Tuberculosis Model : A Mathematical Analysis / Nadhirah bt Abdul Halim

Abdul Halim, Nadhirah (2013) Tuberculosis Model : A Mathematical Analysis / Nadhirah bt Abdul Halim. Masters thesis, University of Malaya.

Preview

PDF (Full Text) Download (880Kb) | Preview

Abstract

In this thesis, the design and analysis of compartmental deterministic models for the transmission dynamics of infectious disease in a population is studied. A basic Susceptible-Exposed-Infected-Recovered (SEIR) model for the transmission of infectious disease with immigration of latent and infectious individuals is developed and rigorously analyzed. The model is assumed to have permanent immunity and homogenous mixing. The constant immigration of the infected individuals into the population makes it impossible for the disease to die out which means, there will be no disease-free equilibrium. However, it is shown that there exists an endemic equilibrium which is locally asymptotically stable under certain parameters restriction. We then extend the 3-compartment Susceptible-Exposed-Infected (SEI) tuberculosis (TB) model with immigration proposed by McCluskey and van den Driessche (MnD) in 2004 into a 4-compartment SEIR model. The treated individuals are moved into the recovered group with slight immunity against the TB. Results show the importance of treatment to the infected and that treatment for the latently infected are more effective in curbing the disease. In the last model, we analyze the best approach in containing the spread of the disease under different factors. We incorporate the idea of immigration into the TB transmission model with chemoprophylaxis treatment as proposed by Bhunu et al. [3]. The results show that the immigration effects are overwhelmed by the other contributing factors such as the high rate of re-infection, making it insignificant; contradicting with reality. Simply giving treatments also does not give the best result iv on a long term basis as the population will eventually die out. Different kinds of intervention are needed to ensure a more successful prevention plan and one way is to reduce the contact rate of the infectious individuals.

Actions (For repository staff only : Login required)