Dynamical Analysis of a Diphtheria Transmission Model with Epidemiological Data Fitting
Abstract
Diphtheria is a serious infectious disease caused by Corynebacterium diphtheriae, which affects the respiratory system and can lead to severe complications if not properly controlled. In this study, a compartmental deterministic epidemiological model governed by a system of nonlinear differential equations was formulated to investigate the transmission dynamics of diphtheria. Rigorous analysis of the model showed that the disease-free equilibrium was both locally and globally asymptotically stable when the basic reproduction number was less than unity, indicating that the spread of the disease could be effectively controlled under this condition. Real-life data on diphtheria were collected and fitted into the model in order to estimate key parameters. These estimated parameter values were then used to perform numerical simulations using MATLAB, which helped validate the analytical results obtained from the model. The simulations further explored the interaction dynamics of diphtheria in humans, including transmission patterns, disease progression, and its effects on the host population. Based on the findings, recommendations were made to healthcare policymakers on effective strategies for controlling and reducing the spread of the disease and minimizing its public health burden.
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References
World Health Organization. (2023). Diphtheria outbreak news and updates. World Health Organization. https://www.who.int/emergencies/disease-outbreak-news/item/2023-DON-diphtheria
World Health Organization. (2022). Diphtheria vaccine position paper and immunization schedule. World Health Organization. https://www.who.int/publications
World Health Organization. (2023). Global immunization coverage report 2023. World Health Organization. https://www.who.int/teams/immunization-vaccines-and-biologicals
Centers for Disease Control and Prevention. (2023). Diphtheria: Clinical information for healthcare professionals. Centers for Disease Control and Prevention. https://www.cdc.gov/diphtheria/hcp/clinical-overview.html
Centers for Disease Control and Prevention. (2022). Epidemiology and prevention of vaccine-preventable diseases. Centers for Disease Control and Prevention. https://www.cdc.gov/vaccines/pubs/pinkbook/diphtheria.html
Truelove, S. A., Keegan, L. T., Moss, W. J., Chaisson, L. H., Macher, E., Azman, A. S., & Lessler, J. (2019). Clinical and epidemiological aspects of diphtheria: A systematic review and pooled analysis. Clinical Infectious Diseases, 71(1), 89–97. https://doi.org/10.1093/cid/ciz808
Adegboye, O. A., Alele, F. O., Pak, A., Castellanos, M. E., Abdullahi, M. A. S., Okeke, M. I., Emeto, T. I., & McBryde, E. S. (2023). A resurgence and re-emergence of diphtheria in Nigeria. Transactions of the Royal Society of Tropical Medicine and Hygiene. https://doi.org/10.1177/20499361231161936
Elsinga, J., van Meijeren, D., & Reubsaet, F. (2023). Surveillance of diphtheria in the Netherlands between 2000–2021. BMC Infectious Diseases, 23, 420. https://doi.org/10.1186/s12879-023-08388-5
Will, R. C., Sharma, N. C., Ramamurthy, T., Veeraraghavan, B., Sangal, L., Haldar, P., Pragasam, A. K., Vasudevan, K., Kumar, D., Das, B., Heinz, E., Melnikov, V., Baker, S., Sangal, V., & Mutreja, A. (2021). Spatiotemporal persistence of multiple clades of Corynebacterium diphtheriae. Nature Communications, 12, 1500. https://doi.org/10.1038/s41467-021-21870-5
Tafrikan, M., Fatmawati, F., Windarto, W., & Madubueze, C. E. (2022). A mathematical model of diphtheria transmission dynamics with vaccination and treatment. AIMS Mathematics, 7(10), 18245–18264. https://doi.org/10.3934/math.20221005
Amalia, P., Toaha, S., & Kasbawati. (2023). Optimal control of mathematical model of diphtheria spreading. Daya Matematis: Jurnal Inovasi Pendidikan Matematika, 10(2), 138–147. https://doi.org/10.26858/jdm.v10i2.35776
Gatto, M., Bertuzzo, E., Mari, L., Miccoli, S., Carraro, L., Casagrandi, R., & Rinaldo, A. (2021). Spread and dynamics of the COVID-19 epidemic in Italy: Effects of emergency containment measures. Proceedings of the National Academy of Sciences, 118(19), e2020125118. https://doi.org/10.1073/pnas.2020125118
Zhang, J., Xiao, X., & Wang, Y. (2020). Mathematical modelling and analysis of measles transmission dynamics with vaccination. Applied Mathematics and Computation, 373, 125015. https://doi.org/10.1016/j.amc.2019.125015
Zhao, S., Stone, L., Gao, D., & Zhang, M. (2020). A mathematical model for Ebola virus disease transmission with isolation and hospitalization. Bulletin of Mathematical Biology, 82(8), 1–24. https://doi.org/10.1007/s11538-020-00766-2
Wagner, K. S., White, J. M., Crowcroft, N. S., De Martin, S., Mann, G., & Efstratiou, A. (2010). Diphtheria in the United Kingdom, 1986–2008: The increasing role of Corynebacterium ulcerans. Epidemiology and Infection, 138(11), 1519–1530. https://doi.org/10.1017/S0950268810000203
Wagner, K. S., White, J. M., Andrews, N. J., Borrow, R., Stanford, E., Newton, E., & Pebody, R. G. (2012). Immunity to tetanus and diphtheria in the UK in 2009. Vaccine, 30(43), 7111–7117. https://doi.org/10.1016/j.vaccine.2012.09.023
Adewale, S. O., Olopade, I. A., Adeniran, S. O., Ajao, S. O., & Mohammed, I. T. (2017). Mathematical analysis of quarantine on the dynamical transmission of diphtheria disease. International Journal of Science and Engineering Investigations, 6(64), 17–22. https://www.ijsei.com/papers/ijsei-66417-02.pdf
Robins, S. L. (1974). Infectious diseases. In Pathologic basis of disease (pp. 390–392). W. B. Saunders. https://scholar.google.com/scholar?q=Robbins+Pathologic+Basis+of+Disease+1974+infectious+diseases
Sanches, R. P., Ferreira, C. P., & Kraenkel, R. A. (2011). The role of immunity and seasonality in cholera epidemics. Bulletin of Mathematical Biology, 73(12), 2916–2931. https://doi.org/10.1007/s11538-011-9658-0
Puspita, G., Kharis, M., & Supriyono. (2017). Pemodelan matematika pada penyebaran penyakit difteri dengan pengaruh karantina dan vaksinasi. Unnes Journal of Mathematics, 6(1), 25–35. https://doi.org/10.15294/ujm.v6i1.11867
https://journal.unnes.ac.id/sju/index.php/ujm/article/view/11867
Fathoni, M. I., Mardlijah, & Hariyanto. (2015). Proceedings of Seminar Nasional Matematika Pendidikan Matematika 2015 (pp. 229–238). Universitas Negeri Surabaya.
Nwankwo, A., & Okuonghae, D. (2018). Mathematical analysis of the transmission dynamics of HIV–syphilis co-infection in the presence of treatment for syphilis. Bulletin of Mathematical Biology, 80, 437–492. https://doi.org/10.1007/s11538-017-0380-8
https://link.springer.com/article/10.1007/s11538-017-0380-8
Islam, Z., Ahmed, S., Rahman, M. M., Karim, M. F., & Amin, M. R. (2022). Global stability analysis and parameter estimation for a diphtheria model: A case study of an epidemic in Rohingya refugee camp in Bangladesh. Computational and Mathematical Methods in Medicine, 2022, 6545179. https://doi.org/10.1155/2022/6545179
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8813233/ (PMC)
Adegboye, O. A., Alele, F. O., Pak, A., Castellanos, M. E., Abdullahi, M. A. S., Okeke, M. I., Emeto, T. I., & McBryde, E. S. (2023). A resurgence and re-emergence of diphtheria in Nigeria, 2023. Therapeutic Advances in Infectious Disease, 10, 20499361231161936. https://doi.org/10.1177/20499361231161936 (Sage Journals)
Castillo-Chávez, C., & Song, B. (2004). Dynamical models of tuberculosis and their applications. Mathematical Biosciences and Engineering, 1(2), 361–404. https://doi.org/10.3934/mbe.2004.1.361
Agbata, B. C., Shior, M. M., Obeng-Denteh, W., Omotehinwa, T. O., Paul, R. V., Kwabi, P. A., & Asante-Mensa, F. (2023). A mathematical model of COVID-19 transmission dynamics with effects of awareness and vaccination program. Journal of Ghana Science Association, 21(2), 59–61. https://ir.knust.edu.gh/items/c0a14f3d-cdbf-4721-8d14-260a77bd98fc
Omede, B. I., Odionyenma, U. B., Ibrahim, A. A., & Bolaji, B. (2022). Third wave of COVID-19: mathematical model with optimal control strategy for reducing the disease burden in Nigeria. International Journal of Dynamics and Control, 11(1), 411–427. https://doi.org/10.1007/s40435-022-00982-w
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