Eur. Phys. J. Plus (2023) 138:242 https://doi.org/10.1140/epjp/s13360-023-03865-x Regular Article Mathematical model and analysis of monkeypox with control strategies Olumuyiwa James Peter 1,2,a , Afeez Abidemi 3,b , Mayowa M. Ojo 4,5,c , Tawakalt Abosede Ayoola 6 1 Department of Mathematical and Computer Sciences, University of Medical Sciences, Ondo City, Ondo State, Nigeria 2 Department of Epidemiology and Biostatistics, School of Public Health, University of Medical Sciences, Ondo City, Ondo State, Nigeria 3 Department of Mathematical Sciences, Federal University of Technology, Akure, Ondo State, Nigeria 4 Department of Mathematical Sciences, University of South Africa, Florida, South Africa 5 Thermo Fisher Scientific, Microbiology Division, Lenexa, KS, USA 6 Department of Mathematics, Osun State University Osogbo, Osogbo, Osun State, Nigeria Received: 9 February 2023 / Accepted: 5 March 2023 © The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023 Abstract This paper takes into consideration the development and rigorous analysis of a compartmental mathematical model of monkeypox dynamics in the presence of quarantine and isolation compartments. The newly proposed model is governed by 7-dimensional system of ordinary differential equations which describes the monkeypox transmission and spread between the inter- acting populations of human and rodent. In view of positivity and boundedness of solutions, the model is shown to be mathematically well posed. The control monkeypox reproduction number, R 0 , is obtained using the next generation matrix approach. The threshold quantity is used to investigate the stability analysis of the monkeypox-free equilibrium. Further qualitative analysis suggests that the model undergoes the phenomenon of backward bifurcation in the presence of the fraction of exposed individuals that are quarantined (κ ) whenever R 0 of the model is below unity. By employing center manifold theory, the possibility of ruling out the occurrence of backward bifurcation when κ  0 is shown. The global asymptotic behaviour of the model around the monkeypox-free equilibrium is established using Lyapunov function method. The respective sensitivity index of individual model parameter with respect to R 0 is obtained to gain epidemiological insights into intervention strategies for monkeypox prevention and control. The effects of variation in the effective contact rate of human to human and other key parameters on the disease transmission dynamics under different scenarios are demonstrated quantitatively. The findings of this study show that, we can attain a monkeypox-free state if quarantine and isolation guidelines are carefully followed, as well as preventative measures that minimize the effective contact rates between humans and rodents as well as between rodents and humans during the monkeypox outbreak. 1 Introduction Monkeypox is a viral zoonotic disease that has previously been detected primarily in West and Central Africa, [1], with symptoms similar to those seen in smallpox patients, though clinically less severe. Monkeypox virus that has been identified as the most significant orthopoxvirus infection since the eradication of smallpox. Over 15,000 cases of monkeypox have been confirmed from every continent except Antarctica since May 2022 [2]. In the 1950 s, monkeypox was discovered. Prior to this outbreak, it was endemic in parts of western and central Africa, with cases frequently linked to contact with infected animals. The current outbreak is unusual in its scope, global reach, and person-to-person transmission. Experts are still trying to figure out why this is happening, but possible explanations include viral mutations, decreased use of the smallpox vaccine, and behavioral shifts [3–5]. The monkeypox virus has been circulating for decades in areas where it has been historically endemic, but research on the disease has been ignored in the past and underfunded. The World Health Organization declared monkeypox a moderate public health concern on June 23, 2022, after more than 3000 monkeypox virus infections were detected in more than 50 nations and five regions since early May 2022 [6–11]. There isn’t a specific medication for the monkeypox virus infection right now. However, a number of antiviral drugs, including tecovirimat or ST-246 (TPOXX), brincidofovir (Tembexa), and cidofovir, are used to treat smallpox (Vistide). Due to the genetic similarity between the monkeypox and smallpox viruses, antiviral medications and vaccinations created to guard against smallpox may be used to prevent and cure infections with the monkeypox virus. A smallpox vaccine offers defense against monkeypox, but because smallpox has been eradicated worldwide, its usage is currently restricted to clinical trials. Efforts to limit person to person transmission and reduce human contact with infected animals are essential to prevention [12]. Many researchers a e-mail: peterjames4real@gmail.com (corresponding author) b e-mail: aabidemi@futa.edu.ng c e-mail: mmojomth@gmail.com 0123456789().: V,-vol 123