An analytical study of the dynamic behavior of Lotka-Volterra based models of COVID-19

Abstract

COVID-19 has become a world wide pandemic since its first appearance at the end of the year 2019. Although some vaccines have already been announced, a new mutant version has been reported in UK. We certainly should be more careful and make further investigations to the virus spread and dynamics. This work investigates dynamics in Lotka-Volterra based Models of COVID-19. The proposed models involve fractional derivatives which provide more adequacy and realistic description of the natural phenomena arising from such models. Existence and boundedness of non-negative solution of the fractional model is proved. Local stability is also discussed based on Matignon’s stability conditions. Numerical results show that the fractional parameter has effect on flattening the curves of the coexistence steady state. This interesting foundation might be used among the public health strategies to control the spread of COVID-19 and its mutated versions.

The complex interplay between COVID-19 and economic activity

“…This outcome is confirmed also from the simulations. With respect to the existing literature this is a novelty because while some models assume the Lotka–Volterra co-dynamics ( Younes and Hasan, 2020 , Mohammed et al, 2021 ) our analysis attains it as a result of the preliminary analysis of the considered economic-pandemic context.…”

Fractional Lotka–Volterra model with Holling type III functional response

“…Now, we emphasize that models with derivatives of fractional order are more consistent with real phenomena than models of integer order (see [11][12][13][14][15][16][17]). In particular, fractional models of the Lotka-Volterra type have been studied; for example, Mohammed et al [18] studied existence and boundedness of non-negative solution and local stability for a fractional Lotka-Volterra model, Ahmed et al [19] have proved the existence and uniqueness of solutions and gave numerical solutions for a fractional-order predator-prey model. Also, Ariza et al [20] have obtained parameter estimations for a fractional Lotka-Volterra models applying a Bayesian statistical inversion method.…”

The Influence of Multiplicative Noise and Fractional Derivative on the Solutions of the Stochastic Fractional Hirota–Maccari System

“…Recently, numerous significant phenomena have been represented by fractional derivatives, including electro-magnetic, image processing, acoustics, electrochemistry and anomalous diffusion phenomena [1][2][3][4][5][6]. One benefit of fractional models is that they may be stated more specifically than integer models, which encourages us to construct a number of significant and practical fractional models.…”