,the jigger-present equilibrium is proved to be globally asymptotically stable when the basic reproduction number,RE is greater than unity,and unstable otherwise.Analytical findings show that as the educated-susceptible popula-tion increases the jigger-infested population decreases.The study,therefore,concludes that public health education could be a very effective control intervention in eliminating jigger infestation.