In December 2019, the novel coronavirus (SARS-CoV-2) was discovered for the first time in Wuhan, China. On March 11, 2020, the World Health Organization (WHO) proclaimed a novel coronavirus outbreak as a global pandemic (Cooper et al., 2020). For countries all over the globe, to manage the epidemic, WHO issued some early public health care guidelines. Coronavirus disease 2019 (COVID-19) is a contagious disease caused by a virus, the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). SARS-CoV-2 is part of a family of viruses called Coronaviridae and can infect humans and other animals. In COVID-19, CO stands for Corona, VI for Virus, D for Disease, and 19 for 2019, the year when the outbreak was first discovered (WHO, 2019).

Fever, cough, headache, tiredness, breathing problems, loss of smell, muscle soreness, sore throat, diarrhoea, toes swelling or turning purple, and loss of taste are some of the symptoms of COVID-19. The symptoms may occur one to fourteen days after being exposed to the virus. COVID-19 is largely spread by inhaling virus-containing droplets/aerosols and small airborne particles contaminated with the virus. These particles are expelled by infected people as they breathe, talk, cough, sneeze, or sing. When people are nearby, transmission is more likely to occur (CDC, 2022). Infectious disease modelling has been employed as a method to analyze the behaviour of disease transmission, forecast the trajectory of an outbreak, and assess epidemic control measures (Seventer and Hochberg, 2017). There are some crucial measures of infectious disease models such as the Basic Reproduction Number (R0) and the Effective Reproduction Number (Re). The Basic Reproduction Number (R0) of an illness represents the predicted number of cases generated directly by one case in a susceptible population. The role of the Effective Reproduction Number (Re) is significant in determining the rate of transmission of infectious disease, as it represents the average number of secondary cases that can be caused by an infected individual in a population of susceptible individuals (Fig. 1). Often, a contagious illness will propagate among a group of individuals who are susceptible to it. Whenever R0is more than one i.e. R0>1, implies that infection will become more prevalent. On the other hand, the disease will never spread when R0<1, (Yadav and Akhter, 2022a; Yadav et al., 2022b). R0 depends on the host population and the disease which varies depending on the disease, for example, R0= for influenza in humans, R0= for smallpox in humans, R0= for measles in humans and R0= for TB in cattle (Yadav and Akhter, 2021).

In a population of susceptible and non-susceptible hosts, the Effective Reproduction Number Re is the average number of secondary infections per infectious case (Yadav and Akhter, 2022b). The number of infections increases withRe>1, such as, at the beginning of the epidemic, for Re=1, the disease will be endemic, and if Re<1, indicates that infections will decrease. The effective reproductive number can be calculated by multiplying the basic reproductive number (R0) and the proportion of the host population that is susceptible (X). Thus, Re=R0*X, for instance, in a population with R0=12 for people infected with influenza and half (50%) of the people are immune to the virus, thus the effective number for influenza is 12*0.5=6. In such circumstances, a single case of influenza would result in an average of six additional secondary cases. Thus, to eradicate a disease from a population successfully, the Effective Reproductive number (Re) must be less than 1 i.e. Re<1 (Yadav and Akhter, 2022b).

India reported its first case of COVID-19 on January 27, 2020, in Thrissur, Kerala, of a 20-year-old female who had returned to Kerala on January 23, 2020, from Wuhan City, China after the COVID-outbreak situation there. Omicron is the most disseminated variant of the Coronavirus. The Omicron variety (B.1.1.529) is a variant of concern, according to the World Health Organization (WHO), since it mutates rapidly, and every mutation produces a new variety. The WHO divided these variations into two groups, VOC (a variant of concern), which includes the coronavirus variants Alpha, Beta, Gamma, and Delta. The Eta, Iota, Kappa, and Lambda coronavirus variants are classified as a variation of interest (VOI) by the World Health Organization. Variants categorized as a variant of concern are easily transmissible from one person to another, have a higher fatality rate, and have a worse overall therapeutic effectiveness. Omicron has become the fifth variant of concern due to its high rate of mutation, with over 30 mutations identified thus far. The initial case of Omicron was identified in South Africa (WHO, 2021). In India, the first case of the Omicron variant was reported in Karnataka. In India, the disease is spreading quickly. The most popular strategies for the mitigation and control of the pandemic at this time include wearing a facemask, social isolation, and self-quarantine in the absence of an effective medication or vaccine (BBC, 2021). In such situations, the mathematical models are very useful and necessary to estimate disease transmission, recovery, fatalities, and other critical factors separately for several states. It is challenging to treat such a highly contagious and lethal disease, especially in a high population-density nation like India. Due to significant aspects like population density, a lack of relevant data regarding various symptoms, the mode of transmission, and the lack of a suitable vaccine. Mathematical models must be created to provide information and make close predictions regarding the disease, as well as to design efficient control measures and policies (Chin azzi et al., 2020; Rüdiger et al., 2020). Recently, many works have been published, where the modelling approach was adopted, utilizing genuine incidence records from the affected nations. Researchers have looked at numerous characteristics as a function of the outbreak, many other aspects, and the results of intervention efforts in various countries according to their current circumstances (Abolmaali and Shirzaei, 2021; Alanaziet al., 2020; Moein et al., 2021; AlQadi and Bani-Yaghoub, 2020; Din and Algehyne, 2021; Kröger and Schlickeiser; 2021; Wang et al., 2022). In the current study, we have used the SIR model because the SIR model is the simplest among all compartmental models, which enables modellers to roughly predict disease behaviour by predicting two parameters only. The SIR model simplifies things by assuming that newly infected people are immediately contagious and not taking into account the latent period after exposure (Taylor and Carr, 2009; McCluskey, C.C., 2010; Augeraud-Véron and Sari, 2014; Schlickeiser and Kroger, 2021; Ucar and Celik, 2021).

Sefik et al. (2022) developed a humanized mouse model of chronic COVID-19. Sun et al. (2022) investigated the role of aerosol transmission in SARS-CoV-2 Omicron dissemination in Shanghai. Talmor-Barkan et al. (2022) demonstrated that metabolomic and microbiome profiling can identify personalized risk factors for coronary artery disease. Ma et al. (2022) analyzed the transmission dynamics of brucellosis in the Jilin province of China and assessed the effectiveness of different control measures. Tran et al. (2022) documented the course of post-COVID-19 disease symptoms over time in the ComPaRe long COVID prospective e-cohort. Chang et al. (2022) proposed a sparse optimal control strategy for pattern formations in an SIR reaction-diffusion epidemic model. Sun et al. (2022) formulated a diffusive foot-and-mouth disease model with nonlocal infections. Sasanami et al. (2023) developed projections of the COVID-19 immune landscape in Japan, considering waning immunity and the impact of booster vaccination.

In this study, the SIR model is used to study and forecast the dissemination of infectious disease COVID-19 after the emergence of the Omicron variant of SARS-CoV-2 for the top 10 provinces of India by infection incidence. In addition to the SIR model, a time series model (ARIMA) and a machine learning model (Random Forest) have been used to forecast the infected cases and compared through RMSE scores, which model is best in forecasting the disease. Parametric probability distribution models are also fitted to the Omicron dissemination data to see the best-fitted probability distribution.

Evaluate the relative performance of different models in predicting COVID-19 spread in Indian provinces to determine the most effective model for forecasting future trends and informing policy decisions.

Assess the statistical efficiency of different models in estimating model parameters and generating predictions close to real parameter values to ensure the validity and reliability of the models' predictions.

Identify any models that exhibit superior performance in terms of prediction accuracy compared to other models, allowing for the selection of the most effective model for forecasting and policy guidance.