Mathematical Modelling on the Transmission Dynamics of MERS-CoV Using a Fractional Order Derivative
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Festus Abiodun Oguntolu
Federal University of Technology, Minna, Niger State
Nigeria
 
 Introduction:  
  In this study, we developed and conducted a comprehensive analysis of a Caputo fractional order epidemic model to describe the transmission dynamics of MERS-CoV between human and camel populations. The analysis begins by establishing the positivity and boundedness of the model`s solutions, employing Laplace transform techniques in conjunction with the Mittag Leffler function. The existence and uniqueness of solutions are rigorously proven using Banach’s and Schaefar’s fixed point theorems. Moreover, we demonstrate that the proposed fractional order MERS-CoV model satisfies the Ulam-Hyers-Rassias stability criteria. To further explore the model’s behavior, numerical simulations were performed for varying fractional orders, specifically 0.65, 0.75, 0.85, and 0.95, highlighting the impact of fractional dynamics on the spread of the disease. The numerical simulations reveal that for both human and camel populations, the highest value of the fractional order ( ) results in the highest peak values in the infected compartments, specifically the exposed, asymptomatic, and symptomatic groups, during the initial weeks. However, in the later stages of the simulation, these compartments exhibit a reversal, with the highest fractional order leading to the lowest number of infections.