Dynamic analysis and optimal control of SEITR mpox model with three transmission routes

Understanding the hidden transmission mechanism of monkeypox epidemics is essential to avoid the local or global prevalence via the sexual transmission route, the direct contact transmission route and the aerosol transmission route. First of all, we establish modified model with three transmission routes to characterize the transmission dynamics of monkeypox epidemics, of which the basic reproduction number of modified model is derived via the next-generation matrix method, the local and global stabilities of equilibrium points are explored by the Routh Hurwitz criterion and LaSalle's invariant principle, and the existence and the expressions of the optimal controls are derived by the Pontryagin's maximum principle. Then, the numerical analysis are performed with respect to the optimal fittings, the estimation of the basic reproduction number, the global sensitivity analysis and the cost-effectiveness analysis. More precisely, the weekly surveillance data of the Democratic Republic of the Congo from 2022 to 2025 are carried out for the optimal fittings of modified model. The basic reproduction number of 2022-2025 monkeypox outbreak is estimated from 1.67 to 4.60. The sensitive parameters of modified model are chosen by using of Partial Rank Correlation Coefficients to estimate the cumulative infection scales. The cost-effectiveness analysis point out that the combined strategy yields the smallest infection scale, and that the treatment strategy is the most cost-effectiveness strategy. It is recommended to strengthen sexual health awareness for high-risk groups, to optimize ventilation and air purification in high-risk environments, and to ensure comprehensive and timely treatment for infected individuals, against the increase of cumulative infection scale of monkeypox epidemics.