Mathematical Analysis of a Diarrhoea Model in the Presence of Vaccination and Treatment Waves with Sensitivity Analysis

E.I Akinola,B.E Awoyemi,O.D Falowo,T.O Akinwumi,I.A Olopade

doi:10.4314/jasem.v25i7.2

Abstract

   In this study, the diarrhoea model is developed based on basic mathematical modelling techniques leading to a system (five compartmental model) of ordinary differential equations (ODEs). Mathematical analysis of the model is then carried out on the uniqueness and existence of the model to know the region where the model is epidemiologically feasible. The equilibrium points of the model and the stability of the disease-free state were also derived by finding the reproduction number. We then progressed to running a global sensitivity analysis on the reproduction number with respect to all the parameters in it, and four (4) parameters were found sensitive. The work was concluded with numerical simulations on Maple 18 using Runge-Kutta method of order four (4) where the values of six (6) parameters present in the model were each varied successively while all other parameters were held constant so as to know the behaviour and effect of the varied parameter on how diarrhoea spreads in the population. The results from the sensitivity analysis and simulations were found to be in sync.  

Highlights

The growth of some diseases has been on a rise and not enough preventive or treatment measures are being put in place
The diarrhoea model is developed based on basic mathematical modelling techniques leading to a system of ordinary differential equations (ODEs)
The equilibrium points of the model and the stability of the disease-free state were derived by finding the reproduction number

Summary

Introduction

The growth of some diseases has been on a rise and not enough preventive or treatment measures are being put in place. Some diseases like diarrhoea are even very much neglected because they are considered trivial. Though many researchers have put in much effort in formulating models that could help in eradicating some of these diseases, many of these models have turned out not to be mathematically and epidemiologically well posed. This research work was set out to investigate the movement of the disease-diarrhoea throughout a population from susceptible to recovered in all realistic terms, and to evaluate the modelling of infectious diarrhoea in the presence of vaccination, determine the basic reproduction number R0, carry out a sensitivity analysis on it, and at the same time stimulate the model so as to draw conclusions that can help medical practitioners/health policy makers know the best control measures to be employed

Methods

Results

Conclusion