Application of optimal control to the onchocerciasis transmission model with treatment

In this paper, we present a model for onchocerciasis that considers mass administration of ivermectin, contact prevention controls and vector elimination. The model equilibria are computed and stability analysis carried out in terms of the basic reproduction number R0. The model is found to exhibit a backward bifurcation so that for R0 less than unity is not sufficient to eradicate the disease from the population and the need is to lower R0 to below a certain threshold, R0c for effective disease control. The model is fitted to data on individuals with onchocerciasis in Ghana. A sensitivity analysis reveals that the parameters with the most control over the epidemic are the vector death rate and the effective contact rates between susceptible individuals and infected vector and susceptible vector with infected individuals. This suggests that programs aimed controlling vector will be significantly more effective in combating the disease. Optimal control theory is applied to investigate optimal control strategies for controlling onchocerciasis using insect repellent and both insecticide and larvicide as system control variables. We use Pontryagin's Maximum Principle to show the necessary conditions for the optimal control of onchocerciasis. Numerical simulations of the model show that restricted and proper use of control measures might considerably decrease the number of infections in the human population.