A Compartmental Model for Chickenpox Transmission Dynamics Incorporating Control Interventions
Keywords:
Chickenpox transmission, Mathematical modeling, Stability analysis, Sensitivity analysis, Numerical simulation
Abstract
Abstract: Chickenpox remains a highly contagious viral disease that poses significant public health challenges, particularly in populations with low vaccination coverage. Understanding its transmission dynamics is essential for designing effective control strategies. This study presents a comprehensive mathematical model to analyze the spread of Chickenpox, incorporating key intervention measures such as vaccination, isolation, and treatment. The model categorizes the human population into six compartments: susceptible, exposed, infected, isolated, treated, and recovered individuals. A system of ordinary differential equations is employed to describe the interactions among these groups. The model is further examined through the determination of disease-free and endemic equilibrium states, and stability analysis is conducted to establish the conditions under which the disease can either be eliminated or persist within the population. Sensitivity analysis is performed to identified the most influential parameters affecting disease transmission, revealing that transmission rates, vaccination coverage, and recovery rates play critical roles. Numerical simulations are also carried out to evaluate the impact of various intervention strategies. The results demonstrate that increased vaccination coverage, timely isolation of infected individuals, and effective treatment significantly reduce the number of new infections and overall disease burden. The findings highlight the importance of integrated public health strategies in controlling Chickenpox transmission. This study provides valuable insights that can inform policy decisions and guide the implementation of effective disease prevention and control measures.
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References
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https://ijmcr.in/index.php/ijmcr/article/view/826
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https://arxiv.org/abs/2309.00274
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https://www.sciencedirect.com/science/article/abs/pii/S0378475423002707
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https://www.frontiersin.org/articles/10.3389/fepid.2024.1334964/full
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https://www.cdc.gov/chickenpox/hcp/clinical-overview/index.html
[2] World Health Organization. (2023). Varicella (chickenpox): Key facts.
https://www.who.int/news-room/fact-sheets/detail/varicella-(chickenpox)
[3] Marra, Fanny, Parhar, Kanwar, Huang, Bing, and Vadlamudi, Nandini K. (2023). Global prevalence of varicella-associated complications: A systematic review and meta-analysis. Infectious Diseases and Therapy, 12(1), 1–15.
https://link.springer.com/article/10.1007/s40121-023-00899-7
[4] Bardsley, Martin, Morbey, Rebecca A., Hughes, Helen E., Harcourt, Stephen E., Smith, Gillian E., and Elliot, Andrew J. (2023). The epidemiology of chickenpox in England, 2016–2022: An observational study. Epidemiology and Infection, 151, e120.
https://www.cambridge.org/core/journals/epidemiology-and-infection/article/epidemiology-of-chickenpox-in-england
[5] Franczak, Joanna, Mrozek-Budzyn, Dorota, and Kwiecien, Jolanta. (2024). Has COVID-19 affected the course of chickenpox in children? A retrospective observational study. Viruses, 16(12), 1912.
https://www.mdpi.com/1999-4915/16/12/1912
[6] Ogunjimi, Benson, Van Damme, Pierre, and Beutels, Philippe. (2019). Herpes zoster risk reduction through exposure to chickenpox patients: A systematic multidisciplinary review. PLoS ONE, 14(6), e0218219.
https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0218219
[7] Lopez, Adriana S., Marin, Mona, and Seward, Jane F. (2019). Varicella vaccine effectiveness and duration of protection: A systematic review and meta-analysis. Pediatrics, 144(3), e20191310.
https://publications.aap.org/pediatrics/article/144/3/e20191310
[8] Wodi, A. Patrick, Murthy, Nandini, Bernstein, Henry H., McNally, Victoria V., Wallace, Megan, and MacNeil, Jessica R. (2024). Epidemiology and prevention of vaccine-preventable diseases (Varicella). CDC Pink Book.
https://www.cdc.gov/pinkbook/hcp/table-of-contents/chapter-22-varicella.html
[9] Leung, Jessica, Harpaz, Rafael, Molinari, Nicole-Aline, Jumaan, Aisha O., and Zhou, Fangjun. (2020). Herpes zoster incidence among insured persons in the United States, 2010–2018: Impact of varicella vaccination. Clinical Infectious Diseases, 71(12), 3010–3017.
https://academic.oup.com/cid/article/71/12/3010
[10] Breuer, Judith, Pacou, Mireia, Gauthier, Alain, and Brown, Michael M. (2019). Herpes zoster as a risk factor for stroke and myocardial infarction: A retrospective cohort study. Clinical Infectious Diseases, 69(3), 444–450.
https://academic.oup.com/cid/article/69/3/444
[11] El-Mesady, A., & Ali, H. M. (2024). The influence of prevention and isolation measures to control the infections of the fractional chickenpox disease model. Mathematics and Computers in Simulation, 226, 606–630.
https://www.sciencedirect.com/science/article/abs/pii/S0378475424002854
[12] Adepoju, O. A., Ibrahim, H. O., Adetunji, J. A., & Olanrewaju, S. O. (2024). Chickenpox childhood disease: An insight from mathematical modelling. International Journal of Mathematics and Computer Research, 12(12), 4670–4678.
https://ijmcr.in/index.php/ijmcr/article/view/826
[13] Okafor, C. E., Ibrahim, M., & Lawal, A. (2024). Mathematical modeling of chickenpox transmission using the Laplace Adomian decomposition method. Results in Control and Optimization, 15, 100436.
https://www.sciencedirect.com/science/article/pii/S2666720724000663
[14] Anwar, M. N., Smith, L., Devine, A., Mehra, S., Walker, C. R., Ivory, E., Conway, E., Mueller, I., McCaw, J. M., Flegg, J. A., & Hickson, R. I. (2023). Mathematical models of Plasmodium vivax transmission: A scoping review. arXiv.
https://arxiv.org/abs/2309.00274
[15] Anwar, M. N., Smith, L., Devine, A., Mehra, S., Walker, C. R., Ivory, E., Conway, E., Mueller, I., McCaw, J. M., Flegg, J. A., & Hickson, R. I. (2023). Advances in malaria transmission modeling and implications for control strategies. arXiv.
https://arxiv.org/abs/2309.00274
[16] Kumar, P., Vellappandi, M., Khan, Z. A., Sivalingam, S. M., Kaziboni, A., & Govindaraj, V. (2023). A case study of monkeypox disease in the United States using mathematical modeling with real data. Mathematics and Computers in Simulation.
https://www.sciencedirect.com/science/article/abs/pii/S0378475423002707
[17] Meharry, L. P., Oshinubi, K., Olaniyi, S., & Alade, T. (2024). Exploring the dynamics of monkeypox transmission with data-driven methods and a deterministic model. Frontiers in Epidemiology, 4, 1334964.
https://www.frontiersin.org/articles/10.3389/fepid.2024.1334964/full
[18] Anderson, R. M., May, R. M., & Anderson, B. (1985). Vaccination and herd immunity to infectious diseases. Nature, 318(6044), 323–329. https://doi.org/10.1038/318323a0
[19] Bonanni, P., Breuer, J., Gershon, A., Gershon, M., Hryniewicz, W., Papaevangelou, V., ... & Wutzler, P. (2009). Varicella vaccination in Europe – taking the practical approach. BMC Medicine, 7, 26. https://doi.org/10.1186/1741-7015-7-26
[20] Brisson, M., Edmunds, W. J., & Gay, N. J. (2001). Varicella vaccination: Impact of vaccine efficacy on the epidemiology of VZV. Journal of Infectious Diseases, 183(7), 1123–1130. https://doi.org/10.1086/319272
[21] Chaves, S. S., Gargiullo, P., Zhang, J. X., Civen, R., Guris, D., Mascola, L., & Seward, J. F. (2004). Loss of vaccine-induced immunity to varicella over time. New England Journal of Medicine, 356(11), 1121–1129. https://doi.org/10.1056/NEJMoa064040
[22] Galil, K., Brown, C., Lin, F., Seward, J., & others. (2002). Hospitalizations for varicella in the United States. Pediatrics, 109(5), 906–910. https://doi.org/10.1542/peds.109.5.906
[23] Gershon, A. A., Takahashi, M., & Seward, J. F. (2008). Varicella vaccine. In Vaccines (5th ed.). Elsevier. https://doi.org/10.1016/B978-1-4160-3611-1.50038-8
[24] Hambleton, S., Gershon, A. A., & Steinberg, S. P. (2008). Clinical and epidemiological aspects of varicella. Journal of Infection, 57(Suppl 1), S27–S32. https://doi.org/10.1016/j.jinf.2008.08.003
[25] Hope-Simpson, R. E. (1965). The nature of herpes zoster: A long-term study. Proceedings of the Royal Society of Medicine, 58(1), 9–20. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1898271/
[26] Marin, M., Güris, D., Chaves, S. S., Schmid, S., & Seward, J. F. (2007). Prevention of varicella: Recommendations of the Advisory Committee on Immunization Practices (ACIP). MMWR Recommendations and Reports, 56(RR-4), 1–40. https://www.cdc.gov/mmwr/preview/mmwrhtml/rr5604a1.htm
[27] Mikaeloff, Y., Caridade, G., Suissa, S., & Tardieu, M. (2008). Hepatitis B vaccine and the risk of CNS inflammatory demyelination in childhood. Neurology, 71(3), 196–201. https://doi.org/10.1212/01.wnl.0000316917.45049.a1
[28] Nguyen, H. Q., Jumaan, A. O., Seward, J. F., & others. (2005). Decline in mortality due to varicella after implementation of vaccination in the United States. New England Journal of Medicine, 352(5), 450–458. https://doi.org/10.1056/NEJMoa042271
[29] Seward, J. F., Watson, B. M., Peterson, C. L., Mascola, L., Pelosi, J. W., Zhang, J. X., ... & Wharton, M. (2002). Varicella disease after introduction of varicella vaccine in the United States. JAMA, 287(5), 606–611. https://doi.org/10.1001/jama.287.5.606
[30] World Bank. (2023). Population, total. https://data.worldbank.org/indicator/SP.POP.TOTL
[31] World Health Organization (WHO). (2014). Varicella and herpes zoster vaccines: WHO position paper. https://www.who.int/publications/i/item/WER8949
[32] United Nations Population Division. (2022). World population prospects 2022. https://population.un.org/wpp/
[33] Ziebold, C., von Kries, R., Lang, R., Weigl, J., & Schmitt, H. J. (2001). Severe complications of varicella in previously healthy children in Germany. Pediatric Infectious Disease Journal, 20(5), 471–474. https://doi.org/10.1097/00006454-200105000-00007
Published
2026-07-16
How to Cite
Yahaya, J., Celestine, A., Chukwuma, U., Bassey, O., Onuche, A., Omonile, J., & Ogala, E. (2026). A Compartmental Model for Chickenpox Transmission Dynamics Incorporating Control Interventions. GPH-International Journal of Mathematics, 8(11), 21-51. https://doi.org/10.5281/zenodo.21396172
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Articles
Copyright (c) 2025 Jibrin Danjuma Yahaya, Agbata Benedict Celestine, Ugo Donald Chukwuma, Okofu Mary Bassey, Acheneje Godwin Onuche, Jacob Funsho Omonile, Emmanuel Ogala
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