Modelling the effects of insecticide-treated cattle on the control of African animal Trypanosomiasis to improve cattle productivity.

African Animal Trypanosomiasis (AAT) is a big threat to cattle productivity and human health. The disease has effects on milk and meat production. This study intends to model the effects of insecticide-treated cattle (ITC) on the control of African Animal Trypanosomiasis to improve cattle productivity (milk and meat production). A mathematical model for the transmission and control of AAT in cattle was developed. The model incorporates Insecticides-Treated Cattle as a control measure where cattle are sprayed with insecticides in two forms, namely restricted and whole-body applications. Using the next generation matrix method, we derived the effective reproduction number and from it the basic reproduction number was deduced. We proved that the disease free equilibrium point is locally and globally asymptotically stable when the reproduction number is less than one. We also showed that the endemic equilibrium point exists and it is unique. Sensitivity analysis showed that the additional mortality in tsetse fly due to insecticides has the greatest impact on the effective reproduction number followed by recruitment rate for cattle and that of tsetse flies. Results from simulations showed that there is a significant decrease in tsetse flies population caused by ITC and hence Trypanosomiasis incidence on cattle is reduced. It was also observed that the application of ITC leads to an increase in milk and meat productivity.