Data analysis and prediction of the COVID-19 outbreak in the first and second waves for top 5 affected countries in the world

Nonlinear Dyn https://doi.org/10.1007/s11071-022-07473-9 (0123456789().,-volV) ( 01234567 89().,-volV) ORIGINAL PAPER Data analysis and prediction of the COVID-19 outbreak in the first and second waves for top 5 affected countries in the world Ashabul Hoque . Abdul Malek . K. M. Rukhsad Asif Zaman Received: 6 November 2021 / Accepted: 20 April 2022 Ó The Author(s), under exclusive licence to Springer Nature B.V. 2022 Abstract In this paper, we introduce a SEIATR compartmental model to analyze and predict the COVID-19 outbreak in the Top 5 affected countries in the world, namely the USA, India, Brazil, France, and Russia. The officially confirmed cases and death due to COVID-19 from the day of the official confirmation to June 30, 2021 are considered for each country. Primarily, we use the data to make a comparison between the cumulative cases and deaths due to COVID-19 among these five different countries. This analysis allows us to infer the key parameters associated with the dynamics of the disease for these five different countries. For example, the analysis reveals that the infection rate is much higher in the USA, Brazil, and France compared to that of India and Russia, while the recovery rate is found almost the same for these countries. Further, the death rate is measured higher in Brazil as opposed to India, where it is found much lower among the remaining countries. We then use the SEIART compartmental model to characterize the first and second waves of these countries, as well as to investigate and identify the influential model parameters and nature of the virus transmissibility in respective countries. Besides estimating the time-dependent reproduction number (Rt) for these countries, we also use the model to predict the peak size and the time occurring peak in respective countries. The analysis demonstrates that COVID-19 was observed to be much more infectious in the second wave than the first wave in all countries except France. The results also demonstrate that the epidemic took off very quickly in the USA, India, and Brazil compared to two other countries considered in this study. Furthermore, the prediction of the epidemic peak size and time produced by our model provides a very good agreement with the officially confirmed cases data for all countries expect Brazil. Keywords COVID-19  SEIATR model  Reproduction number  Second wave  Peak period  Epidemic evolution A. Hoque (&)  A. Malek Department of Mathematics, University of Rajshahi, Rajshahi 6205, Bangladesh e-mail: 1 Introduction A. Malek e-mail: 1.1 COVID-19 and its characteristics K. M. R. A. Zaman Department of Public Health, North South University, Dhaka, Bangladesh e-mail: The coronavirus disease (COVID-19) from China has spread globally since January 2020 and has become a pandemic. Currently, there are around 222 countries 123 A. Hoque et al. that report laboratory-confirmed cases across the World (WHO). Cumulative data of confirmed cases (182,688,695), recovered (167,288,083), and deaths (3,956,008) are taken from the beginning to June 30, 2021 (Johns Hopkins University). An infectious disease is the episode of an illness that is not generally expected in a particular group of people, geographical region, or time. Due to the relatively new nature of this disease, proper control measures and therapeutic interventions are still under development, which in turn is creating tremendous tension and panic around the World. Not only is the COVID-19 pandemic threatening our social and personal life and the broader aspects, such as our economy, health, and development in both the national and global sense. Due to uncertainties of the disease, investigators have used several models to forecast the characteristics of transmission parameters, primary reproduction number (R0), time-depended reproduction number (Rt), the time of peak (tp), etc. 1.2 Related works The researches on mathematical modeling are playing a key role in understanding the epidemics, and it may help to predict the intensity of pandemics in the early stages. This also demonstrates a significant role in making the right decision during outbreak control [1]. In this regard, several researchers have developed mathematical models for the COVID-19 epidemic [2–13]. Very recently, Kuddus and Rahman [2] have used the improved SLIR model with nonlinear incidence, and they have observed that the transmission rate of each parameter had a significant impact on COVID-19. Lobato et al. [3] proposed a dynamic data segmentation approach to provide reasonable estimates for all parameters. A three-party differential game model including epidemic prevention and risk coefficient was proposed by [14], and results were presented based on theoretical and numerical analysis. Toda [4] estimated the COVID-19 transmission rates for several countries based on the SIR model for regular data of confirmed cases. Tang et al. [15] proposed a compartmental model with a clinical progress compartment and epidemiological compartment, and they showed that the isolation compartment could successfully reduce the transmission hazard. Biswas et al. [16] formulated a deterministic compartmental model to estimate the model parameters 123 and compared these against the reported data. Wu et al. [5] used a four-compartment (SEIR) model to explain the transmission rates and forecast the countrywide and worldwide feast of the COVID-19 epidemic based on published data from December 31, 2019, to January 28, 2020. They also determined the basic reproduction number for COVID-19, and it was nearly 2.68 for China. COVID-19 outbreaks on human-to-human transmission based on the computational modeling of probable epidemic trajectories were estimated by Imai et al. [17]. They focused that the control actions needed to block over 60% of transmission to control the outbreak effectively. Ahmed et al. [18] developed a SEIR time-fractional model to investigate the nature of coronavirus in Pakistan and discussed the stability analysis. Pedersen et al. [19] proposed the SIQR model to discuss the dynamics of COVID-19 in Italy. Hoertel et al. [20] represented a stochastic agent-based microsimulation model of COVID-19 to examine the impact of maskwearing, physical distancing, and shielding individuals and showed that those were slowing the spread of the epidemic and reducing the mortality rate. In epidemiology, the average basic reproduction number (R0) is defined as the average number of secondary cases that would be generated by a primary infectious disease in a susceptible population [21]. Determining R0 is often stimulating for the involvement of numerous factors and a deficiency of unbiased data. In most cases, secondary infections cannot be estimated precisely, particularly for COVID-19, where asymptomatic patients are barely recognized. There are many techniques to calculate R0 [22], some of them agree with each other, and some are developed based on the secondary infe (...truncated)