Author(s)

Sarbaz H. A. Khoshnaw¹, Najem A. Mohammad², Rizgar H. Salih³

¹Department of Mathematics, University of Raparin, Ranya, Kurdistan Region, Iraq.
²Department of Mathematics, Koya University, Koy Sanjaq, Kurdistan Region, Iraq.
³Faculty of Science, University of Raparin, Ranya, Kurdistan Region, Iraq.

Calculating analytical approximate solutions for non-linear infectious disease models is a difficult task. Such models often require computational tools to analyse analytical approximate methods which appear in some theoretical and practical applications in systems biology. They represent key critical elements and give some approximate solutions for such systems. The SIR epidemic disease model is given as the non-linear system of ODE’s. Then, we use a proper scaling to reduce the number of parameters. We suggest Elzaki transform method to find analytical approximate solutions for the simplified model. The technique plays an important role in calculating the analytical approximate solutions. The local and global dynamics of the model are also studied. An investigation of the behaviour at infinity was conducted via finding the lines and singular points at infinity. Model dynamic results are computed in numerical simulations using Pplane8 and SimBiology Toolbox for Mathlab. Results provide a good step forward for describing the model dynamics. More interestingly, the simplified model could be accurate, robust, and used by biologists for different purposes such as identifying critical model elements.

Mathematical Modelling, Epidemic SIR Disease Model, Stability Analysis, Analytical Approximate Solutions, Sensitivity Analysis

Khoshnaw, S. , Mohammad, N. and Salih, R. (2017) Identifying Critical Parameters in SIR Model for Spread of Disease. Open Journal of Modelling and Simulation, 5, 32-46. doi: 10.4236/ojmsi.2017.51003.