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.
Cite this paper
E. Chiyaka, T. Muyendesi, P. Nyamugure and F. Mutasa, "Theoretical Assessment of the Transmission Dynamics of Leprosy," Applied Mathematics
, Vol. 4 No. 2, 2013, pp. 387-401. doi: 10.4236/am.2013.42059
 World Health Organization (WHO), “Fact Sheet on Leprosy,” 2009. www.who.int
 “Definitions and Technical Guidelines for Leprosy Case Holding in the Frame of the Leprosy Elimination Strategy,” Regional Leprosy Elimination Programme, Regional Office for Africa Division of Prevention and Control of Communicable Diseases, 2002.
 “Principles of Medicine in Africa (P575-P590),” Cambridge University Press, Cambridge, 3rd Edition, 2004.
 “Oxford Handbook of Tropical Medicine,” Oxford University Press, Oxford, 3rd Edition, 2008.
 Centre for Disease Control (CDC), “Leprosy: Technical Information,” 2009. www.cdc.gov
 P. van den Driessche and J. Watmough, “Reproduction Numbers and Sub-Threshold Endemic Equilibrium for Compartmental Models of Disease Transmission,” Mathematical Biosciences, Vol. 180, No. 1-2, 2002, pp. 29-48. doi:10.1016/S0025-5564(02)00108-6
 C. Castillo-Chavez, Z. Feng and W. Huang, “On the Computation of and Its Role in Global Stability. Mathematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction,” The IMA Volumes in Mathematics and Its Applications, Vol. 125, 2002, pp. 229-250.
 J. Watmough, “Computation of the Basic Reproduction Number,” MITACS-PIMS Summer School on Mathematical Modelling of Infectious Disease, University of Alberta, Edmonton, 2008.
 C. Castillo-Chavez and B. Song, “Dynamical Models of Tuberculosis and Their Applications,” Mathematical Biosciences and Engineering, Vol. 1, No. 2, 2004, pp. 361-404. doi:10.3934/mbe.2004.1.361
 J. Carr, “Applications Centre Manifold Theory,” SpringerVelag, New York, 1981. doi:10.1007/978-1-4612-5929-9
 A. Meima, M. D. Gupte, G. J. van Oortmarssen and J. D. Habbema, “SIMLEP: A Simulation Model for Leprosy Transmission and Control,” International Journal of Leprosy and Other Mycobacterial Diseases, Vol. 67, No. 3, 1999, pp. 215-236.
 C. Bandit, “Recent Advances in Leprosy Chemotherapy,” Journal of Tropical Medicine & Parasitology, Vol. 29, No. 2, 2006, pp. 68-76.
 B. K. Girdhar and D. A. Girdhar, “Short Course Treatment of Leprosy,” Central JALMA Institute for Leprosy, Present Status, 2002.
 S. R. Pattyn, J. A. Husser, L. Janssens, S. Grillone and J. Bourland, “Inadequate Treatment in Multibacillary Leprody and Incubation Times for Relapses,” Acta Leprologica, Vol. 4, No. 4, 1986, pp. 495-499.
 T. Hussain, “Leprosy Patients Attending the Out Patient’s Clinic at Agra: A Retrospective Analysis of the Characteristics and Frequency of Regularity VS Irregularity for Determining Absenteeism, Non-Adherence and NonCompliance Division of Biostatistics,” National JALMA Institute for Leprosy and Other Mycobacterial Diseases, 2007.
 J. D. Habbema, “Trends in Leprosy Case Detection Worldwide since 1985,” University Medical Center Rotterdam, Erasmus, 2004.
 B. R. Bloom and T. Godal, “Selective Primary Health Care: Strategies for Control of Disease in the Developing World,” V. Leprosy, Vol. 5, No. 4, 1983, pp. 765-780.
 J. H. Richardus and J. D. F. Habbema, “The Impact of Leprosy Control on the Transmission of M. leprae: Is Elimination Being Attained?” Leprosy Review, Vol. 78, No. 4, 2007, pp. 330-337.
 M. F. Lechat, C. B. Misson, M. Vanderveken, C. M. Vellut and E. E. Declercq, “A Computer Simulation of the Effect of MDT on the Incidence of Leprosy,” Annales de la Societe Belge de Medecine Tropicale, Vol. 67, 1987, pp. 59-65.
 A. Meima, L. M. Irgens, G. J. van Oortmarssen, J. H. Richardusa and J. D. Habbema, “Disappearance of Leprosy from Norway: An Exploration of Critical Factors Using Anepidemiological Modelling Approach,” International Journal of Epidemiology, Vol. 31, No. 5, 2002, pp. 991-1000. doi:10.1093/ije/31.5.991
 A. Meima, W. Cairns, S. Smith, G. J. van Oortmarssen, J. H. Richardus and J. D. F. Habbema, “The Future Incidence of Leprosy: A Scenario Analysis,” Bulletin of the World Health Organization, Vol. 82, No. 5, 2004, pp. 373-385.