Identifying Critical Parameters in SIR Model for Spread of Disease

Abstract

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.

A Flexible Rolling Regression Framework for Time-Varying SIRD models: Application to COVID-19

“…Croccolo and Roman (2020), on the other hand, presented a percolation-type model based on an SIR model that aimed at mimicking the effect of lockdowns in the United States. In any case, most epidemiology models of this sort are complicated to solve analytically and it is common to resort to simulation or other techniques to attain solutions(e.g., the work by Khoshnaw et al (2017) with Elzaki transforms).…”

Model Reduction for Non-linear Protein Translation Pathways Using Slow and Fast Subsystems

“…We use stoichiometric vectors, reaction rates and mass action law to define the model equations (Khoshnaw, 2015a, Khoshnaw et al, 2016, Khoshnaw, 2015b. The model is described by the following system of nonlinear differential equations:…”

“…The method can be applied for nonlinear models to classify such systems into fast and slow subsystems and identify some analytical approximate solutions. More details about the QSSA method can be seen in (Khoshnaw, 2015a, Khoshnaw et al, 2016, Khoshnaw, 2015b. Based on conservation laws (2), we can remove the following variables:…”

Mathematical modeling for enzyme inhibitors with slow and fast subsystems

“…We have a variety of techniques of model reduction for systems biology. Methods of model reduction here are very important in systems biology for minimizing chemical reaction parameters and species (Khoshnaw, 2015a;Khoshnaw, Mohammad, & Salih, 2017). In this study, some essential techniques of model reductions are reviewed and applied for some enzymatic reactions.…”