Stability and Hopf Bifurcation Analysis of a Vector-Borne Disease Model with Two Delays and Reinfection

Yan-xia, Zhang; Li, Long; Huang, Junjian; Liu, Yanjun

doi:10.1155/2021/6648959

Cited by 2 publications

(1 citation statement)

References 24 publications

(53 reference statements)

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“…The saturation incidence rate and inhibitory effect rate were discussed by Hu. Z et al [10] and Yanxia Zhang et al [22] in the vector-borne disease model. Wan and Cui [18] investigated the local stability criteria for a model equilibrium with two-time delays.…”

Section: Introductionmentioning

confidence: 99%

Mathematical analysis for the vector-host Dengue epidemic model with time delay

Murugadoss¹,

Ambalarajan²,

Karuppusamy³

et al. 2023

Preprint

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This study used a system of delay differential equations (DDE) to construct a time-delayed vector-host dengue epidemic model that accounts for inhibitory impact rates, immunity loss rates, and partial immunity rates. The model's solution is investigated and is determined to be positive and bounded. Using the next-generation matrix technique, the reproduction number is utilized to assess the model's stability. The virus-free equilibrium points were found to be locally asymptotically unstable. The existence of endemic equilibrium stability with and without time delay was investigated; as a result, endemic equilibrium points were locally stable with delay under certain conditions. For dengue transmission sensitivity analysis, the epidemiological model was analyzed. Finally, our theoretical results are validated by numerical simulations.

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Section: Introductionmentioning

confidence: 99%

Mathematical analysis for the vector-host Dengue epidemic model with time delay

Murugadoss¹,

Ambalarajan²,

Karuppusamy³

et al. 2023

Preprint

View full text Add to dashboard Cite

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Bifurcations in a Plant-Pollinator Model with Multiple Delays

Yan-xia

Yao

et al. 2023

Journal of Mathematics

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The plant-pollinator model is a common model widely researched by scholars in population dynamics. In fact, its complex dynamical behaviors are universally and simply expressed as a class of delay differential-difference equations. In this paper, based on several early plant-pollinator models, we consider a plant-pollinator model with two combined delays to further describe the mutual constraints between the two populations under different time delays and qualitatively analyze its stability and Hopf bifurcation. Specifically, by selecting different combinations of two delays as branch parameters and analyzing in detail the distribution of roots of the corresponding characteristic transcendental equation, we investigate the local stability of the positive equilibrium point of equations, derive the sufficient conditions of asymptotic stability, and demonstrate the Hopf bifurcation for the system. Under the condition that two delays are not equal, some explicit formulas for determining the direction of Hopf bifurcation and some conditions for the stability of periodic solutions of bifurcation are obtained for delay differential equations by using the theory of norm form and the theorem of center manifold. In the end, some examples are presented and corresponding computer numerical simulations are taken to demonstrate and support effectiveness of our theoretical predictions.

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Stability and Hopf Bifurcation Analysis of a Vector-Borne Disease Model with Two Delays and Reinfection

Cited by 2 publications

References 24 publications

Mathematical analysis for the vector-host Dengue epidemic model with time delay

Mathematical analysis for the vector-host Dengue epidemic model with time delay

Bifurcations in a Plant-Pollinator Model with Multiple Delays

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