Formulation And Analyses Of Epidemiological Models Of Rotavirus And Tumor Infections

Epidemiological models give a clear definition of how a disease spreads among groups of human beings and animals. They also provide an insight into how a disease can be controlled, duration or extent of an outbreak, and a prediction for both short and long term behavior of an outbreak. With the emergence of new pathogens, researchers are putting more effort in trying to form new models that will help in understanding effects of both existing and these new pathogens on human beings and animals. In line with this search for new models, we have developed a mathematical model of rotavirus infection incorporating vaccination and comprehensively analyzed it. The basic reproduction number, Rv, has been established and a proof of existence of a unique positive endemic equilibrium is established. By using Lyapunov direct method, we have proved that both disease-free and endemic equilibria are globally stable provided that Rv< 1 and Rv> 1respectively. Real data has been fitted to this model showing that it can be used to predict the nature of a rotavirus infection in a population. The results of both analysis and simulation show that vaccination is a very effective way of controlling rotavirus infection. A model to explore the co-infection of malaria and typhoid has also been developed. We analyzed the co-infection model by establishing the basic reproduction number Rmrand proved that it is locally stable. It has been shown that the disease-free equilibrium is not globally stable due to co-infection. However, it has been observed that if maximum protection is given against co-infection, the global stability may be achieved. Further analysis of co-infection model indicates that it may undergo a backward bifurcation. Numerical simulation using reasonable parameter values indicates that co-infection persists whenever Rmris greater than unity and dies out when Rmris less than unity. Finally, we have simplified the Kirschner-Panetta model on the interaction of tumor cells and effector cells by considering linear growth term as opposed to logistic growth term used by Kirschner and Panetta. Establishment of existence of a positive endemic equilibrium is done. In addition, a fixed point bifurcation is investigated using the rate of spread of tumor as a varying parameter, suggesting that backward bifurcation can occur under reasonable choice of parameters. Through mathematical deduction and numerical simulation, an elaborate uncertainty and sensitivity analysis of the rate of spread of tumor, Rs, is performed. The distribution of Rsis derived, and the sensitivity of the magnitude of Rsto the uncertainty in estimating values of input parameters is assessed. The results indicate that the external source of effector cells and its death rate are influential in the rate of spread of tumor.