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Lyapunov stability analysis and optimization measures for a dengue disease transmission model

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  • Abidemi, Afeez
  • Ackora-Prah, Joseph
  • Fatoyinbo, Hammed Olawale
  • Asamoah, Joshua Kiddy K.

Abstract

In this paper, we study a dengue model governed by an eight-dimensional autonomous system of ordinary differential equations using dynamical system theory. Appropriate Lyapunov functions are used to carry out an extensive investigation of the global asymptotic dynamics of the model around the dengue-free and dengue-present equilibria. The model is shown to exhibit a forward bifurcation phenomenon using Center Manifold Theory. Sensitivity analysis is carried out to determine the relative importance of the model parameters to the spread of the disease. Using optimal control theory, the model is further extended to a nonlinear optimal control model to explore the impact of four time-dependent control variables, namely, personal protection, treatment drug therapy for latently infected individuals, treatment control for symptomatic individuals and insecticide control for mosquito reduction, on dengue disease dynamics in a population. Cost-effectiveness analysis is conducted on various strategies with combinations of at least three optimal controls to determine the least costly and most effective strategy that can be implemented to contain the spread of dengue in a population.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:602:y:2022:i:c:s037843712200437x
    DOI: 10.1016/j.physa.2022.127646
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    References listed on IDEAS

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    1. Asamoah, Joshua Kiddy K. & Owusu, Mark A. & Jin, Zhen & Oduro, F. T. & Abidemi, Afeez & Gyasi, Esther Opoku, 2020. "Global stability and cost-effectiveness analysis of COVID-19 considering the impact of the environment: using data from Ghana," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    2. Sharma, Naveen & Singh, Ram & Cattani, Carlo & Pathak, Rachana, 2021. "Modeling and complexity in dynamics of T-cells and cytokines in dengue fever based on antiviral treatment," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    3. Asamoah, Joshua Kiddy K. & Nyabadza, Farai & Jin, Zhen & Bonyah, Ebenezer & Khan, Muhammad Altaf & Li, Michael Y. & Hayat, Tasawar, 2020. "Backward bifurcation and sensitivity analysis for bacterial meningitis transmission dynamics with a nonlinear recovery rate," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    4. Auliya Abdurrohim Suwantika & Woro Supadmi & Mohammad Ali & Rizky Abdulah, 2021. "Cost-effectiveness and budget impact analyses of dengue vaccination in Indonesia," PLOS Neglected Tropical Diseases, Public Library of Science, vol. 15(8), pages 1-16, August.
    5. Asamoah, Joshua Kiddy K. & Jin, Zhen & Sun, Gui-Quan & Seidu, Baba & Yankson, Ernest & Abidemi, Afeez & Oduro, F.T. & Moore, Stephen E. & Okyere, Eric, 2021. "Sensitivity assessment and optimal economic evaluation of a new COVID-19 compartmental epidemic model with control interventions," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    6. Abidemi, A. & Abd Aziz, M.I. & Ahmad, R., 2020. "Vaccination and vector control effect on dengue virus transmission dynamics: Modelling and simulation," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    7. 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).
    8. Brito da Cruz, Artur M.C. & Rodrigues, Helena Sofia, 2021. "Personal protective strategies for dengue disease: Simulations in two coexisting virus serotypes scenarios," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 254-267.
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    Cited by:

    1. Omame, Andrew & Abbas, Mujahid, 2023. "Modeling SARS-CoV-2 and HBV co-dynamics with optimal control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 615(C).

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