Modelling the Effect of Public Campaign, Case Detection, Vaccine, Quarantine and Sanitarium on the Transmission of Tuberculosis Infections

In this paper, a mathematical model for transmission of TB was developed. In developing the model, the human population was positioned into; susceptible, exposed, vaccinated, quarantine, sanitarium, infected and recovered compartments. A basic model consisting of seven differential equations was developed where the existence and uniqueness of solution to the differential equations was proofed. Qualitative analysis of model by proving the positivity of solution and establishment of the invariant region of the solution. The reproduction number R0 was also obtained, and local stability analysis of the solution was carried out and we established that ; disease free equilibrium point was locally asymptotically stable (LAS). We also carried out sensitivity analysis of the parameter. Where the parameters (  , d2 ,  ,  , , , p ,  ) were shown to have been an inverse proportional relationship with R0. The numerical experiment also suggest that case detection, quarantine, sanitarium and public campaign plays a vital role in curtailing the spread of TB among populace.