WITH CROSS INFECTION HYPOTH-ESIS VIA EPIDEMIOLOGICAL MODEL

Abstract

A new re-emerging infectious disease of monkeypox 2022 is structurally related to smallpox that is induced by the monkeypox viruses and has caused 59,606 active cases with 18 deaths up to September 15, 2022. To end this ongoing epidemic, there is a need for population-wide control policies like reducing social interaction by keeping social distance, treatment of infected individuals, and restriction on animals, etc. We forecast the progression of the epidemic and come up with an efficient control mechanism by formulating a mathematical model. The biological feasibility and dynamical behavior of the proposed model are then investigated together with sensitivity analysis to obtain the effect of various epidemic parameters mitigating the spread of the disease. Subsequently, by taking non-pharmaceutical and pharmaceutical intervention strategies as control measures, an optimal control theory is applied to mitigate the fatality of the disease to minimize the infectious population and reduce the cost of controls, we construct an objective functional and solve it by using Pontryagin's maximum principle. Finally, extensive numerical simulations are performed to show the impact of the application of intervention mechanisms in controlling the transmission of the monkeypox epidemic.

1. INTRODUCTION

The infection of monkeypox is a contagious disease resulting from the orthopoxvirus. This infection is zoonotic and was initially transported to humans by wild rodents in central and western Africa. But human-to-human spread (horizontal transmission) is also possible, particularly within the family home or in the context of care (Farahat et al., 2022) . The monkeypox viruses can be diffused by immediate contact with lesions on the skin or mucous membranes of a sick person, as well as by droplets (sneezing, saliva, sputters, etc.) (Singh et al., 2021) . Generally, an individual can become infected through contact with patient's environment. It is, therefore, important that patients respect isolation measures throughout the illness. Humans can also become infected through active contact with animals (rodents and monkeys) (Oladoye, 2021). Usually, the monkeypox infection starts from fever, headaches, body aches, weakness, etc. (Deresinski, 2022) . The symptoms may lead to the appearance of a blistering rash consisting of fluid-filled blisters that progress to dryness and crusting, then scarring and itching after two days. The bubbles are most concentrated on the face, the forehands, and the feet soles. The disease is more severe in children as well as those who have weak immune systems. Historically, monkeypox was identified first in the 1970s, but recently the reemerging of the disease, cases are reported in various countries around the globe (ASSESSMENT, 2022). Usually monkeypox virus transmits from human interaction, but there is a significant risk of cross-infection (animal-to-human) spread (Petersen et al., 2019) . Therefore, the hypothesis of cross-infection between human and animals play a significant role and can not be neglected. Modeling and forecasting with the aid of dynamical system is a challenging domain in various discipline, e.g., infectious disease epidemiology (Brauer, 2017; Saravanakumar et al., 2020; Guo et al., 2020) , health sciences (Choi et al., 2016) , and various other fields of applied science and technology (Rolnick et al., 2022) , and therefore attracted the considerable attention of researchers, see for instance, (Das et al., 2020b; Yin et al., 2021; Saha et al., 2021) . Similarly, various models demonstrate different outlooks regarding the dynamical behavior of an epidemic (Busenberg & Cooke, 2012; Khajanchi et al., 2018; Das et al., 2020a) . With the aim of these mathematical models, researchers want to understand the dynamics of a disease and then suggest control strategies to control or completely eradicate the infection (Chen & Guo, 2016; Kumar et al., 2019) . Besides the rich literature on

