Mathematical model on pulmonary and multidrug-resistant tuberculosis patients with vaccination

Tuberculosis is a global epidemic disease and almost two billion people across the globe are infected with the tuberculosis bacilli. Many countries like China, Europe and United States has achieved dramatic decrease in TB mortality rate but country like India is still struggling hard to control this epidemic. Jharkhand one of the states of India is highly epidemic toward this disease. We propose a mathematical model to understand the spread of tuberculosis disease in human population for both pulmonary and drug-resistant subjects. A number of new vaccines are currently in development. Keeping in mind, vaccination as one of the treatment for TB patients may be infant or adult in future; an assumption for the transfer of proportion of susceptible population to the vaccination class is considered. Quarantine class is also considered in our epidemic model for multidrug-resistant patients, and it is observed that it may play a vital role for controlling the disease. Threshold and equilibria are obtained and the condition for epidemic under different conditions of threshold is established. Real parametric values of the Jharkhand state are taken into account to simulate the system developed, and the results so obtained validate our analytical results.