The optimal control of age-structured models for cholera using ordinary differential equations

The use of systems of differential equations in mathematical modelling in conjunction with epidemiology continues to be an area of focused research. Chapter one briefly acquaints readers with epidemiology, cholera, and the need for effective control strategies. Chapter two of this paper discusses cholera dynamics through a variation on the SIR epidemiological model in which two separate age classes exist in a population. Using our derived system of ordinary differential equations, we calculated the general formula for R 0, estimated parameters using data for Bangladesh, and found the numeric value for R0 to be approximately 1.54. We then constructed the proof for the necessary conditions for the existence of an optimal protection control minimizing infected classes and societal costs using Fleming and Rishel's existence theorem. We then employed an optimal control resulting in a suggestion that a protection control be implemented at the end of the monsoon season. A similar process was used to analyze the case of three significant age classes in chapter three regarding a morbidity reduction control (through oral hydration). We observed that the optimal strategy required a maximum control efficacy of around 1.1% which gradually decreased over the treatment period of five years.