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Transmission dynamics of multi-strain dengue virus with cross-immunity

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  • Xue, Ling
  • Zhang, Hongyu
  • Sun, Wei
  • Scoglio, Caterina

Abstract

Since infection with one of the five strains of dengue virus produces life-long immunity to only this strain and temporary cross-immunity to other strains, we incorporated cross-immunity and exposed states for humans and mosquitoes in our compartmental model. We proved the globally and locally asymptotic stability of the disease-free equilibrium, the locally asymptotic stability of two boundary equilibria with the existence of only one strain, and the existence and uniqueness of the interior equilibrium with the coexistence of two strains. In addition, we found that the backward bifurcation exists. We evaluated the impact of parameters on the basic reproduction number by sensitivity analysis, and optimized the mitigation strategies according to Pontryagin’s Maximum Principle, taking into account corresponding costs. The numerical simulation results showed that increasing the economic costs may not always increase the effectiveness of optimal control, since the time for putting full control effort is shortened.

Suggested Citation

  • Xue, Ling & Zhang, Hongyu & Sun, Wei & Scoglio, Caterina, 2021. "Transmission dynamics of multi-strain dengue virus with cross-immunity," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    • Handle: RePEc:eee:apmaco:v:392:y:2021:i:c:s0096300320306950
    DOI: 10.1016/j.amc.2020.125742
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    References listed on IDEAS

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    1. Tewa, Jean Jules & Dimi, Jean Luc & Bowong, Samuel, 2009. "Lyapunov functions for a dengue disease transmission model," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 936-941.
    2. Xu, C. & Gertner, G., 2007. "Extending a global sensitivity analysis technique to models with correlated parameters," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5579-5590, August.
    3. Anggriani, N. & Tasman, H. & Ndii, M.Z. & Supriatna, A.K. & Soewono, E. & Siregar, E, 2019. "The effect of reinfection with the same serotype on dengue transmission dynamics," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 62-80.
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    1. Srivastav, Akhil Kumar & Steindorf, Vanessa & Stollenwerk, Nico & Aguiar, Maíra, 2023. "The effects of public health measures on severe dengue cases: An optimal control approach," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    2. Li, Tianyu & Wu, Yong & Ding, Qianming & Xie, Ying & Yu, Dong & Yang, Lijian & Jia, Ya, 2024. "Social contagion in high-order network with mutation," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    3. Abidemi, Afeez & Ackora-Prah, Joseph & Fatoyinbo, Hammed Olawale & Asamoah, Joshua Kiddy K., 2022. "Lyapunov stability analysis and optimization measures for a dengue disease transmission model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 602(C).

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