Rabies is a zoonotic viral disease that aects all mammals including human beings. Dogs are responsible for 99% of human rabies cases and the disease is always fatal once the symptoms appear. In Kenya the disease is still endemic despite the fact that there are ecient vaccines for controlling the disease. In this project, we developed SIRS mathematical model using a system of ordinary dierential equations from the model to study the transmission dynamics of rabies virusin dogs using public health education as a control strategy. The reproduction number R0 was calculated using the Next Generation Matrix. Both disease free and endemics equilibrium points were determined and their stability analysis performed. From the stability analysis results it was found out that the disease free equilibrium point is both locally and globally asymptotically stable when R0 < 1 and the endemic equilibrium point is both locally and globally asymptotically stable when R0 > 1. Numerical simulations done using Matlab indicated that education of the public on administration of both pre and post exposure vaccines to dogs and responsible dog ownership leads to a decrease in the numbers of rabies virus infected dogs which shows that public health education is an ecient means for controlling rabies.

In this paper, we propose a mathematical model for the transmission of typhoid which analyzes the impact of treatment of the infected individuals on the dynamics of the disease. The model consists of human population and pathogen population. The human population is subdivided into three compartments, namely susceptible individuals, infected individuals, and recovered individuals and pathogen population comprises one compartment. We derived the basic reproduction number $${\mathcal {R}}_0$$ R 0 , and analyzed the dynamical behaviors of both disease free equilibrium and endemic equilibrium by the theory of ordinary differential equations. Using MATLAB, we carried out numerical simulation and the findings indicate that effective treatment is adequate in eradicating typhoid fever.