ENHANCEMENT AND NUMERICAL ASSESSMENT OF NOVEL SARS-COV-2 VIRUS TRANSMISSION MODEL Anonymous authors Paper under double-blind review

Abstract

Recent pandemic of the coronavirus started in December 2019, which has affected almost all groups of humankind. In this regard, accurate epidemic models are not only crucial for demonstrating the mitigation of the current pandemic but also helpful for forecasting their future dynamics. In this work, we propose a model for SARS-CoV-2 virus transmission to forecast the temporal dynamics of the novel coronavirus disease by considering the characteristics of the disease and the recent literature. Due to the nondeterministic and stochastic nature of the novel-coronavirus disease, we present the model with the aid of stochastic differential equations by considering two infectious phases: pre-symptomatic and symptomatic, because both are significant in the spread of SARS-CoV-2 virus transmission. We ensure that the model is well-posed and identify the necessary conditions for disease eradication by proving the existence, uniqueness, and extinction analysis. The efficacy of the model and the importance of the current study are demonstrated using the actual data. Finally, the model will be simulated using Euler-Maruyama and Milstein's numerical schemes to support the theoretical findings and show the significance of the results obtained.

1. INTRODUCTION

Diseases are mainly categorized into two groups: infectious and non-infectious diseases. Infectious are those caused by viruses, fungi, parasites, and bacteria, and usually transferred in numerous ways while causing fifty thousand deaths approximately every day all over the world. Some infectious diseases can be directly communicated, while many transfer indirectly. Infectious diseases like hepatitis B, seasonal influenza, HIV (human immunodeficiency virus), Middle East Respiratory Syndrome (MERS), and SARS-CoV-2 are major health issues, affecting millions of populations around the globe (Altamimi et al., 2020; Holmdahl & Buckee, 2020; Mann & Roberts, 2011; Reich et al., 2019; Park et al., 2021) . SARS-CoV is a family of viruses that usually cause illnesses such as MERS and severe respiratory syndrome coronavirus (Syed, 2020) . Coronaviruses are zoonotic diseases, and the novel one is a new strain known as the SARS-CoV-2 virus, which broke out in 2019 and spread throughout the world (Rabaan et al., 2020) . Bats are the most plausible ecological reservoirs for SARS-CoV-2, but it's also possible that the virus infected humans via an intermediate animal host. This intermediate animal host could be an unidentified domesticated food animal, a wild animal, or a domesticated wild animal. Millions of people are infected and face consequences due to the novel disease of coronavirus (Shereen et al., 2020) . Novel coronavirus transmits from one person to another by direct contact with an infected individual and indirect with objects used by the infected person (Chan et al., 2020) . A novel coronavirus disease has multiple phases of infections, pre-symptomatic, asymptomatic, environmental, and symptomatic (He et al., 2020) . Especially, the pre-symptomatic and symptomatic phases are very significant because 47% and 38% of cases are reported respectively, by contact with these individuals (Ferretti et al., 2020) . Generally, preasymptomatic individuals have no symptoms while transmitting the disease to others. Therefore, the immigration of pre-symptomatic and symptomatic patients from one place to another place leads to a major source of novel coronavirus transmission. So, most countries around the globe restricted air traffic and announced a lockdown to use the precautionary measure to minimize human lives as much as possible. Also, every country tried to reduce unnecessary traveling, which helped in the reduction of the newly reported cases. Many countries are badly affected by the pandemic of SARS-CoV-2. Moreover, the economy of different countries has been influenced by the novel deadly virus

