Model Development and Prediction of Covid-19 Pandemic in Bangladesh with Nonlinear Incident

Iran J Sci Technol Trans Sci https://doi.org/10.1007/s40995-022-01410-6 (0123456789().,-volV)(0123456789(). ,- volV) RESEARCH PAPER Model Development and Prediction of Covid-19 Pandemic in Bangladesh with Nonlinear Incident Abdul Malek1 • Ashabul Hoque1 Received: 28 May 2022 / Accepted: 23 December 2022 Ó The Author(s), under exclusive licence to Shiraz University 2023 Abstract We introduce a SEIRD compartmental model to analyze the dynamics of the pandemic in Bangladesh. The multi-wave patterns of the new infective in Bangladesh from the day of the official confirmation to August 15, 2021, are simulated in the proposed SEIRD model. To solve the model equations numerically, we use the RK-45 method. Primarily, we establish some theorems including local and global stability for the proposed model. The analysis shows that the death curve simulated by the model provides a very good agreement with the officially confirmed death data for the Covid-19 pandemic in Bangladesh. Furthermore, the proposed model estimates the duration and peaks of Covid-19 in Bangladesh which are compared with the real data. Keywords SEIRD model  Multi-wave  Covid-19  Pendamic  Stability analysis  Bifurcation analysis  Nonlinear incident 1 Introduction The Chinese authorities notified a new virus (novel coronavirus called Covid-19) outbreak in Wuhan City, Hubei Province, China, at the end of December 2019. World Health Organization (WHO) recognized it as a pandemic on March 11, 2020 (López et al. 2021). In Bangladesh, three Covid-19 confirmed cases were identified on March 8, 2020 (Worldometer), and the government declared a ‘‘lockdown’’ throughout the nation from March 23, 2020, to May 30, 2020, to control the disease’s speed. Then lockdown was relaxed for the sake of the lives and livelihoods of people because long-term lockdown affects economic and social activities, and it is not possible to restrict people’s activities for a long time. However, Bangladesh is a highly densely populated and developing country, so a hard lockdown is not possible to apply to the people. In Bangladesh, there was the lowest infection rate from December 2020 to the end of February 2021 since the outbreak of the pandemic. Due to the low infection rate from January 2021 to February 2021, people relax their & Abdul Malek 1 Department of Mathematics, University of Rajshahi, Rajshahi, Bangladesh hygiene and social activities. As a result, in March 2021, a rapid increase in infections with positivity rates increasing to over 23 percent in early April was shown. The Government announced 7 days lockdown all over the country, and the infection rate saw decreasing day by day. From May 2021 to August 2021, Bangladesh observes another wave of Covid-19. The mathematical model is an important tool to understand the dynamics of the infectious disease, which helps to take public policies due to control the disease, and causal models can be used for epidemic forecasting (Adiga et al. 2020). Some compartmental models SIR, SEIR, and SUQC are the easy and simplest way to explain the epidemiological nature (Abou-Ismai, 2020). López et al. (2021) presented a two-step phenomenological epidemic to characterize of first two waves and showed that it is possible to characterize the curves of case incidence and construct a short-term forecast of 60 days even in the absence of accurate data series. Vasconceloset al. (2021) introduced a generalized logistic model with time-dependent parameters to analyze the dynamics of second and third waves of the Covid-19 and showed that the subsequent waves can be generically classified into two main types, namely standard and anomalous waves, according to whether a given wave starts well after or well before the preceding one has subsided, respectively. The rate of spreading of the disease can 123 Iran J Sci Technol Trans Sci be interpreted as a time-dilation symmetry; the endemic period between two waves is a sign of instability in the system (Cacciapaglia et al. 2021). SIR is the first and most easy compartmental model to discuss the dynamics of transmitted disease; Alqahtani (2021) analyzed the dynamics of the SIR model with fractional derivatives and showed that the free steady state is locally stable when the reproductive number is less than unity and unstable otherwise. Mahikul et al. (2021) implemented SEIR compartmental model using the Bayesian approach to evaluate the impact of intervention strategies on the first wave and predicted the second wave of Covid-19 in Thailand. Peter et al. (2021) considered a new mathematical SEIQR model to analyze the dynamics of the first wave of Covid-19 in Pakistan including the data from July 01, 2020, to August 14, 2020, and discussed its stability and sensitivity of the parameters of the proposed model. In addition, several mathematical models performed on Covid-19 (Malek and Hoque (2021); Pandey et al. (2021); Javeed et al. (2021); Hong et al. (2020); Hisaka et al. (2020) to discuss the transmission dynamics of the diseases in a single wave. Malek and Hoque (2021) estimated the peak time and size of the first wave of Covid19 in the south Asian countries using the SEITR compartmental model. Pandey et al. (2021) investigated the frictional epidemic model and dynamic of the first wave of Covid-19 and used the Laguerre collocation technique to solve the model numerically and compared the experimental data from April 15 to 21, 2020, in Maharashtra state, India. Javeed et al. (2021) proposed SEIQRG compartmental model and used the RK-4 model to solve it numerically. In the paper, they investigated the stability analysis of covid pandemic in Pakistan, Italy, Japan, and Spain. Hong and Li (2020) proposed a Poisson model with a time-dependent transmission rate and investigated the dynamical analysis Driessche and Watmough (2020) of Covid-19 in the USA and China. Overall, Chadha et al. (2015) focused that the transmission rate of respiratory infection depends on several factors, such as population, climate, socioeconomic conditions, immunization situation, and vaccination coverage. Mathematical models were developed by several researchers (Gao et al. 2022, Srinivasa et al. 2021, Javeed et al. 2021, etc.) and analyzed the nature of Covid-19, and these models used a single pattern of disease transmission. Kumar et al. (2022) provided the dynamical behavior of the Covid-19 model using a powerful fractional homotopy perturbation transform method with Caputo–Fabrizio fractional derivative and investigated a few numerical approximations to explain the efficiency of the proposed method for various values of fractional order. Gao et al. (2020) investigated and simulated the dynamical behavior of Covid-19 using the mathematical model from the 123 reservoir to people using variational iteration method. Gao et al. (2022) analyzed a fractional order model of Covid-19 and showed that the projected solution technique was highly efficient in solving a nonlinear (...truncated)