Mathematical modelling of tuberculosis epidemics

Abstract

The strengths and limitations of using homogeneous mixing andheterogeneous mixing epidemic models are explored in the contextof the transmission dynamics of tuberculosis. The focus is onthree types of models: a standard incidence homogeneous mixingmodel, a non-homogeneous mixing model that incorporates'household' contacts, and an age-structured model. The models areparameterized using demographic and epidemiological data and thepatterns generated from these models are compared. Furthermore,the effects of population growth, stochasticity, clustering ofcontacts, and age structure on disease dynamics are explored. Thisframework is used to asses the possible causes for the observedhistorical decline of tuberculosis notifications.

Keywords

• demography.
• stochastic models
• tuberculosis
• non-autonomous systems