Analytical Investigation of the Impact of Failed Treatments on the Transmission Dynamics of Onchocerciasis

The drug Ivermectin is considered the medicine of choice in combating onchocerciasis. However, treatment needs to be repeated once annually or biannually within a period of 10-15 years which covers the worm’s adult life cycle. Therefore, a model was designed to evaluate the impact of failure to complete treatment on the dynamics of onchocerciasis within the whole number of human inhabitants domiciled in an environment. The backward bifurcation phenomenon, via the model, was induced by human deaths caused by Onchocerciasis and the bifurcation range was also shown to be affected by the proportion of the infected population who complete their treatment. Numerical study of the model reveals that the proportion of affected human individuals who complete their treatment as well as the relative infectiousness of humans who failed to complete their treatment have significant influence on the movement of onchocerciasis in the whole number of human inhabitants domiciled in an environment. In particular, it was seen that an increase in the percentage of individuals who did not complete their structured medical care has significant impact on the backward bifurcation range. It was also shown that while increasing the treatment rate of infectious humans is important, control strategies that would encourage people to stay through the treatment period should also be implemented alongside failure to do this will undermine the gains of improved treatment rates.