Mathematical modelling using improved SIR model with more realistic assumptions

Hamid A. Adamu, Murtala Muhammad, Abdullahi M.Jingi, Mahmud A. Usman

David and Lang developed a mathematical model (SIR) i.e Susceptible-Infective-Recovered, for the spread of infectious in a given population over a time. The model gives a reasonable and sound results. However, some more realistic factors have not been accounted for in their model. These realistic assumptions will give better understanding of the modelling epidemics if included. Therefore, this paper is proposed to include some of these assumptions to improve the SIR model. We provide a number of contributions by incorporating the assumptions to enhance the analysis of the spread of diseases under different conditions. We have classified these conditions into four and provide experiments to each of the condition. We further provide a numerical scheme for the modified model and simulated the scheme using Visual Basic (VB) to test the model’s accuracy. The results show that the modified model proved to be more efficient than the existing SIR model. However, due to the inclusion of new assumptions to the existing model, the modified model shows faster decrease in infected population and high recovery rate than the existing SIR model. Moreover, we also investigate the reproductive ration, stability analysis, equilibrium points of the model, the Jacobean and the eigenvalues of the model.

https://dx.doi.org/10.31873/IJEAS.6.1.22