Theoretical Assessment of the Transmission Dynamics of Leprosy

Edward T. Chiyaka, Tazvitya Muyendesi, Philimon Nyamugure, Farikayi K. Mutasa

Modelling Biomedical Systems Research Group, Department of Applied Mathematics, National University of Science and Technology, Bulawayo, Zimbabwe.

DOI: 10.4236/am.2013.42059                

Abstract

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.

Keywords

Leprosy; Mycobacterium leprae; Mathematical Model; Multibacillary

Conflicts of Interest

The authors declare no conflicts of interest.

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