IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v209y2023icp16-43.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475423000848
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2023.02.011?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    4. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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).
    2. Srivastav, Akhil Kumar & Ghosh, Mini, 2019. "Assessing the impact of treatment on the dynamics of dengue fever: A case study of India," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    3. Sakirul Khan & Sheikh Mohammad Fazle Akbar & Takaaki Yahiro & Mamun Al Mahtab & Kazunori Kimitsuki & Takehiro Hashimoto & Akira Nishizono, 2022. "Dengue Infections during COVID-19 Period: Reflection of Reality or Elusive Data Due to Effect of Pandemic," IJERPH, MDPI, vol. 19(17), pages 1-12, August.
    4. Shengzhang Dong & George Dimopoulos, 2023. "Aedes aegypti Argonaute 2 controls arbovirus infection and host mortality," Nature Communications, Nature, vol. 14(1), pages 1-16, December.
    5. Zhao, Xinxing & Li, Kainan & Ang, Candice Ke En & Cheong, Kang Hao, 2023. "A deep learning based hybrid architecture for weekly dengue incidences forecasting," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    6. Eunha Shim, 2017. "Cost-effectiveness of dengue vaccination in Yucatán, Mexico using a dynamic dengue transmission model," PLOS ONE, Public Library of Science, vol. 12(4), pages 1-17, April.
    7. Hone-Jay Chu & Bo-Cheng Lin & Ming-Run Yu & Ta-Chien Chan, 2016. "Minimizing Spatial Variability of Healthcare Spatial Accessibility—The Case of a Dengue Fever Outbreak," IJERPH, MDPI, vol. 13(12), pages 1-11, December.
    8. Cheng-Te Lin & Yu-Sheng Huang & Lu-Wen Liao & Chung-Te Ting, 2020. "Measuring Consumer Willingness to Pay to Reduce Health Risks of Contracting Dengue Fever," IJERPH, MDPI, vol. 17(5), pages 1-15, March.
    9. Amy R. Krystosik & Andrew Curtis & A. Desiree LaBeaud & Diana M. Dávalos & Robinson Pacheco & Paola Buritica & Álvaro A. Álvarez & Madhav P. Bhatta & Jorge Humberto Rojas Palacios & Mark A. James, 2018. "Neighborhood Violence Impacts Disease Control and Surveillance: Case Study of Cali, Colombia from 2014 to 2016," IJERPH, MDPI, vol. 15(10), pages 1-20, September.
    10. Laith Hussain-Alkhateeb & Tatiana Rivera Ramírez & Axel Kroeger & Ernesto Gozzer & Silvia Runge-Ranzinger, 2021. "Early warning systems (EWSs) for chikungunya, dengue, malaria, yellow fever, and Zika outbreaks: What is the evidence? A scoping review," PLOS Neglected Tropical Diseases, Public Library of Science, vol. 15(9), pages 1-25, September.
    11. Jiang, Dong & Wang, Qian & Ding, Fangyu & Fu, Jingying & Hao, Mengmeng, 2019. "Potential marginal land resources of cassava worldwide: A data-driven analysis," Renewable and Sustainable Energy Reviews, Elsevier, vol. 104(C), pages 167-173.
    12. Gerhart Knerer & Christine S M Currie & Sally C Brailsford, 2020. "The economic impact and cost-effectiveness of combined vector-control and dengue vaccination strategies in Thailand: results from a dynamic transmission model," PLOS Neglected Tropical Diseases, Public Library of Science, vol. 14(10), pages 1-32, October.
    13. Benjamin Lopez-Jimena & Michaël Bekaert & Mohammed Bakheit & Sieghard Frischmann & Pranav Patel & Etienne Simon-Loriere & Louis Lambrechts & Veasna Duong & Philippe Dussart & Graham Harold & Cheikh Fa, 2018. "Development and validation of four one-step real-time RT-LAMP assays for specific detection of each dengue virus serotype," PLOS Neglected Tropical Diseases, Public Library of Science, vol. 12(5), pages 1-22, May.
    14. Adriana Zubieta-Zavala & Guillermo Salinas-Escudero & Adrian Ramírez-Chávez & Luis García-Valladares & Malaquias López-Cervantes & Juan Guillermo López Yescas & Luis Durán-Arenas, 2016. "Calculation of the Average Cost per Case of Dengue Fever in Mexico Using a Micro-Costing Approach," PLOS Neglected Tropical Diseases, Public Library of Science, vol. 10(8), pages 1-14, August.
    15. Fazli Wahid & Dr.Sajjad Ali & Jan Muhammad, 2021. "Effective Sources of Information in Winter Seasonal Diseases: The Perception of Residents of District Buner, KP," Journal of Media & Communication (JMC), Ilma University, Faculty of Media & Design, vol. 1(2), pages 215-229.
    16. Maria Glória Teixeira & Enny S Paixão & Maria da Conceição N Costa & Rivaldo V Cunha & Luciano Pamplona & Juarez P Dias & Camila A Figueiredo & Maria Aparecida A Figueiredo & Ronald Blanton & Vanessa , 2015. "Arterial Hypertension and Skin Allergy Are Risk Factors for Progression from Dengue to Dengue Hemorrhagic Fever: A Case Control Study," PLOS Neglected Tropical Diseases, Public Library of Science, vol. 9(5), pages 1-8, May.
    17. Maneerat, Somsakun & Daudé, Eric, 2016. "A spatial agent-based simulation model of the dengue vector Aedes aegypti to explore its population dynamics in urban areas," Ecological Modelling, Elsevier, vol. 333(C), pages 66-78.
    18. Mohd Hanief Ahmad & Mohd Ismail Ibrahim & Zeehaida Mohamed & Nabilah Ismail & Muhammad Amiruddin Abdullah & Rafidah Hanim Shueb & Mohd Nazri Shafei, 2018. "The Sensitivity, Specificity and Accuracy of Warning Signs in Predicting Severe Dengue, the Severe Dengue Prevalence and Its Associated Factors," IJERPH, MDPI, vol. 15(9), pages 1-12, September.
    19. Arenas, Abraham J. & González-Parra, Gilberto & Villanueva Micó, Rafael-J., 2010. "Modeling toxoplasmosis spread in cat populations under vaccination," Theoretical Population Biology, Elsevier, vol. 77(4), pages 227-237.
    20. Zhichao Li, 2022. "Forecasting Weekly Dengue Cases by Integrating Google Earth Engine-Based Risk Predictor Generation and Google Colab-Based Deep Learning Modeling in Fortaleza and the Federal District, Brazil," IJERPH, MDPI, vol. 19(20), pages 1-16, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:209:y:2023:i:c:p:16-43. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.