Dynamic modeling and optimal control of Mpox among MSM in a central Chinese city
4 affiliations
- 1Hunan Key Laboratory of Molecular Epidemiology, Hunan Normal University Health Science Center, Changsha, Hunan Province 410013 China
- 2Infectious Disease Early Warning and Decision Center, Hunan Normal University Health Science Center, Changsha, Hunan Province China
- 3Hunan Provincial Center for Disease Control and Prevention, Changsha, Hunan Province China
- 4Changsha Center for Disease Control and Prevention, Changsha, Hunan Province China
Abstract
Background: Since 2022, the mpox outbreak has become a global public health threat, with transmission mainly among men who have sex with men (MSM). Mpox is the only infectious disease other than Ebola to have been declared a PHEIC twice. Following its importation and local spread in China, developing prevention strategies is essential. This study aims to formulate the optimal control strategy for mpox within MSM population in urban China.
Methods: We developed a compartmental transmission dynamics model for mpox among MSM in a Chinese city. The framework extends SEIR by including asymptomatic infections (A) and symptomatic but undiagnosed infections (B) alongside S, E, I, R, with transmission arising from A, I, B. We then formulated an optimal control problem with 4 interventions: MSM community based prevention and control (u1), Early detection/Early treatment/Isolation (u2), Increasing medical consultation rate (u3), and Vaccination (u4), and evaluated 15 schemes over 100 days. In addition, we set several constant control combinations and compared their costs and effects with optimal control.
Results: In the no-control scenario simulation, cumulative infections reached 6331 by day 100. Across 15 optimal control schemes ranging from single to quadruple controls, implementing any scheme reduced total infections effectively. With a single control measure, u1 achieved the best performance and averted 6238 infections. For dual control measures, u1 + u4 showed the strongest effect and averted 6250 infections. For triple control measures, u1 + u3 + u4 averted 6256 infections. Quadruple control measures provided the most effective overall strategy and averted 6258 infections. The quadruple constant control settings C1–C5 averted 5980, 6202, 6154, 6165 and 6181 infections, respectively. Under quadruple controls, the accumulated control-only cost was 1209.57 for optimal control. The costs of constant control settings C1–C5 were 1260.00, 2845.00, 3600.00, 3015.00, and 4575.00, respectively.
Conclusions: The no-control simulation suggests that mpox transmission among MSM can produce a large number of infections. The optimal control measures can effectively control the epidemic. MSM community based prevention and control (u1) is the best single control measure. Quadruple control measures avert the largest number of infections overall. Compared with constant control measures, optimal control achieves higher effectiveness at comparable cost.
Trial registration: Clinical trial number: not applicable.
Supplementary Information: The online version contains supplementary material available at https://doi.org/10.1186/s12889-026-28925-6.
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BibTeX
@article{wang2026dynamic,
title = {{Dynamic modeling and optimal control of Mpox among MSM in a central Chinese city}},
author = {Dan Wang and Si Wu and Siyu Zhang and Han Ni and Yuxi He and Liuyi Fu and Jin Zhao and Yuan Lv and Wenting Zha},
journal = {BMC Public Health},
year = {2026},
month = aug,
doi = {10.1186/s12889-026-28925-6},
url = {https://doi.org/10.1186/s12889-026-28925-6},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Dynamic modeling and optimal control of Mpox among MSM in a central Chinese city
AU - Dan Wang
AU - Si Wu
AU - Siyu Zhang
AU - Han Ni
AU - Yuxi He
AU - Liuyi Fu
AU - Jin Zhao
AU - Yuan Lv
AU - Wenting Zha
PY - 2026
DA - 2026/08/15
JO - BMC Public Health
DO - 10.1186/s12889-026-28925-6
UR - https://doi.org/10.1186/s12889-026-28925-6
AB - Background: Since 2022, the mpox outbreak has become a global public health threat, with transmission mainly among men who have sex with men (MSM). Mpox is the only infectious disease other than Ebola to have been declared a PHEIC twice. Following its importation and local spread in China, developing prevention strategies is essential. This study aims to formulate the optimal control strategy for mpox within MSM population in urban China. Methods: We developed a compartmental transmission dynamics model for mpox among MSM in a Chinese city. The framework extends SEIR by including asymptomatic infections (A) and symptomatic but undiagnosed infections (B) alongside S, E, I, R, with transmission arising from A, I, B. We then formulated an optimal control problem with 4 interventions: MSM community based prevention and control (u1), Early detection/Early treatment/Isolation (u2), Increasing medical consultation rate (u3), and Vaccination (u4), and evaluated 15 schemes over 100 days. In addition, we set several constant control combinations and compared their costs and effects with optimal control. Results: In the no-control scenario simulation, cumulative infections reached 6331 by day 100. Across 15 optimal control schemes ranging from single to quadruple controls, implementing any scheme reduced total infections effectively. With a single control measure, u1 achieved the best performance and averted 6238 infections. For dual control measures, u1 + u4 showed the strongest effect and averted 6250 infections. For triple control measures, u1 + u3 + u4 averted 6256 infections. Quadruple control measures provided the most effective overall strategy and averted 6258 infections. The quadruple constant control settings C1–C5 averted 5980, 6202, 6154, 6165 and 6181 infections, respectively. Under quadruple controls, the accumulated control-only cost was 1209.57 for optimal control. The costs of constant control settings C1–C5 were 1260.00, 2845.00, 3600.00, 3015.00, and 4575.00, respectively. Conclusions: The no-control simulation suggests that mpox transmission among MSM can produce a large number of infections. The optimal control measures can effectively control the epidemic. MSM community based prevention and control (u1) is the best single control measure. Quadruple control measures avert the largest number of infections overall. Compared with constant control measures, optimal control achieves higher effectiveness at comparable cost. Trial registration: Clinical trial number: not applicable. Supplementary Information: The online version contains supplementary material available at https://doi.org/10.1186/s12889-026-28925-6.
SN - 1471-2458
ER -