Modelling and control of a fractional-order epidemic model with fear effect
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ORIGINAL ARTICLE
Modelling and control of a fractional-order epidemic model with fear effect Manotosh Mandal1,4 • Soovoojeet Jana2 T. K. Kar4 1 2 3 4
Department Department Department Department
of of of of
Mathematics, Mathematics, Mathematics, Mathematics,
•
Swapan Kumar Nandi3
•
Tamralipta Mahavidyalaya, Tamluk, West Bengal 721636, India Ramsaday College, Amta, Howrah, West Bengal 711401, India Nayabasat P.M. Sikshaniketan, Paschim Medinipur, West Bengal 721253, India Indian Institute of Engineering Science and Technology, Shibpur, Howrah, West Bengal 711103, India
Received: 11 July 2020 / Revised: 6 September 2020 / Accepted: 9 September 2020 Ó The Joint Center on Global Change and Earth System Science of the University of Maryland and Beijing Normal University 2020
Abstract In this paper, we formulate and study a new fractional-order SIS epidemic model with fear effect of an infectious disease and treatment control. The existence and uniqueness, nonnegativity and finiteness of the system solutions for the proposed model have been analysed. All equilibria of the model system are found, and their local and also global stability analyses are examined. Conditions for fractional backward and fractional Hopf bifurcation are also analysed. We study how the disease control parameter, level of fear and fractional order play a role in the stability of equilibria and Hopf bifurcation. Further, we have established our analytical results through several numerical simulations. Keywords Fractional derivative Fractional SIS epidemic model Fractional stability conditions Fractional Hopf bifurcation Fear effect Fractional backward bifurcation
1 Introduction Infectious diseases have become one of the most threatening issues in todays lifestyle. The infectious diseases including chickenpox, measles, cholera, tuberculosis, influenza, SARS, COVID-19, etc., have massive impact & Soovoojeet Jana [email protected] Manotosh Mandal [email protected] Swapan Kumar Nandi [email protected] T. K. Kar [email protected]
than the other types of noninfectious diseases as these types of diseases can be transmitted from one individual to another, some are spread out by bites from insects or animals, and some diseases are acquired by consuming flagitious water or food or being exposed to organisms in the environment. Hence, an infectious disease may spread in a huge region throughout the globe within a very short time period. Due to the improvement of lifestyle of common people and massive enhancement in transportation and globalization, an infectious diseases become pandemic in a less amount of time compared to earlier days (for example Spanish flu in twentieth century had taken a long period of time to become a pandemic compared to the pandemic due to COVID-19 in ongoing time period). Thus, not only to study the dynamics of an infectious disease, but also to control or determining the procedure to control an infectious disease, researchers from various fields have engaged themselves. Several mathematical tools i
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