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 3 publications

(7 citation statements)

References 24 publications

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“…(c) Natural death occurs at a rate of d h and d v [21] (according to their limited life span) for all humans and mosquitoes respectively, regardless of condition.…”

Section: Model Formulationmentioning

confidence: 99%

“…(d) Individuals who have recovered in the human population acquire partial immunity (σ) or loss of immunity (ρ) [21].…”

Section: Model Formulationmentioning

confidence: 99%

“…Nowadays, many authors do their research on epidemic models [18][19][20] with various strategies. To take into consideration the amount of time required for a viral infection to spread to host and vector populations, Yanxia et al [21] design an associated upgraded vector-borne epidemic model with two latency periods and reinfection. We created a new model using the information in this article and included three new parameters, including loss of immunity, recovery from infectiousness, and partial protection of the human population.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of Dengue Transmission Dynamic Model by Stability and Hopf Bifurcation with Two-Time Delays

Murugadoss¹,

Ambalarajan²,

Sivakumar³

et al. 2023

Front. Biosci. (Landmark Ed)

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Background: Mathematical models reflecting the epidemiological dynamics of dengue infection have been discovered dating back to 1970. The four serotypes (DENV-1 to DENV-4) that cause dengue fever are antigenically related but different viruses that are transmitted by mosquitoes. It is a significant global public health issue since 2.5 billion individuals are at risk of contracting the virus. Methods: The purpose of this study is to carefully examine the transmission of dengue with a time delay. A dengue transmission dynamic model with two delays, the standard incidence, loss of immunity, recovery from infectiousness, and partial protection of the human population was developed. Results: Both endemic equilibrium and illness-free equilibrium were examined in terms of the stability theory of delay differential equations. As long as the basic reproduction number (R0) is less than unity, the illness-free equilibrium is locally asymptotically stable; however, when R0 exceeds unity, the equilibrium becomes unstable. The existence of Hopf bifurcation with delay as a bifurcation parameter and the conditions for endemic equilibrium stability were examined. To validate the theoretical results, numerical simulations were done. Conclusions: The length of the time delay in the dengue transmission epidemic model has no effect on the stability of the illness-free equilibrium. Regardless, Hopf bifurcation may occur depending on how much the delay impacts the stability of the underlying equilibrium. This mathematical modelling is effective for providing qualitative evaluations for the recovery of a huge population of afflicted community members with a time delay.

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“…(c) Natural death occurs at a rate of d h and d v [21] (according to their limited life span) for all humans and mosquitoes respectively, regardless of condition.…”

Section: Model Formulationmentioning

confidence: 99%

“…(d) Individuals who have recovered in the human population acquire partial immunity (σ) or loss of immunity (ρ) [21].…”

Section: Model Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Analysis of Dengue Transmission Dynamic Model by Stability and Hopf Bifurcation with Two-Time Delays

Murugadoss¹,

Ambalarajan²,

Sivakumar³

et al. 2023

Front. Biosci. (Landmark Ed)

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show abstract

“…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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“…However, in these existing mathematical models, most researchers did not consider the time delay factor. Due to its inevitability and importance, the infuence of time delay on dynamic behavior has been adequately considered in some models, such as the predator-prey model [10][11][12][13][14], the competition and cooperation model of two enterprises [15][16][17][18][19], the neuron network model [20][21][22], the competition model of internet [23,24], the chemical reaction model [25,26], and the epidemic model [27][28][29][30][31]. Te introduction of the delay factor can more accurately refect the objective facts and development laws of things.…”

Section: Introductionmentioning

confidence: 99%

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 3 publications

References 24 publications

Analysis of Dengue Transmission Dynamic Model by Stability and Hopf Bifurcation with Two-Time Delays

Analysis of Dengue Transmission Dynamic Model by Stability and Hopf Bifurcation with Two-Time Delays

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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