Stability and Hopf bifurcation dynamics of a food chain system: plant–pest–natural enemy with dual gestation delay as a biological control strategy

Kumar, Vijay; Dhar, Joydip; Bhatti, Harbax Singh

doi:10.1007/s40808-018-0417-1

Cited by 14 publications

(6 citation statements)

References 25 publications

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“…The local stability dynamic of the disease free equilibrium E 0 is derived as calculated in given lemmas of [17,31,32]. For a equation of the form (first degree transcendental) λ + r 0 + q 0 e −λτ = 0 (4.1)…”

Section: Stability Criterion For Disease-free Equilibrium Ementioning

confidence: 99%

“…Lin and Wang, generalized the characteristic equation of two delay problems and given more effective analysis [22]. Recently many researchers used the single and multiple delays in the eco-epidemic model and demonstrated the stabilization effect of the disease [17,18]. They studied the dynamics of the interior steady-state's stability for different pairs of delay factors and showed that delay could lead to oscillation through a hop bifurcation.…”

Section: Introductionmentioning

confidence: 99%

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Co-infection dynamics of two short term diseases with effect of recovery delay

Tomar¹,

Dhar²,

Kumar³

2022

J. Math. Computer Sci.

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A co-infection model with two short-term diseases with delay in recovery is proposed. Here, we consider the simultaneous transmission of infection does not happen but of simultaneous recovery from both illnesses. The system consists of four epidemiological classes populations, namely: susceptible (S), an infected class with the first disease (I 1 ), an infected class with the second disease (I 2 ), co-infected class (I 12 ). We have found all possible equilibrium states, and the basic reproduction number also examined their stability without and with delay. Analytically, we have established that the local stability of equilibrium points depends on the basic reproduction number in the absence of recovery delay. But with delay, it requires some additional conditions. We have also checked the effect of delay on stability of endemic steady state numerically and showed that beyond a critical threshold value of delay parameter, the system loses its stability, and Hopf bifurcation occurs. Finally, a numerical simulation presented supports the analytical findings.

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Section: Stability Criterion For Disease-free Equilibrium Ementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Co-infection dynamics of two short term diseases with effect of recovery delay

Tomar¹,

Dhar²,

Kumar³

2022

J. Math. Computer Sci.

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“…Some authors assumed that healthy prey needs more handling time for predators than infected ones [24]. A variety of researchers in population dynamics incorporated gestation time lags in their research and analyzed the gestation delay's effects on the prey-predator dynamics [25][26][27]. For a better understanding of the food chain dynamic, further investigation is needed.…”

Section: Introductionmentioning

confidence: 99%

“…It is clear from Case I that all roots of the equation ( 29) are negative except the root corresponds to the equation (26). Now, we compare (26) to (12) and get v = v * and q = q * .…”

mentioning

confidence: 99%

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Effect of multiple gestation delays in a prey–predator food chain system with infected class of prey

Gupta,

Dhar,

Sinha

2024

SeMA

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This article investigates a tri-trophic food chain model with the epidemic at the bottom level (prey) and gestation delays for the next two levels( the intermediate predator and top predator). The steady states' positivity, boundedness, existence, and stability have been analyzed. The study of Hopf bifurcation has been carried out for different steady states. It is shown that when the gestation delay for intermediate predator τ 1 is absent, the interior equilibrium is locally stable for gestation delays of top predators τ 2 ∈ (0, τ + 20 ) and performs Hopf bifurcation for all τ 2 > τ + 20 . Further, in the presence both the delay τ 1 and τ 2 , the system becomes unstable when τ 1 , τ 2 crosses their critical values τ ++ 10 , τ ++ 20

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