Leprosy is a communicable disease which can cause hideous deformities to the afflicted and social stigmatization to them and their families. The continued high endemicity of leprosy in pockets of Sub-Saharan Africa is a source of bafflement to researchers. In this paper, we investigate non-compliant behavior by patients on treatment and possible inadequacy of the prescribed treatments as the reason for the persistence of the disease in the region. We construct theoretical, deterministic mathematical models of the transmission dynamics of leprosy. These models are modified to encapsulate non-compliance and inadequate treatment. The models are then analyzed to gain insight into the qualitative features of the equilibrium states, which enable us to determine the basic reproduction number. We also employ analytical and numerical techniques to investigate the impact of non-compliance and inadequate treatment on the transmission dynamics of the disease. Our results show that, as long as there is treatment, leprosy will eventually be eliminated from the region and that the disposition under investigation only serves to slow the rate at which the disease is eradicated.

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While most linear programming (LP) problems can be solved in polynomial time, pure and mixed integer problems are NP-hard and there are no known polynomial time algorithms to solve these problems. A characteristic equation (CE) was developed to solve a pure integer program (PIP). This paper presents a heuristic that generates a feasible solution along with the bounds for the NP-hard mixed integer program (MIP) model by solving the LP relaxation and the PIP, using the CE.