Modelling and control of a fractional-order epidemic model with fear effect

Mandal, Manotosh; Jana, Soovoojeet; Nandi, Swapan Kumar; Kar, Tapan Kumar

doi:10.1007/s40974-020-00192-0

Cited by 32 publications

(21 citation statements)

References 34 publications

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“…Our model differs from the model proposed by Sha et al [49] in functional response, fear effect (no impact of fear effect in disease transmission ), and type of the equations. In a fractional-order sense, Mandal et al [48] discussed an epidemic model with the fear effect of an infectious disease. Our model is more realistic than the models studied in [35,37] in the sense of fear induced in prey and the type of the differential equations.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

A fractional model in exploring the role of fear in mass mortality of pelicans in the Salton Sea

Kashyap

Bhattacharjee

Sarmah

2021

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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The fear response is an important anti-predator adaptation that can significantly reduce prey's reproduction by inducing many physiological and psychological changes in the prey. Recent studies in behavioral sciences reveal this fact. Other than terrestrial vertebrates, aquatic vertebrates also exhibit fear responses. Many mathematical studies have been done on the mass mortality of pelican birds in the Salton Sea in Southern California and New Mexico in recent years. Still, no one has investigated the scenario incorporating the fear effect. This work investigates how the mass mortality of pelican birds (predator) gets influenced by the fear response in tilapia fish (prey). For novelty, we investigate a modified fractional-order eco-epidemiological model by incorporating fear response in the prey population in the Caputo-fractional derivative sense. The fundamental mathematical requisites like existence, uniqueness, non-negativity and boundedness of the system's solutions are analyzed. Local and global asymptotic stability of the system at all the possible steady states are investigated. Routh-Hurwitz criterion is used to analyze the local stability of the endemic equilibrium. Fractional Lyapunov functions are constructed to determine the global asymptotic stability of the disease-free and endemic equilibrium. Finally, numerical simulations are conducted with the help of some biologically plausible parameter values to compare the theoretical findings. The order $\alpha$ of the fractional derivative is determined using Matignon's theorem, above which the system loses its stability via a Hopf bifurcation. It is observed that an increase in the fear coefficient above a threshold value destabilizes the system. The mortality rate of the infected prey population has a stabilization effect on the system dynamics that helps in the coexistence of all the populations. Moreover, it can be concluded that the fractional-order may help to control the coexistence of all the populations.

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Section: Conclusion and Discussionmentioning

confidence: 99%

A fractional model in exploring the role of fear in mass mortality of pelicans in the Salton Sea

Kashyap

Bhattacharjee

Sarmah

2021

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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“…When infected population increases, the uninfected production decreases Population dynamics and epidemic dynamics models considering fear effect have been widely studied [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] . This paper focus on the influence of fear factor on the pattern formation of host parasite model and the complex dynamic changes.…”

Section: Conditionsmentioning

confidence: 99%

“…After that, the researchers consider that the outbreak and spread of infectious diseases would bring people fear. In literature 15 , they think that the susceptible population has a fear effect, which shows that the fear effect can reduce the growth rate of the susceptible population. Follow-ing their ideas, we assume that the uninfected population has anti-infected behavior, that is, the fear effect on infected population.…”

Section: Introductionmentioning

confidence: 99%

Pattern formation of parasite-host model induced by fear effect

Ye¹,

Zhao²,

Zhou³

2022

Preprint

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In this paper, based on the epidemiological microparasite model, a parasite-host model is established by considering the fear effect of susceptible individuals on infectors. We ex-Pattern formation of parasite-host model induced by fear effect With the development of reaction-diffusion equation, the research on the pattern formation of population model has been widely concerned. Among them, the research on spatiotemporal dynamics of predator-prey model is particularly rich. Recently, Wang et al. 1 first proposed the mathematical expression of fear effect and considered the fear effect in the traditional predator-prey model. It was found that the addition of fear effect brought complex dynamic phenomena. Since then, many predator-prey models with fear effect have been studied. Considering that the fear effect also exists between uninfected host and infected host. Therefore, this paper attempts to introduce the fear effect into the epidemiological microparasite model and construct a parasite-host model with fear effect. With the help of computer, we simulate the distribution of population under different degrees of fear, and combined with other ecological factors to explore how the distribution of population will change under the interference of various factors. Our results show that the growth of pattern satisfies some laws under different ecological factors. Hopefully, this work will provide us further understanding of population dynamics in a real environment stimulated by the fear effect.

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“…Torvik et al [35] have studied that fractional derivatives appear naturally to describe some properties of motions of a Newtonian fluid. At present, there are several works involving the application of fractional-order systems in various fields including epidemic models [15,26].…”

Section: Introductionmentioning

confidence: 99%

Complex dynamics of a fractional-order SIR system in the context of COVID-19

Majee

Adak

Jana³

et al. 2022

J. Appl. Math. Comput.

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This paper proposes and analyses a new fractional-order SIR type epidemic model with a saturated treatment function. The detailed dynamics of the corresponding system, including the equilibrium points and their existence and uniqueness, uniformboundedness, and stability of the solutions are studied. The threshold parameter, basic reproduction number of the system which determines the disease dynamics is derived, and the condition of occurrence of backward bifurcation is also determined. Some numerical works are conducted to validate our analytical results for the commensurate fractional-order system. Hopf bifurcations for the fractional-order system are studied by taking the order of the fractional differential as a bifurcation parameter.

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Modelling and control of a fractional-order epidemic model with fear effect

Cited by 32 publications

References 34 publications

A fractional model in exploring the role of fear in mass mortality of pelicans in the Salton Sea

A fractional model in exploring the role of fear in mass mortality of pelicans in the Salton Sea

Pattern formation of parasite-host model induced by fear effect

Complex dynamics of a fractional-order SIR system in the context of COVID-19

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