Modeling Tuberculosis Transmission Dynamics In The Ashanti Region Of Ghana

ABSTRACT

In attempt to model tuberculosis epidemic in the Ashanti Region of Ghana, SIR and SEIR deterministic and stochastic epidemiological models with demographic characteristics were employed. Both models showed success in modeling the infection dynamics of tuberculosis in the region. These models equilibrium points were established and their stability investigated through the Routh - Hurwitz stability criterion. The models predicted tuberculosis dying out in the entire region (Disease free equilibrium point stable) and an outbreak in Obuasi municipal and Amansie West district (endemic equilibrium point stable). It was revealed that SEIR model is the ideal model for modeling tuberculosis epidemic in the region since it characterized the infection dynamics of tuberculosis; the initial condition of the exposed compartment has influence on tuberculosis infection dynamics. Also, the branching process approximation of the epidemic revealed that there is a probability of one (1) for TB to be extinct or die out in the entire region. This was confirmed by the values of the thresholds: Malthusian parameter and the average number of offspring in a single generation. Sensitivity analysis was performed to investigate the impact of the model parameters on the reproduction number and it brought to light that increasing the infection and exposed rates increases the reproduction number while increasing the recovery/removal rate decreases the reproduction number. Finally, numerical simulations were done to validate the empirical results obtained and it revealed that all empirical estimates are good approximations for studying TB infection dynamics in the region.