A Fractional Order SITR Model for Forecasting of Transmission of COVID-19: Sensitivity Statistical Analysis

Abstract

In this work, we investigate the effects of the contact rate between people on the covid-19 virus transmission through a susceptible-infected-treatment-recovered (SITR) fractional mathematical model. Several strategies are introduced, and the development methodology is constructed up in various cases based on the rate of individual contact, due to confinement and social distancing rules, which can be useful in reducing infection. The existence and uniqueness of the proposed model solution are established, as well as the basic reproduction number. The basic reproduction number has been used to control the dynamics of the fractional SITR model completely, which determines whether or not the infection is extinguished. The global stability of the infection-free balance and endemic equilibrium point of the proposed model has been fully established using the Lyapunov-LaSalle type theorem. Furthermore, a sensitivity analysis is carried out to find out which parameter is the most dominant to affect the disease's endemicity and to see how changes in parameters affect Covid-19's beginning disease transmission. The fractional Adams-Bashforth method is used to compute an iterative solution to the model. Finally, using the model parameter values to explain the importance of the arbitrary fractional-order derivative, the numerical results using MATLAB are presented.

Modeling and Analysis of a Fractional Visceral Leishmaniosis with Caputo and Caputo–Fabrizio derivatives

“…This research was carried out in the hope that it will be a useful resource for future applications and explorations of simulation by using a Caputo derivative, and to investigate new methods such as those in Refs. [18][19][20][21][22][23][24][25][26][27][28][29]…”

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“…Several techniques exist right now for forecasting the onset of infectious disease outbreaks. The neural network prediction model [12,13,14], the SEIR model [2,15,16], and ARIMA [17,18,19] are notable examples, each with unique benefits and drawbacks. The best model must be chosen in order to increase prediction accuracy, which necessitates a thorough study of the particular disease and the data that are available.…”

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“…Therefore, it is mostly applied in physics, biology, medicine, viscoelasticity, bioengineering, economics, and control theory, and it would be too long to list all the research dealing with that. For instance, the reader can refer to [4,10,12] and references therein, among others.…”