Stability analysis and optimal control of Covid-19 pandemic SEIQR fractional mathematical model with harmonic mean type incidence rate and treatment

Abstract

In the present work, we investigated the transmission dynamics of fractional order SARS-CoV-2 mathematical model with the help of Susceptible , Exposed , Infected , Quarantine , and Recovered . The aims of this work is to investigate the stability and optimal control of the concerned mathematical model for both local and global stability by third additive compound matrix approach and we also obtained threshold value by the next generation approach. The author’s visualized the desired results graphically. We also control each of the population of underlying model with control variables by optimal control strategies with Pontryagin’s maximum Principle and obtained the desired numerical results by using the homotopy perturbation method. The proposed model is locally asymptotically unstable, while stable globally asymptotically on endemic equilibrium. We also explored the results graphically in numerical section for better understanding of transmission dynamics.

Asymptotic behavior and semi-analytic solution of a novel compartmental biological model

“…After the recent invention of the vaccination, we implemented the vaccinated individuals compartment V(t) also the Figure (12) which is the graphical behaviour. We discuss the outcomes of the Homotopy Perturbation Method by applying it to the COVID-19 model, (2). In Figure (9), the dynamics of susceptible human population ion has been shown in which the population decreases with time due to the large transmission b and vaccination a rates.…”

“…In [2], researchers studied COVID-19 using a mathematical model that included Susceptible S(t), Exposed E(t), Infected I(t), Quarantine Q(t), and Recovered R(t). The goals were to examine the stability and optimal management of the concerned mathematical model for both ➤ Received: 24.03.2022 ➤ Revised: 20.06.2022 ➤ Accepted: 21.06.2022 ➤ Published: 24.06.2022 local and global stability using a third additive compound matrix technique, as well as to produce threshold values using a next-generation approach.…”

A novel technique to analyze the fractional model of Williamson and Casson non-Newtonian boundary layer flow

“…In mathematics, the fractional derivative is more accurate than ordinary examples because it makes us better describe and understand the phenomena that occur in reality, including chemical, physical, biological and other phenomena (Podlubny, 1999; Sweilam et al. , 2020; Sinan et al. , 2021; Khader, 2011).…”

Approximate Solutions of the Jet Engine Vibration Equation by the Homotopy Perturbation Method

“…He applied successfully this method to solve a variety of nonlinear equations in science and engineering [17][18][19]. Tis HPM has already been efectively employed by numerous researchers to resolve numerous linear and nonlinear issues such as solving heat radiation equations [20], KdV PDE studied by Ganji and Rafei [21], nonconservative oscillators [22], Laplace equation [23], time fractional partial integro-diferential equations [24], wave equations [25], heat conduction and convection equations [26], integral equations [27], couple spring mass system [28] and is also applicable in other areas [29][30][31]. He [32] applied HPM for solving Blasius diferential equation [33] and nonlinear boundary value problems.…”