A New Incommensurate Fractional-Order COVID 19: Modelling and Dynamical Analysis

Abstract

Nowadays, a lot of research papers are concentrating on the diffusion dynamics of infectious diseases, especially the most recent one: COVID-19. The primary goal of this work is to explore the stability analysis of a new version of the SEIR model formulated with incommensurate fractional-order derivatives. In particular, several existence and uniqueness results of the solution of the proposed model are derived by means of the Picard–Lindelöf method. Several stability analysis results related to the disease-free equilibrium of the model are reported in light of computing the so-called basic reproduction number, as well as in view of utilising a certain Lyapunov function. In conclusion, various numerical simulations are performed to confirm the theoretical findings.

Fractional commensurate model on COVID‐19 with microbial co‐infection: An optimal control analysis

“…Several fractional studies of deterministic, stochastic and incommensurate models on COVID-19 illness were delved in the literature examining various fear factors, diagnosed, threatened, awareness of pathogen spread, vaccination schemes, vaccine hesitancy, vaccine inefficacy, treatment, isolation, exposure to the virulent environment, effective vaccination with self-precautions, vaccine breakthrough infections, symptomatic and asymptomatic carriers and mutant strains, and so on. [30][31][32][33][34][35][36][37][38][39][40][41][42] COVID-19-related coinfections were studied with other superinfections namely hepatitis-B, 43 Tuberculosis, 44 and diabetes mellitus. 45 Optimal control modeling analysis were very effective in epidemical studies implementing effective control measures for disease annihilation found in References 46-50.…”

“…Motivated from the works of References 30,31 which explains the hesitation and threatening of virus, isolation effects, vaccination and environmental exposure, age factors, demographic changes, 32,33 symptomatic and asymptomatic carriers and mutations visualized in References 34,35, fear effects due to isolation and quarantine, vaccination, self‐precautionary measures, and associated coinfections studied in References 36–45. However, we present vaccine breakthrough infections, vaccine efficiency and microbial pathogen coinfections in a novel way on our proposed COVID‐19 coinfection model.…”

“…(2 + 1)‐dimensional Hirota–Satsuma–Ito equation, 25 and Wu–Zhang system mounted for earthquake aftereffects (dispersive gravitation of ocean waves) 26 and epidemiological behaviors of influenza, cholera and dengue in References 27–30. Fractional modeling of COVID‐19 pandemic with various approaches, control practices and fractional operators are found in References 30–42.…”

“…Memory, encapsulated by the Mittag–Leffler function of the ABC derivative, recaptures the past historical evidence, which will perfectly match the immune history of mankind in response to epidemics or sudden pandemic breakouts. Several fractional studies of deterministic, stochastic and incommensurate models on COVID‐19 illness were delved in the literature examining various fear factors, diagnosed, threatened, awareness of pathogen spread, vaccination schemes, vaccine hesitancy, vaccine inefficacy, treatment, isolation, exposure to the virulent environment, effective vaccination with self‐precautions, vaccine breakthrough infections, symptomatic and asymptomatic carriers and mutant strains, and so on 30–42 . COVID‐19‐related coinfections were studied with other superinfections namely hepatitis–B, 43 Tuberculosis, 44 and diabetes mellitus 45 .…”

Research on the Impacts of Different Model Parameters on the Trends of Infectious Diseases Based on Improved SEIR Model

“…The traditional SEIR model is equivalent to the Markov chain that includes the four states: S(Susceptible), persons who have no immunity to the virus and are not yet infected, and if they contact with someone who is already infected, they may be infected; E(Exposed), persons who have been infected but have no corresponding symptoms, and they are temporarily not contagious; I(Infected), persons who are already infected and there are corresponding symptoms with them, and they are contagious; R(Removed), persons who have dropped out of the model, which included two parts: those who are successfully cured and return to normal, and those who are dead after treatment failure. At present, many scholars have simulated and analyzed the novel coronavirus epidemic through SEIR model and its derivative models [2][3][4][5][6][7][8][9]. According to Reference 1 [1], the mathematical expression of the modified SEIR model is shown in Equation 1.…”