Eur. Phys. J. Plus (2025) 140: 1009
https://doi.org/10.1140/epjp/s13360-025-06938-1

Regular Article

Modeling and economic evaluation of monkeypox transmission with nonlinear incidence rates using an optimal control

Department of Mathematics, National Institute of Technology Raipur, Raipur, India

^a aksinha.maths@nitrr.ac.in

Received: 30 July 2025
Accepted: 5 October 2025
Published online: 21 October 2025

Abstract

The recent monkeypox outbreaks highlight the urgent need for substantial access to surveillance, preparedness, and rapid response strategies. Therefore, evaluating the efficiency and economics of monkeypox transmission is essential to control the outbreak effectively. We present a mathematical model of the monkeypox virus that integrates previously untouched aspects, such as awareness, vaccination, self-care, hospitalization, and nonlinear incidence rates with efficiency and economic evaluation to reduce the monkeypox virus infection. We affirm the proposed model’s positivity, boundedness, existence, and uniqueness. We calculate the reproduction numbers for humans (${\mathcal{R}}_0^h$) and rodents (${\mathcal{R}}_0^r$) to assess the stability of each equilibrium. We obtain transcritical bifurcation for any value of ${\mathcal{R}}_0^h$ when ${\mathcal{R}}_0^r=1$ and ${\mathcal{R}}_0^h=1$ for ${\mathcal{R}}_0^r<1$. We validate and estimate model parameters using data from the USA outbreak. Local and global sensitivity analyses are performed to identify key parameters influencing ${\mathcal{R}}_0$. We introduce the optimal control model with awareness programs, vaccination, and the efficacy of hospitalization. We propose four strategies namely: strategy I-awareness and vaccination; strategy II-awareness and hospitalization efficacy; strategy III-vaccination and hospitalization efficacy; and strategy IV-all three controls for efficiency and cost-effective analysis. Strategy IV has the highest efficiency index of $62.23\%$, indicating that strategy IV is the most effective in reducing monkeypox infections. Further, we explore the most cost-effective strategy by average (ACER) and incremental (ICER) cost-effectiveness ratio approaches. We obtain that strategy II, the lowest ACER value of 0.06521, is the most cost-effective strategy among all the strategies that align with the ICER approach. Our findings indicate that strategy IV, all three controls, is the most effective in reducing monkeypox virus infections; however, strategy II, which combines awareness and hospitalization efficacy, is the most cost-effective approach for controlling monkeypox virus infections. One-way sensitivity analysis of ICER with respect to cost weights further supports these findings. This research will aid in formulating policies for countries globally based on their financial status to manage monkeypox virus infections.