Haar wavelet collocation approach for the solution of fractional order COVID-19 model using Caputo derivative

Abstract

This article is devoted to study a compartmental mathematical model for the transmission dynamics of the novel Coronavirus-19 under Caputo fractional order derivative. By using fixed point theory of Schauder’s and Banach we establish some necessary conditions for existence of at least one solution to model under investigation and its uniqueness. After the existence a general numerical algorithm based on Haar collocation method is established to compute the approximate solution of the model. Using some real data we simulate the results for various fractional order using Matlab to reveal the transmission dynamics of the current disease due to Coronavirus-19 through graphs.

A fractional-order SIRD model with time-dependent memory indexes for encompassing the multi-fractional characteristics of the COVID-19

“…6 (a) gives the simulation result when the system is considered in the integer-order domain, i.e., the system has no memory at all. We observe that there is no correlation between the experimental data and the prediction of the model, which agrees well with previous works [7] , [19] , [20] , [21] , [22] , [23] , [24] , [25] , [26] , [27] . It indicates that the COVID-19 evolution and control cannot be considered without any memory effect.…”

“…The SIRD system (2) represents a Markovian process where the previous states do not affect the current conditions, i.e., a memoryless SIRD system. Nevertheless, the network-like human interactions (including the COVID-19) evolve to a pattern with memory properties were past events impact recent events [19] , [20] , [21] , [22] , [23] , [24] , [25] , [26] , [27] . To cope with that, we apply the fractional-order calculus as a mechanism to represent the memory of the biological system since the fractional-order derivative operators represent more accurately the real phenomena in nature [17] , [18] .…”

“…Finally, if the system has no memory. In the previous studies, the memory property is almost all considered as a constant parameter and similar for the whole system [19] , [20] , [21] , [22] , [23] , [24] , [25] , [26] , [27] . This imply that the fractional-order is the same for the entire analysis.…”

“…In both cases, they are ”full-memory indexes” because their contributions are since the initial conditions. In literature, recent works have proposed fractional-order mathematical models for studying the COVID-19 [19] , [20] , [21] , [22] , [23] , [24] , [25] , [26] , [27] . Based on the fractional-order derivative with singular kernel we found that Rezapour et al.…”

“…determined a reproduction number of COVID-19 from a fractional-order mathematical model; Shah et al. studied a constant fractional-order model with the Haar collocation method as numerical solver to reveal the transmission dynamics [24] ; Rajagopal et al. proposed a fractional-order SEIRD model for the spread of COVID-19 and compared it with the real data and integer-order cases [25] ; Abadias et al.…”