Approximate solution for the nonlinear fractional order mathematical model

Abstract

Health organizations are working to reduce the outbreak of infectious diseases with the help of several techniques so that exposure to infectious diseases can be minimized. Mathematics is also an important tool in the study of epidemiology. Mathematical modeling presents mathematical expressions and offers a clear view of how variables and interactions between variables affect the results. The objective of this work is to solve the mathematical model of MERS-CoV with the simplest, easiest and most proficient techniques considering the fractional Caputo derivative. To acquire the approximate solution, we apply the Adomian decomposition technique coupled with the Laplace transformation. Also, a convergence analysis of the method is conducted. For the comparison of the obtained results, we apply another semi-analytic technique called the homotopy perturbation method and compare the results. We also investigate the positivity and boundedness of the selected model. The dynamics and solution of the MERS-CoV compartmental mathematical fractional order model and its transmission between the human populace and the camels are investigated graphically for θ=0.5,0.7,0.9,1.0. It is seen that the recommended schemes are proficient and powerful for the given model considering the fractional Caputo derivative.

Keywords

• adomian decomposition method
• convergent series
• laplace transformation
• caputo fractional derivative
• homotopy perturbation method
• invariant set