Abstract
One of the control measures available that are believed to be the most reliable methods of curbing the spread of coronavirus at the moment if they were to be successfully applied is lockdown. In this paper a mathematical model of fractional order is constructed to study the significance of the lockdown in mitigating the virus spread. The model consists of a system of five nonlinear fractional-order differential equations in the Caputo sense. In addition, existence and uniqueness of solutions for the fractional-order coronavirus model under lockdown are examined via the well-known Schauder and Banach fixed theorems technique, and stability analysis in the context of Ulam–Hyers and generalized Ulam–Hyers criteria is discussed. The well-known and effective numerical scheme called fractional Euler method has been employed to analyze the approximate solution and dynamical behavior of the model under consideration. It is worth noting that, unlike many studies recently conducted, dimensional consistency has been taken into account during the fractionalization process of the classical model.
Highlights
Coronavirus (COVID-19) pandemic cut across more than 190 countries in the first 20 weeks after its emergence
It is of paramount importance to understand the transmission dynamics of the disease and to predict whether the control measures available will help in curtailing the spread of the disease [4, 5]
Shaikh et al [24] used batshosts-reservoir-people transmission fractional-order COVID-19 model to estimate the effectiveness of preventive measures and various mitigation strategies, predicting future outbreaks and potential control strategies
Summary
Coronavirus (COVID-19) pandemic cut across more than 190 countries in the first 20 weeks after its emergence. Shaikh et al [24] used batshosts-reservoir-people transmission fractional-order COVID-19 model to estimate the effectiveness of preventive measures and various mitigation strategies, predicting future outbreaks and potential control strategies. Definition 4 Problem (7), which is equivalent to model (4), is referred to as being generalized Ulam–Hyers stable if there exists a continuous function φK : R+ → R+, with φK(0) = 0, such that, for each solution Φ ∈ E of the inequality (16), there is exist a solution Φ ∈ E of problem (7) such that. We discuss the obtained numerical outcomes of the governing model in respect of the approximate solutions To this aim, we employed the effective Euler method under the Caputo fractional operator to do the job.
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