Analysis of Mpox Dynamic Model with Reinfection and Treatment

Siti Laelatul Chasanah; Dina Eka Nurvazly; Ikhlas Pratama Sandy; Arvi Hasanah

doi:10.37905/euler.v13i2.32358

Analysis of Mpox Dynamic Model with Reinfection and Treatment

Siti Laelatul Chasanah, Dina Eka Nurvazly, Ikhlas Pratama Sandy, Arvi Hasanah

Abstract

This research aims to develop a mathematical model of monkeypox disease spread with reinfection and hospitalization. This model divided the human population into five sub-populations: susceptible, exposed, infectious, hospitalized, and recovered. On the other hand, the animal population is divided into three: susceptible, exposed, and infectious. The results of the model analysis show that the stability of the two equilibrium points, disease-free and endemic, is asymptotically stable when and , respectively. A sensitivity analysis was conducted on the parameter of the rate at which infected individuals are hospitalized. Based on numerical simulations, a disease-free state has been achieved when more than 68.87% of infected individuals receive hospital treatment. Hospital treatment has a positive impact on efforts to reduce the number of infected individuals in the population. The more individuals who are hospitalized, the greater the number of individuals who are exposed, hospitalized, and recover will increase.

Keywords

Mpox; Reinfection; Treatment

Full Text:

PDF

References

WHO, “Mpox (monkeypox),” from who.int. Accessed: Aug. 26, 2024. [Online]. Available: https://www.who.int/news-room/fact-sheets/detail/monkeypox

Y.-H. Luo, T. Zhang, J.-L. Cao, W.-S. Hou, A.-Q. Wang, and C.-H. Jin, “Monkeypox: An outbreak of a rare viral disease,” Journal of Microbiology, Immunology and Infection, vol. 57, no. 1, pp. 1–10, Feb. 2024, doi: 10.1016/j.jmii.2023.12.006.

CDC, “Mpox,” cdc.gov. Accessed: Sep. 15, 2024. [Online]. Available: https://www.cdc.gov/mpox/signs-symptoms/?CDC_AAref_Val=https://www.cdc.gov/poxvirus/mpox/symptoms/index.html

M. E. DeWitt et al., “Global monkeypox case hospitalisation rates: A rapid systematic review and meta-analysis,” EClinicalMedicine, vol. 54, p. 101710, Dec. 2022, doi: 10.1016/j.eclinm.2022.101710.

T. Li, Z. Li, Y. Xia, J. Long, and L. Qi, “Mpox reinfection: A rapid systematic review of case reports,” Infectious Medicine, vol. 3, no. 1, p. 100096, Mar. 2024, doi: 10.1016/j.imj.2024.100096.

C. Ding, X. Liu, and S. Yang, “The value of infectious disease modeling and trend assessment: a public health perspective,” Expert Rev Anti Infect Ther, vol. 19, no. 9, pp. 1135–1145, Sep. 2021, doi: 10.1080/14787210.2021.1882850.

O. J. Peter, S. Kumar, N. Kumari, F. A. Oguntolu, K. Oshinubi, and R. Musa, “Transmission dynamics of Monkeypox virus: a mathematical modelling approach,” Model Earth Syst Environ, vol. 8, no. 3, pp. 3423–3434, Sep. 2022, doi: 10.1007/s40808-021-01313-2.

P. Kumar, M. Vellappandi, Z. A. Khan, S. S M, A. Kaziboni, and V. Govindaraj, “A case study of monkeypox disease in the United States using mathematical modeling with real data,” Math Comput Simul, vol. 213, pp. 444–465, Nov. 2023, doi: 10.1016/j.matcom.2023.06.016.

A. Savinkina et al., “Modelling vaccination approaches for mpox containment and mitigation in the Democratic Republic of the Congo,” Lancet Glob Health, vol. 12, no. 12, pp. e1936–e1944, Dec. 2024, doi: 10.1016/S2214-109X(24)00384-X.

M. Ngungu, E. Addai, A. Adeniji, U. M. Adam, and K. Oshinubi, “Mathematical epidemiological modeling and analysis of monkeypox dynamism with non-pharmaceutical intervention using real data from United Kingdom,” Front Public Health, vol. 11, Feb. 2023, doi: 10.3389/fpubh.2023.1101436.

B. Liu, S. Farid, S. Ullah, M. Altanji, R. Nawaz, and S. Wondimagegnhu Teklu, “Mathematical assessment of monkeypox disease with the impact of vaccination using a fractional epidemiological modeling approach,” Sci Rep, vol. 13, no. 1, p. 13550, Aug. 2023, doi: 10.1038/s41598-023-40745-x.

T. Li, Z. Li, Y. Xia, J. Long, and L. Qi, “Mpox reinfection: A rapid systematic review of case reports,” Infectious Medicine, vol. 3, no. 1, p. 100096, Mar. 2024, doi: 10.1016/j.imj.2024.100096.

Y. O. Afolabi and B. A. Wade, “Dynamics of transmission of a Monkeypox epidemic in the presence of an Imperfect Vaccination,” Results in Applied Mathematics, vol. 19, p. 100391, Aug. 2023, doi: 10.1016/j.rinam.2023.100391.

K. T. Kubra, S. Gulshan, and R. Ali, “An Atangana–Baleanu derivative-based fractal-fractional order model for the monkey pox virus: A case study of USA,” Partial Differential Equations in Applied Mathematics, vol. 9, p. 100623, Mar. 2024, doi: 10.1016/j.padiff.2024.100623.

P. L. Delamater, E. J. Street, T. F. Leslie, Y. T. Yang, and K. H. Jacobsen, “Complexity of the Basic Reproduction Number (R 0 ),” Emerg Infect Dis, vol. 25, no. 1, pp. 1–4, Jan. 2019, doi: 10.3201/eid2501.171901.

O. Diekmann, J. A. P. Heesterbeek, and M. G. Roberts, “The construction of next-generation matrices for compartmental epidemic models,” J R Soc Interface, vol. 7, no. 47, pp. 873–885, Jun. 2010, doi: 10.1098/rsif.2009.0386.

F. Brauer and C. Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology, Second., vol. 40. New York, NY: Springer New York, 2012. doi: 10.1007/978-1-4614-1686-9.

DOI: https://doi.org/10.37905/euler.v13i2.32358