Modeling the impact of vaccination on the epidemiology of measles in a metapopulation

A Dissertation Submitted in Partial Fulfilment of the Requirements for the Degree of Master's in Mathematical and Computer Sciences and Engineering of the Nelson Mandela African Institution of Science and TechnologyIn this research, a metapopulation model is formulated as a system of ordinary differential equations to study the impact of vaccination on the spread of measles. An expression for the effective reproduction number for the metapopulation system and ( = 1,2) for the two patches when there are no individual movements between them are derived using the next generation approach for controlling the disease. The disease-free equilibrium is computed and proved to be locally and globally asymptotically stable if 1. We show that when there are no movements between the two patches, there exists at least one endemic equilibrium for all > 1 and bifurcation analysis of the endemic equilibrium point proves that forward (supercritical) bifurcation occurs in each patch. Sensitivity analysis of the basic reproduction number 0 for metapopulation system is performed and we found that movement rates from patch 2 to patch 1 tend to increases measles infection in a metapopulation while movement rates from patch 1 to patch 2 tend to decrease measles infection in a metapopulation. Numerical simulation results are also presented to validate analytical results and to show the impact of vaccination on incidence and prevalence of measles in the metapopulation