Fractional COVID-19 Modeling and Analysis on Successive Optimal Control Policies

Abstract

A fractional-order coronavirus disease of 2019 (COVID-19) model is constructed of five compartments in the Caputo-Fabrizio sense. The main aim of the paper is to study the effects of successive optimal control policies in different susceptible classes; a susceptible unaware class where awareness control is observed, a susceptible aware class where vaccine control is observed, and a susceptible vaccinated class where optimal vaccination control is observed. These control policies are considered awareness and actions toward vaccination and non-pharmaceuticals to control infection. Equilibrium points are calculated, which subsequently leads to the computation of the basic reproduction ratio. The existence and uniqueness properties of the model are established. The optimal control problem is constructed and subsequently analyzed. Numerical simulations are carried out and the significance of the fractional-order from the biological point of view is established. The results showed that applying various control functions will lead to a decrease in the infected population, and it is evident that introducing the three control measures together causes a drastic decrease in the infected population.

Implicit feedback policies for COVID-19: why “zero-COVID” policies remain elusive

“…Ali Jadbabaie 1,2 , Arnab Sarker 1* & Devavrat Shah 1,3 Successful epidemic modeling requires understanding the implicit feedback control strategies used by populations to modulate the spread of contagion. While such strategies can be replicated with intricate modeling assumptions, here we propose a simple model where infection dynamics are described by a three parameter feedback policy.…”

“…Due to this complexity, simplified models of epidemic spread are often used in order to develop guidelines and understand the impact of policies on the level of infection. Throughout the COVID-19 pandemic, a wide range of models have been implemented in order to provide forecasts for important time series related to the pandemic as well as estimate causal effects of various policies [1][2][3][4][5][6] . Such approaches have been developed since as early as the 19th century, and have been successfully applied to forecast epidemics such as seasonal influenza, smallpox, and H1N1 7,8 .…”

“…One can make similar comparisons to variants of the model such as SEIR, SIR with vaccination, or other compartmental models 12 . The SIR model and relevant variants have been used extensively throughout the COVID-19 pandemic, for both forecasting and inference of population dynamics (a non-exhaustive list includes [1][2][3][15][16][17] ). In discrete time, the SIR model consists of the following set of dynamic equations 18 : In the model, N represents population size, and S(t), I(t) and R(t) represent the parts of the population that are susceptible, infected, and recovered from infection, respectively.…”

Long-Term Side Effects: A Mathematical Modeling of COVID-19 and Stroke with Real Data

“…In [24], Alkahtani et al analyzed the mathematical COVID-19 model using a fractional-order Caputo operator while considering an asymptomatic class. In [25], a fractional-order coronavirus disease model was built with five compartments. The study examined the effects of successive optimal control strategies in various susceptible classes.…”