Derivation of the Reproduction Number and Simulation of the Tuberculosis-Lymphatic filariasis Co-infection Model with Treatment for both Diseases

Abstract

An Ordinary Differential Equation(ODE) co-infection model of Tuberculosis-Lymphatic filariasis is proposed with 17 mutually disjoint compartments. We showed that the model is Mathematically and Epidemiologically well-posed and the disease-free equilibrium(DFE) of the co-infection model is locally asymptotically stable if Ro<1, it is unstable if Ro>1. The numerical results show that lymphatic filariasis infection increases susceptibility to tuberculosis infection. This is in agreement with literature that, persons with lowered immunity such as HIV, diabetes, immune disorder etc are at a higher risk of contacting infectious diseases. We also found that increasing the rate of diagnosis and treatment of active tuberculosis and symptomatic lymphatic filariasis cases, the incidence of co-infection in the community can be reduced, and that if resources are limited, efforts should be targeted at treating only the co-infected cases.