Nonlinear SIRS Fractional-Order Model: Analysing the Impact of Public Attitudes towards Vaccination, Government Actions, and Social Behavior on Disease Spread

Protyusha Dutta, Nirapada Santra, Guruprasad Samanta and Manuel De la Sen ()
Additional contact information
Protyusha Dutta: Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, India
Nirapada Santra: Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, India
Guruprasad Samanta: Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, India
Manuel De la Sen: Institute of Research and Development of Processes, University of the Basque Country, 48940 Leioa, Bizkaia, Spain

Mathematics, 2024, vol. 12, issue 14, 1-29

Abstract: This present work develops a nonlinear SIRS fractional-order model with a system of four equations in the Caputo sense. This study examines the impact of positive and negative attitudes towards vaccination, as well as the role of government actions, social behavior and public reaction on the spread of infectious diseases. The local stability of the equilibrium points is analyzed. Sensitivity analysis is conducted to calculate and discuss the sensitivity index of various parameters. It has been established that the illness would spread across this system when the basic reproduction number is larger than 1, the system becomes infection-free when the reproduction number lies below its threshold value of 1. Numerical figures depict the effects of positive and negative attitudes towards vaccination to make the system disease-free sooner. A comprehensive study regarding various values of the order of fractional derivatives together with integer-order derivatives has been discussed in the numerical section to obtain some useful insights into the intricate dynamics of the proposed system. The Pontryagin principle is used in the formulation and subsequent discussion of an optimum control issue. The study also reveals the significant role of government actions in controlling the epidemic. A numerical analysis has been conducted to compare the system’s behavior under optimal control and without optimal control, aiming to discern their differences. The policies implemented by the government are regarded as the most adequate control strategy, and it is determined that the execution of control mechanisms considerably diminishes the ailment burden.

Keywords: fractional-order SIRS model; basic reproduction number; asymptotic stability; optimal control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/14/2232/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/14/2232/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:14:p:2232-:d:1437259

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().