Mathematical modeling and optimal control approaches for dengue

Document Type : Research Article

Authors

• M. Baroudi ¹
• H. Gourram ¹
• M. Alia ²
• A. Labzai ¹
• M. Belam ¹

¹ Laboratory of Analysis Modeling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M’sik, Hassan II University of Casablanca, Morocco.

² Laboratory of Mathematics and Population Dynamics (LMPD), Faculty of Sciences Semlalia-Marrakech (FSSM), Cadi Ayyad University, Morocco.

10.22067/ijnao.2024.90023.1529

Abstract

This research explores a continuous-time mathematical model that outlines the transmission dynamics of the dengue virus across different regions, in-volving both human and mosquito hosts. We propose an optimal strat-egy that includes awareness campaigns, safety measures, and health inter-ventions in dengue-endemic areas, with the goal of reducing transmission between individuals and mosquitoes, thus lowering human infections and eliminating the virus in mosquito populations. Utilizing the discrete-time Pontryagin’s maximum principle, we identify optimal control measures and employ an iterative approach to solve the optimal system. Numerical sim-ulations are carried out using MATLAB, and a cost-effectiveness ratio is computed. Through an in-depth cost-effectiveness analysis, we highlight the effectiveness of strategies focused on protecting at-risk populations, pre-venting contact between infected humans and mosquitoes, and promoting the use of quarantine facilities as the most powerful methods for controlling the spread of the dengue virus.

Keywords

• Optimal control
• Dengue virus
• Spread of dengue

Main Subjects

• Control and Optimization

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References

[1] Aaskov, J., and Shanks, G.D. The early history of dengue in Australia, Intern. Med. J. 54(3) (2024) 511–515.
[2] Abdelrazec, A., Bélair, J., Shan, C. and Zhu, H. Modeling the spread and control of dengue with limited public health resources, Math.l biosci. 271 (2016) 136–145.
[3] Baker, C.T., Monegato, G. and vanden Berghe, G. Ordinary differential equations and integral equations (Vol. 125) Gulf Professional Publishing, 2001.
[4] Bellini, R., Zeller, H. and Van Bortel, W. A review of the vector man-agement methods to prevent and control outbreaks of West Nile virus infection and the challenge for Europe, Parasites and Vectors 7 (2014), 1–11.
[5] Blaney Jr, J.E., Matro, J.M., Murphy, B.R. and Whitehead, S.S. Re- combinant, live-attenuated tetravalent dengue virus vaccine formulations induce a balanced, broad, and protective neutralizing antibody response against each of the four serotypes in rhesus monkeys, J. Virol. 79(9) (2005) 5516–5528.
[6] Boyce, W.E., DiPrima, R.C. and Meade, D.B. Elementary differential equations, John Wiley and Sons, 2017.
[7] Carvalho, S.A., da Silva, S.O. and Charret, I.D.C. Mathematical mod-eling of dengue epidemic: control methods and vaccination strategies, Theory in Biosci. 138(2) (2019) 223–239.
[8] Dengue, W.H.O.I. Guidelines for diagnosis, treatment. prevention and control, 2009.
[9] Esteva, L. and Vargas, C. Analysis of a dengue disease transmission model, Math. Biosci. 150 (2) (1998) 131–151.
[10] Fischer, A., Chudej, K. and Pesch, H.J. Optimal vaccination and control strategies against dengue. Mathematical Methods in the Applied Sciences, Math. Methods. Appl. Sci. 42(10) (2019) 3496–3507.
[11] Fleming, W.H. and Rishel, R.W. Deterministic and stochastic optimal control, Vol. 1, Springer Science and Business Media, 2012.

[12] Ghosh, I., Tiwari, P.K. and Chattopadhyay, J. Effect of active case finding on dengue control: Implications from a mathematical model, J. Theor. Biol. 464 (2019) 50–62.
[13] Gubler, D.J. Dengue and dengue hemorrhagic fever, Clin. Microbiol. Rev. 11(3) (1998), 480–496.
[14] Guzmán, M.G. and Kouri, G. Dengue: an update, Lancet Infect. Diseas. 2(1) (2002) 33–42.
[15] Kumaran, E., Doum, D., Keo, V., Sokha, L., Sam, B., Chan, V., Alexander, N., Bradley, J., Liverani, M., Prasetyo, D.B. and Rach-mat, A. Dengue knowledge, attitudes and practices and their impact on community-based vector control in rural Cambodia, PLOS Negl. Trop. Dis. 12(2) (2018) e0006268.
[16] Labzai, A., Baroudi, M., Belam, M. and Rachik, M. Stability analysis of an order fractional of a new corona virus disease (COVID-19) model, Commun. Math. Biol. Neurosci. 2023 (2023) 77.
[17] Manikandan, S., Mathivanan, A., Bora, B., Hemaladkshmi, P., Ab-hisubesh, V. and Poopathi, S. A review on vector borne disease transmis-sion: Current strategies of mosquito vector control, Indian J. Entomol. (2023) 503–513.
[18] Narladkar, B.W. Projected economic losses due to vector and vector-borne parasitic diseases in livestock of India and its significance in im-plementing the concept of integrated practices for vector management, Vet. World, 11(2) (2018)151.
[19] Pontryagin, Lev Semenovich. Mathematical theory of optimal processes: Routledge, 2018.
[20] Singh, S., Verma, A.K., Chowdhary, N., Sharma, S. and Awasthi, A. Dengue havoc: overview and eco-friendly strategies to forestall the cur-rent epidemic, Environ. Scie. Pollut. Res. 30(60) (2023) 124806–124828.
[21] Srivastav, A.K., Kumar, A., Srivastava, P.K. and Ghosh, M. Modeling and optimal control of dengue disease with screening and information, Eur. Phys. J. Plus, 136(11) (2021) 1–29.

[22] Srivastav, A.K., Tiwari, P.K. and Ghosh, M. Modeling the impact of early case detection on dengue transmission: deterministic vs. stochastic, Stoch. Anal. Appl. 39(3) (2021) 434–455.
[23] Tissera, H., Pannila-Hetti, N., Samaraweera, P., Weeraman, J., Pali-hawadana, P. and Amarasinghe, A. Sustainable dengue prevention and control through a comprehensive integrated approach: the Sri Lankan perspective, WHO South-East Asia J. Public Health, 5(2) (2016) 106–112.
[24] ul Rehman, A., Singh, R. and Singh, J. Mathematical analysis of multi-compartmental malaria transmission model with reinfection, Chaos, Soli-ton. Fract. 163 (2022) 112527.