An ODE model of Lymphatic filariasis is proposed with eight mutually disjoint compartments. The model is proven to be mathematically and epidemiologically well posed. Epidemiological interpretation of the effective reproduction number is presented. A special case is considered where the death rate due to the disease is negligible. An endemic equilibrium under this special scenario is explicitly computed and the presence of backward bifurcation under this condition is suggested. Bifurcation analysis is performed using the Castillo-Chavez and Song theorem in the special case where death due to disease is zero. When the re-infection rate is zero, backward bifurcation is shown not to be present. In such a situation, global asymptotic stability of the endemic equilibrium is established.

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 R_O<1, it is unstable if R_O>1. The numerical results show that lymphatic \textit{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 \textit{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. Sensitivity analysis showed that increasing mosquito mortality rate, reducing the probability of mosquito infecting humans, reducing the probability of humans infecting mosquitoes, reducing mosquitoes recruitment rate by destroying mosquitoes breeding sites and reducing the number of times a mosquito bites human will bring down the reproduction number to less than unity.

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