Dynamic modeling and optimal control of Mpox among MSM in a central Chinese city

Abstract

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 ( u 1 ), Early detection/Early treatment/Isolation ( u 2 ), Increasing medical consultation rate ( u 3 ), and Vaccination ( u 4 ), 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, u 1 achieved the best performance and averted 6238 infections. For dual control measures, u 1 + u 4 showed the strongest effect and averted 6250 infections. For triple control measures, u 1 + u 3 + u 4 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 ( u 1 ) 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.