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Disease dynamics and optimal control strategies of a two serotypes dengue model with co-infection

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  • Saha, Pritam
  • Sikdar, Gopal Chandra
  • Ghosh, Jayanta Kumar
  • Ghosh, Uttam

Abstract

This paper aims to explore stability and bifurcations with control analysis of a co-infected two serotypes dengue model in presence of three controls, namely protection control, treatment control and mosquito killing efforts. First we analyze the model incorporating with constant controls then find the control path considering variable control. We examine biological feasibility of the considered model along with existence and stability criteria of different equilibrium with respect to basic reproduction number. Stability of serotype-I, serotype-II free equilibrium and positive co-existence equilibrium are investigated. Center manifold theorem is used to prove the stability of the co-infected endemic equilibrium. The model experiences Transcritical bifurcation with respect to basic reproduction number. Sensitivity analysis has been employed to identify most influential model parameters to control the infection. The time dependent optimal control problem is solved analytically and numerically using Pontryagin’s maximum principle. At last efficiency analysis has been carried out to find out more suitable control to combat the dengue disease. It is established from the analysis, protection control with treatment is more powerful than mosquito killing efforts by humans with treatment for controlling dengue.

Suggested Citation

  • Saha, Pritam & Sikdar, Gopal Chandra & Ghosh, Jayanta Kumar & Ghosh, Uttam, 2023. "Disease dynamics and optimal control strategies of a two serotypes dengue model with co-infection," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 209(C), pages 16-43.
    • Handle: RePEc:eee:matcom:v:209:y:2023:i:c:p:16-43
    DOI: 10.1016/j.matcom.2023.02.011
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    References listed on IDEAS

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    1. Cai, Liming & Guo, Shumin & Li, XueZhi & Ghosh, Mini, 2009. "Global dynamics of a dengue epidemic mathematical model," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2297-2304.
    2. 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.
    3. Samir Bhatt & Peter W. Gething & Oliver J. Brady & Jane P. Messina & Andrew W. Farlow & Catherine L. Moyes & John M. Drake & John S. Brownstein & Anne G. Hoen & Osman Sankoh & Monica F. Myers & Dylan , 2013. "The global distribution and burden of dengue," Nature, Nature, vol. 496(7446), pages 504-507, April.
    4. Saha, Sangeeta & Samanta, Guruprasad, 2022. "Analysis of a host–vector dynamics of a dengue disease model with optimal vector control strategy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 195(C), pages 31-55.
    5. Zhu, Min & Xu, Yong, 2019. "A time-periodic dengue fever model in a heterogeneous environment," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 115-129.
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    1. Saha, Pritam & Mondal, Bapin & Ghosh, Uttam, 2023. "Dynamical behaviors of an epidemic model with partial immunity having nonlinear incidence and saturated treatment in deterministic and stochastic environments," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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