Effects of awareness program and delay in the epidemic outbreak

Samanta, Sudip

doi:10.1002/mma.4089

Cited by 21 publications

(11 citation statements)

References 53 publications

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“…It is easy to show hat if d < 0, then the equation (29) has at least one positive real root. Using the fact that β(M ) is a positive decreasing function, we have…”

Section: A2mentioning

confidence: 99%

“…It is to be noted that all the previous simulations were considered in the absence of delay (τ = 0) and we can check that with the chosen set of parameters, the condition of the stability of the positive equilibrium E * cited in the theorem 3.5 holds. Now, to investigate numerically the effect of the delay in reporting the infected cases, we treat the roots of the equation (29). It is found that it admits exactly one positive real root 1.9321e −04 , which gives that the characteristic equation (25) has a pair of purely imaginary roots ±0.0139i, and the critical value of the delay is found to be τ 0 = 79.9.…”

Section: Stability and Direction Of The Hopf-bifurcationmentioning

confidence: 99%

“…Therefore, it is more plausible to consider a time delay in the growth rate of awareness programs related to the number of reported infected cases. In this context, some mathematical models proposed to assess the effect of time delay in execution of awareness programs (see for instance [32,1,25,26,29,12,2]). It was found that incorporation of time delay in the modeling process destabilizes the system and periodic solutions may arise through Hopf-bifurcation.…”

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confidence: 99%

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Dynamic analysis of an $ SEIR $ epidemic model with a time lag in awareness allocated funds

Hajjami¹,

Jarroudi²,

Lahrouz³

et al. 2021

DCDS-B

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The spread of infectious diseases is often accompanied by a rise in the awareness programs to educate the general public about the infection risk and suggest necessary preventive practices. In the present paper we propose to study the impact of awareness on the dynamics of the classical SEIR by considering the budget allocation to warn people as a new dynamic variable. In the model formulation, it is assumed that the susceptible individuals contract the infection via a direct contact with infected individuals, and that the transmission rate is presented by a general decreasing function of the availability of funds. We further introduced a time delay in the growth rate of the budget allocation related to the number of reported infected cases. The existence and the stability criteria of the equilibrium states are obtained in terms of the basic reproduction number Ra. It is shown that Ra ≤ 1 is a necessary and sufficient condition for the global stability of the disease-free equilibrium, and by application of the geometric approach based on the third additive compound matrix we derived sufficient conditions for the global stability of the positive equilibrium state in the absence of delay. Our analysis reveals that awareness programs have the ability to reduce the infection prevalence. However, delay in providing funds destabilizes the system and give rise to periodic oscillations through Hopf-bifurcation. The direction and the stability of the bifurcating periodic solutions are investigated by using the normal form theory and central manifold theorem. Numerical simulations and sensitive analysis are provided to illustrate the theoretical findings. .

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“…It is easy to show hat if d < 0, then the equation (29) has at least one positive real root. Using the fact that β(M ) is a positive decreasing function, we have…”

Section: A2mentioning

confidence: 99%

Section: Stability and Direction Of The Hopf-bifurcationmentioning

confidence: 99%

mentioning

confidence: 99%

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Dynamic analysis of an $ SEIR $ epidemic model with a time lag in awareness allocated funds

Hajjami¹,

Jarroudi²,

Lahrouz³

et al. 2021

DCDS-B

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“…Time delay occurs often in almost every biological situation. Therefore, investigation of any ecological/epidemiological system without time delay is not realistic [23][24][25][26][27][28][29][30][31] . Detailed topics on the use of time delays in real models can be found in the classical books [32][33][34] .…”

Section: Introductionmentioning

confidence: 99%

Chaos in a nonautonomous eco-epidemiological model with delay

Samanta

Tiwari

Alzahrani

2020

Applied Mathematical Modelling

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a b s t r a c tIn this paper, we propose and analyze a nonautonomous predator-prey model with disease in prey, and a discrete time delay for the incubation period in disease transmission. Employing the theory of differential inequalities, we find sufficient conditions for the permanence of the system. Further, we use Lyapunov's functional method to obtain sufficient conditions for global asymptotic stability of the system. We observe that the permanence of the system is unaffected due to presence of incubation delay. However, incubation delay affects the global stability of the positive periodic solution of the system. To reinforce the analytical results and to get more insight into the system's behavior, we perform some numerical simulations of the autonomous and nonautonomous systems with and without time delay. We observe that for the gradual increase in the magnitude of incubation delay, the autonomous system develops limit cycle oscillation through a Hopf-bifurcation while the corresponding nonautonomous system shows chaotic dynamics through quasiperiodic oscillations. We apply basic tools of non-linear dynamics such as Poincaré section and maximum Lyapunov exponent to confirm the chaotic behavior of the system.

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“…38 It is noted that there was a big campaign from media on the Ebola epidemic of 2014-2015 in West Africa, but this did not stop the epidemic and death toll due to the breakdowns and cuts in public health infrastructure. 39,40 For some infectious diseases, mathematical models are also studied to see how the delay in implementing awareness programs impacts the dynamics of infectious disease, [41][42][43] and it is observed that incorporation of time delay in the modeling process destabilizes the system. Recently, Agaba et al 44 have studied an SIS-type delay mathematical model by considering local awareness arising from direct interaction between unaware and aware individuals and global awareness originating from public information campaigns.…”

Section: Introductionmentioning

confidence: 99%

Impacts of TV and radio advertisements on the dynamics of an infectious disease: A modeling study

Misra

Kumar

2018

Math Methods in App Sciences

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TV and radio advertisements are widely acknowledged as important interventions in raising issues of public health care and play promising role to control the infection through propagating awareness among the individuals. In this paper, a nonlinear susceptible‐infected‐susceptible (SIS) model is proposed and analyzed to see the impacts of TV and radio advertisements on the spread of influenza epidemic. In the model formulation, it is assumed that the susceptible individuals contract infection through the direct contact with infected individuals. The information regarding the protection against the disease is propagated via TV and radio advertisements, and their growth rates are assumed to be proportional to the fraction of infected individuals. However, the growth rate of TV advertisements decreases with the increase in number of aware individuals. The information broadcasted through TV and radio advertisements induces behavioral changes among the susceptible individuals, and they form an isolated aware class. The epidemiological feasible equilibria, their stability properties, and direction of bifurcation are discussed. The expression for modified basic reproduction number is obtained. The model analysis shows that the dissemination rate of awareness among susceptible individuals due to TV and radio advertisements and baseline number of TV and radio advertisements have potential to reduce the epidemic peak and, thus, control the spread of infection. Further, the analytical findings are well supported through numerical simulation.

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Effects of awareness program and delay in the epidemic outbreak

Cited by 21 publications

References 53 publications

Dynamic analysis of an $ SEIR $ epidemic model with a time lag in awareness allocated funds

Dynamic analysis of an $ SEIR $ epidemic model with a time lag in awareness allocated funds

Chaos in a nonautonomous eco-epidemiological model with delay

Impacts of TV and radio advertisements on the dynamics of an infectious disease: A modeling study

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