Mathematical models for the coinfection dynamics of cholera and typhoid

Abstract: Due to deteriorating infrastructure and declining infrastructure funding in African countries, There is a resurgence of cholera and typhoid fever. Poor waste disposal systems, poor hygiene and seasonal rains have been the main drivers of these two infections. Recently in Zimbabwe, an outbreak of the two infections was observed. Given that both infections are water-borne, a logical question is: was the outbreak of these two diseases a coincidence, or is there more structural mechanism to explain the observed coinfection? In this work, we attempt to answer such a question. We develop a system of ordinary differential equations to model the transmission dynamics of both diseases. We further add time dependant infection rates to model the dynamics of diseases in fluctuating environments. The model steady states are determined and analysed, and the role of fear is incorporated into the models. Impact analysis - how the diseases impact each other - is carried out. Numerical simulations and sensitivity analysis are used to verify the analytic results. We discover that for the greatest impact of disease control, the management of the diseases should be carried out in tandem. The public health implications of these results are articulated. Keywords: Fear, Seasonality, Stability analysis, Basic reproduction number, Cholera, Typhoid, Coinfection, Impact analysis.Ph.D. (Mathematics and Applied Mathematics