A mathematical modelling approach for childhood vaccination with some computational simulations

Abstract

Computational simulations of infectious disease models have an important role to play in contributing to the understanding of the impact of vaccination programs. The spread of infectious diseases can be predicted by mathematical modelling. Some complex infectious models often require computational tools to analyze. This work introduces a simple model of childhood vaccination that can be addressed important questions regarding to the predicted impact of vaccination programs. We propose a simple variable scaling in order to minimize the number of variables and parameters that helps to identify the steady state solutions. The simplified model includes a smaller number of elements without significantly affecting the dynamics of variables. Techniques of model reduction provide a useful tool to give substructures of the original system and to model a biological process at a different level of abstractions. Interestingly, computational results are obtained using Systems Biology Toolbox (SBToolbox) for MATLAB to simulate the model populations for different values of the model parameters in two dimensional planes. Results helps us to identify critical model parameters in order to understand the impact of childhood vaccination programs.