Optimal control of a fractional order SEIQR epidemic model with non-monotonic incidence and quarantine class.

Publisher: Elsevier Country of Publication: United States NLM ID: 1250250 Publication Model: Print-Electronic Cited Medium: Internet ISSN: 1879-0534 (Electronic) Linking ISSN: 00104825 NLM ISO Abbreviation: Comput Biol Med Subsets: MEDLINE

Publication: New York : Elsevier
Original Publication: New York, Pergamon Press.

Quarantine*; Humans ; Incidence ; Epidemics ; Communicable Diseases/epidemiology ; Communicable Diseases/transmission ; Epidemiological Models ; Models, Biological ; Basic Reproduction Number ; COVID-19/epidemiology ; COVID-19/prevention & control ; COVID-19/transmission ; Computer Simulation

During any infectious disease outbreak, effective and timely quarantine of infected individuals, along with preventive measures by the population, is vital for controlling the spread of infection in society. Therefore, this study attempts to provide a mathematically validated approach for managing the epidemic spread by incorporating the Monod-Haldane incidence rate, which accounts for psychological effects, and a saturated quarantine rate as Holling functional type III that considers the limitation in quarantining of infected individuals into the standard Susceptible-Exposed-Infected-Quarantine-Recovered (SEIQR) model. The rate of change of each subpopulation is considered as the Caputo form of fractional derivative where the order of derivative represents the memory effects in epidemic transmission dynamics and can enhance the accuracy of disease prediction by considering the experience of individuals with previously encountered. The mathematical study of the model reveals that the solutions are well-posed, ensuring nonnegativity and boundedness within an attractive region. Further, the study identifies two equilibria, namely, disease-free (DFE) and endemic (EE); and stability analysis of equilibria is performed for local as well as global behaviours for the same. The stability behaviours of equilibria mainly depend on the basic reproduction number R 0 and its alternative threshold T 0 which is computed using the Next-generation matrix method. It is investigated that DFE is locally and globally asymptotic stable when R 0 <1. Furthermore, we show the existence of EE and investigate that it is locally and globally asymptotic stable using the Routh-Hurwitz criterion and the Lyapunov stability theorem for fractional order systems with R 0 >1 under certain conditions. This study also addresses a fractional optimal control problem (FOCP) using Pontryagin's maximum principle aiming to minimize the spread of infection with minimal expenditure. This approach involves introducing a time-dependent control measure, u(t), representing the behavioural response of susceptible individuals. Finally, numerical simulations are presented to support the analytical findings using the Adams Bashforth Moulton scheme in MATLAB, providing a comprehensive understanding of the proposed SEIQR model.
Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
(Copyright © 2024 Elsevier Ltd. All rights reserved.)

Keywords: Behavioural response; Fractional optimal control; Local and global stability; Lyapunov function; Memory effect; Non-monotone incidence rate; Pontryagin’s maximum principle; Quarantine compartment

Date Created: 20240611 Date Completed: 20240723 Latest Revision: 20240723

20240723

10.1016/j.compbiomed.2024.108682

38861897