This study employed the SIR and SEIR models to mathematically study and describe the epidemiology of measles in six states representing each of the geo-political zones of Nigeria. A dynamical system‘s long term behavior is of paramount biological importance. This behavior is known through the mechanism of stability analysis. This work established the necessary condition for the system to be stable. Qualitative analysis allowed the exploration of the dynamics of the disease without solving the systems. Important parameters with threshold values helped determine under what condition an epidemic is possible. For a wholly susceptible population, this parameter is the basic reproduction number while the replacement number is the threshold parameter for a population that is not wholly susceptible. Numerical simulations were done using MatLab 7.10.0.499 (R2010a) while Math Type 6.9 was used for writing the equations. The data used was obtained from the Surveillance Branch, Epidemiology Division, Nigeria Center for Disease Control, Federal Ministry of Health, Abuja. Although basic, the SIR model is insightful into the mechanism of measles vis-à-vis the constituting compartments but handicapped in adequately describing the incidence of measles in the regions studied. A closer representation of the biology of the disease vis-à-vis its evolution is captured by the SEIR model. Although, it is an improvement of the SIR model, without vital dynamics, it is inadequate in describing the measles incidence of the regions. However, the model with vital dynamics rescued the cyclic repetition observed in time series plot of measles incidence. Consequently, it is the model that is closest to the reality of the incidence data in spite of its inability to sustain the observed oscillations.

TITLE - Mathematical modelling of infectious disease population dynamics: A study of measles in Nigeria
AUTHOR - MATE Olugbenga Philip
••••••IJSER Edition - October 2019

UNIVERSITY - The Catholic University of Eastern Africa
GUIDE NAME -
Mate
Philip