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On mathematical modeling and stability analysis of chickenpox models in the presence of weakened-immune individuals in a population | ||
| Journal of Mathematical Modeling | ||
| دوره 14، شماره 3، آبان 2026، صفحه 861-890 اصل مقاله (2.29 M) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2026.31347.2812 | ||
| نویسندگان | ||
| Charles Iwebuke Nkeki* 1؛ Imuwahen Anthonia Mbarie2 | ||
| 1Department of Mathematics, Faculty of Physical Sciences, University of Benin, Benin City, Edo State, Nigeria | ||
| 2Institute of Child Health, College of Medical Sciences, University of Benin, Benin City, Edo State, Nigeria | ||
| چکیده | ||
| The varicella-zoster virus (VZV) also known as chickenpox is one of the most contagious diseases. Individuals who have never had VZV, have never been vaccinated, or have a compromised immune (which is refers to as immunocompromised) systems, stand the highest risk of VZV infection. This paper considers susceptible-exposed-infectious-weaken immune-recovered-vaccinated (SEIWRV) epidemic model for chickenpox infectious disease, in the presence of treatment. The basic reproduction number, denoted by ${\cal R}_o$ for the model is obtained, and found to be re-enforce by two classes of individuals: -spread from the first-time infected and unvaccinated individuals, and spread by the weaken-immune individuals. This basic reproduction number depends on incidence rate from the susceptible and weaken-immune individuals as well as treatment rate. It is shown in this paper that the model exhibits two equilibria, which include, the disease-free and the endemic equilibriums. By constructing a suitable Lyapunov function, it is observed that the global asymptotic stability of the disease-free equilibrium depends on number of infectious, ${\cal R}_o$ and the treatment rate. The global endemic equilibrium is established using geometric approach, which is applied to a five-dimensional system of differential equations. We found that chickenpox will remain endemic as long as weaken-immune individuals remain in the population. Numerical simulations are also presented to illustrate our main results. It is found that it is possible to eradicate chickenpox from the population, only if the medical practitioners and researchers understand the role of weaken-immune individuals in the spread of chickenpox. | ||
| کلیدواژهها | ||
| Mathematical model؛ SEIWRV؛ chickenpox؛ weakened-immune individuals؛ vaccination؛ stability analysis؛ endemic equilibrium؛ basic reproduction number | ||
| مراجع | ||
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[1] B.C. Agbata, O. Omale, P.B. Ojih, I.U. Omatolam, "Mathematical analysis of chickenpox transmission dynamics with control measures", Cont. J. Appl. Sci. 14(2) (2019) 6–23. [2] A. Alotiby, "Immunology of stress: A review article", J. Clin. Med. 13(21) (2024) 6394. [3] D. Baleanu, A. Jajarmi, S.S. Sajjadi, D. Mozyrska, "A new fractional model and optimal control of a tumor-immune surveillance with non-singular derivative operator", Chaos 29(8) (2019) 083127. [4] O. Baleanu, P. Shekar, I. Torkzadeh, H. Ranjbar, A. Jajarmi, K. Nouri, "Stability analysis and system properties of Nipah virus", Chaos Solit. Fractals 166 (2023) 112990. [5] C.O. Bourke, J.A. Berkley, A.J. Prendergast, "Immune dysfunction as a cause and consequence of malnutrition", Trends Immunol. 37(6) (2016) 386-398. [6] M. Brisson, W.J. Edmunds, N.J. Gay, B. Law, G. De Serres, "Modelling the impact of immunization on the epidemiology of varicella zoster virus", Epidemiol. Infect. 125 (2000) 651–669. [7] CDC, "Varicella surveillance", CDC MMWR report year 2024, Florida Health, https://www.floridahealth.gov/diseases-and-conditions/vaccine-preventable-disease/varicella/index.htm/ [8] X. Chen, J. Cao, J. Park, J. Qiu, "Stability analysis and estimation of domain of attraction for the endemic equilibrium of an SEIQ epidemic model", Nonlinear Dyn. 87 (2017) 975-985. [9] A.A. Dawood, "Chickenpox, review and prevalence varicella virus in Nineveh Province", Asian J. Med. Sci. 2(1) (2020) 6-14. [10] A. Ebrahimzadeh, A. Jajarmi, D. Baleanu, "Enhancing water pollution management through a comprehensive fractional modeling framework and optimal control techniques", J. Nonlinear Math. Phys. 31(48) (2024). [11] S. Edward, D. Kuznetsor, S. Mirau, "Modelling and stability analysis for a varicella zoster virus model with vaccination", Appl. Comput. Math. 3(4) (2014) 150–162. [12] S. Frothingham, Medically reviewed by Angela M. Bell, MD, FACP — By Scott Frothingham — Updated on February 28, 2024. [13] K.A. Graham, R.J. Arciuolo, O. Matalka, B.M. Isaac, A. Jean, N. Majid, L. Seifu, J. Croft, B. Crouch, M. Macaraig, A. Lemkin, G.T. Caceres, R. Lall, C. Lawrence, E. Silverman, F. Laraque, A. Bouscaren, J.B. Rosen, "Varicella outbreak among recent arrivals to New York, 2022-2024". CDC Morbidity and Mortality Weekly Report (MMWR) /May 30,2024/ 73(21) (2024) 478-483. https://www.cdc.gov/mmwr/volumes73/wr/mm7321a1.htm [14] C.N. Inyama, F.N. Mbagwu, C.M. Duru, "Taxonomic relationship on some chrysophyllum species based on anatomical studies", Med. Aromat. Plants, 5(227) (2016) 2167–2412. [15] S.A. Jose, R. Raja, J. Dianavinnarasi, D. Baleanu, A. Jirawattanapanit, "Mathematical modeling of chickenpox in Phuket: Efficacy of precautionary measures and bifurcation analysis", Biomed. Signal Process. Control 84 (2023) 104714. [16] S.A. Jose, Z. Yaagoub, R. Raja, D. Joseph, A. Jirawattanapanit, "Computational dynamics of a fractional order model of chickenpox spread in Phuket province", Biomed. Signal Process. Control 91 (2024) 105994. [17] A.R. Kalyan, "10 factors that weaken immune system, health topics", Continental Hospital. continentalhospital.com, 2023. [18] J. Karsai, R.C. Kovacs, A. Danielisz, Z. Molnar, J. Dudas, T. Borsos, G. Rost, "Modeling the transmission dynamics of varicella in Hungary", J. Math. Ind. 10(12) (2020) 1-16. [19] U.Y. Madaki, H.A. Manu, A.A. Gwani, E.E. Elijah, "Application of mathematical modelling on the spread of chickenpox disease (A case study of Nayinawa clinicdamaturu, Yobe state)", Scholars J. Phys. Math. Stat. 7(10) (2020) 260–271. [20] M. Marin, J.F. Seward, A.A. Gershon, "The Varicella Vaccination Program in the United States: 25 Years of Saving Lives and Preventing Illness", J. Infect. Dis. 226(Suppl 4) (2022) S375–S379. [21] N. Methathien, "Chickenpox", Pediatric Infectious Disease Society of Thailand, Bangkok, 2021. [22] NICE, National Institute for Health and Care Excellence, "Scenario: Immunocompromised, management of chickenpox", 2025, https://cks.nice.org.uk [23] B. Ogunjimi, N. Hens, N. Goeyvaerts, M. Aerts, P.V. Damme, P. Beutels, "Using empirical social contact data to model person to person infectious disease transmission: An illustration for varicella", Math. Biosci. 218 (2009) 80-87. [24] S. Qureshi, A. Yusuf, "Modeling chickenpox disease with fractional derivatives: From caputo to atangana-baleanu", Chaos Solit. Fractals 122 (2019) 111-118. [25] X. Sun, C. Dai, K. Wang, Y. Liu, X. Jin, C. Wang, Y. Yin, Z. Ding, Z. Lu, W. Wang, Z. Wang, F. Tang, K. Wang, Z. Peng, "A dynamic compartmental model to explore the optimal strategy of varicella vaccination: An epidemiological study in Jiangsu Province, China", Trop. Med. Infect. Dis. 8(1) (2023), 17. [26] X. Tang, S. Zhao, A.P.Y. Chiu, H. Ma, X. Xie, S. Mei, O. Kong, Y. Qin, Z. Chen, X. Wang, D. He, "Modelling the transmission and control strategies of varicella among school children in Shenzhen, China", PLoS One 12(5) (2017) e0177514. [27] G.Y. Trivedi, B. Saboo, "The risk factors for immune system impairment and the need for lifestyle changes", J. Soc. Health Diab. 8 (2020) 25-28. [28] United Nations. Iraq Death Rate 1950-2024, United Nations - World Population Prospects. https://www.macrotrends.net/global-metrics/countries/IRQ/iraq/death-rate (Retrieved 2024-03-28). [29] M. Wang, X. Li, M. You, Y. Wang, X. Liu, Z. Li, W. Zhao, Z. Jiang, Y. Hu, D. Yin, "Epidemiological Characteristics of Varicella Outbreaks - China, 2006-2022", China CDC Wkly, Dec 29, 5(52) (2024) 1161-1166. [30] C.M. Weyand, J.J. Goronzy, "Aging of the immune system. Mechanisms and Therapeutic Target", Ann. Am. Thorac. Soc., Dec, 13 (2016) S422-S428. [31] WHO, "Varicella and herpes zoster vaccines: WHO position paper, June 2014". Weekly. Epidemiological Rec. 89 (2014) 265--287. [32] W. Zha, F. Pang, N. Zhou, B. Wu, Y. Liu, Y. Du, X. Hong, Y. Lv, "Research about the optimal strategies for prevention and control of varicella outbreak in a school in a central city of China: based on an SEIR dynamics model", Epidemiol. Infect., 148 (2020) e56. [33] J. Zibolenova, V. Szaboova, T. Baska, D. Sevcovic, H. Hudeckova, "Mathematical modelling of varicella spread in slovakia", Cent. Eur. J. Public Health, 23(3) (2015) 227–232. | ||
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