In this treatise a SEIR model for the transmission of tuberculosis was proposed. It assumes that the latent infected individuals progress to active tuberculosis through endogenous reactivation and exogenous re-infection and that the individuals who have recovered from the disease through treatment are not immune to tuberculosis re-infection. While most features of the original model were kept, the model was modified to incorporate two control measures in the form of post-exposure tuberculosis prophylaxis for the treatment of latent individuals and tuberculosis therapeutics for the treatmentof individuals with active tuberculosis. Mathematical analysis of the modelwas done under the assumption that the two control measures are positiveconstants. The disease-free equilibrium point was locally asymptotically stable when the basic reproduction number was less than unity and unstable when this epidemic threshold exceeds unity. An optimal control problem was formulated and the necessary conditions for optimality were derived.The numerical results based on data from Port Elizabeth suggest that using both forms of control measures simultaneously is more effective in reducing the total number of infected individuals than applying single controls separately.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:nmmu/vital:27124 |
| Date | January 2016 |
| Creators | Zembe, Pumelela Vincent |
| Publisher | Nelson Mandela Metropolitan University, Faculty of Science |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis, Masters, MSc |
| Format | x, 82 leaves, pdf |
| Rights | Nelson Mandela Metropolitan University |
Page generated in 0.0019 seconds