Several investigations nowadays allow the examination of cure fraction in the analysis for the survival function of the disease. This research is being motivated by the fact that an infectious disease with a co-infection is becoming more prominent in recent time but not much research has been done in the area of its epidemiological modeling. Consequently, the use of a survival model that incorporates the cured rate of the management in the analysis which is called cure rate model is adopted. The aim of the study is to model any infectious disease with a co-infection so as to estimate the performance of the management. The specific objectives are to: (i) derive the appropriate probability density functions for the sole infectious and co-infection disease; (ii) determine the distribution that best fits and estimate the cure rate parameter for the two situations; and (iii) examine and determine some risk factors associated with the two situations.rnThe existing model used in literature has been the Exponential distribution. This study was extended to include two forms of the Weibull distribution to estimate the cure rate using maximum likelihood estimation method. Goodness-of-fit was presented to screen the distributions for use. Simulation and Real-life data were used for this study using R and STATA softwares in the estimation procedure.rnThe findings of the study were:rn(i) the two-parameter Weibull distribution was the best fit for TB and TB-HIV co-infected patients in this situation; rn(ii) the cure rate of TB was 26.3% which was higher than that of the TB-HIV co-infection which was 23.1% (0.0001);rn(iii) the non-parametric median survival time of TB patients was 51 months while that of TB-HIV co-infected patients was 33 months; andrn(iv) there was no risk factor associated with TB-HIV co-infected patients while age was significantly a risk factor for TB patients among the suspected risk factors used.rnThe study concluded that appropriate parametric model is applicable and can be used to model an infectious disease with a co-infection. The cure rate model is useful when sufficient information is available to implement it. It recommended that this work is particularly useful to estimate cure rate in Hospital setting or prevalence in cross sectional data and that since hazard increases with age from the real-life data used, early screening of people is highly encouraged. The study therefore provides information which serves as a warning signal to the entire population to intensify the fight against TB and TB-HIV co-infection.