Bifurcation, sensitivity, and optimal control analysis of onchocerciasis disease transmission model with two groups of infectives and saturated treatment function

A model depicting the transmission of onchocerciasis disease in human host community with two distinct groups of infected humans exhibiting low and high microfilariae (mf) output with saturated treatment function is developed and analyzed. The model equilibrium solutions are obtained, and it is found that the model exhibits forward bifurcation and the effective basic reproduction number (R-oc) governing the spread of the disease is computed by the use of the next generation matrix method. The sensitivity results of model parameters reveal that the rates describing the recruitment of humans, blackflies, onchocerciasis disease transmission, and the biting rate of blackflies are positively sensitive to R-oc, which necessitate the need for controls to be implemented in order to curtail the infectious contact between humans and blackflies in the host environment. To this effect, the model is further transformed into an optimal control problem by applying control strategies of personal protection of using treated bednets and wearing of permethrin-treated cloths c(1), surgical care for humans with body deformation and impaired vision c(2), education campaign c(3), and the use of insecticide c(4), respectively. The existence and uniqueness of the optimal control model are established, and the Pontryagin maximum principle (PMP) is employed to characterize the controls. The optimal control model is solved using the Runge-Kutta numerical scheme via MATI,AB, and the simulations under different control combinations show that each of the controls have its own effect in minimizing onchocerciasis transmission, but the combined effects of the four control strategies proved to be more beneficial towards the elimination of the disease in human and blackfly host community. Also, the simulations of the control profiles reveal that each of these controls are sustained at maximum until 3 months before gradually declining to zero in terminal time (T-*) of 12 months.