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Prediction of Second Wave of COVID-19 in India Using the Modifed SEIR Model

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Prediction of Second Wave of COVID-19 in India Using the Modifed SEIR Model Prediction of Second Wave of COVID-19 in India using the Modied SEIR Model Changqing Sun Zhengzhou University Mingyang Zhao Zhengzhou University Zhuoyang Tian Zhengzhou University Wensen Zhang Zhengzhou University Hengzhen Zhang Zhengzhou University Wenqian He Zhengzhou University Rongrong Wang Zhengzhou University Ke Wu Zhengzhou University Biyao Wang Zhengzhou University Nan Sun University of Georgia Weihong Zhang Zhengzhou University Qiang Zhang ( [email protected] ) Zhengzhou University https://orcid.org/0000-0003-1566-1955 Research Article Keywords: COVID-19, pandemic, SEIR model, the second wave, the Delta variant Posted Date: August 23rd, 2021 DOI: https://doi.org/10.21203/rs.3.rs-800978/v1 Page 1/17 License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License Page 2/17 Abstract Background: The second wave of the coronavirus disease 2019 (COVID-19) epidemic in India was caused by the COVID-19 Delta variant. However, the epidemiological characteristics and transmission mechanism of the Delta variant remain unclear. To explore whether the epidemic trend will change after effective isolation measures were taken and what is the minimum number of individuals who need to be vaccinated to end the epidemic. Methods: We used actual data from March 5 to April 15, 2021, of daily updates conrmed cases and deaths, to estimate the parameters of the model and predict the severity of possible infection in the coming months. The classical Susceptible-Exposed-Infected-Removed (SEIR) model and extended models [Susceptible-Exposed-Infected-Removed-Quarantine (SERIQ) model and Susceptible-Exposed- Infected-Removed- medicine (SERIM) model] were developed to simulate the development of epidemic under the circumstances of without any measures, after effective isolation measures were taken and after being fully vaccinated. Results: The result demonstrated good accuracy of the classic model. The SEIRQ model showed that after isolation measures were taken, the infections will decrease by 99.61% compared to the actual number of infections by April 15. And the SEIRQ model demonstrated that if the vaccine ecative rate was 90%, when the vaccination rate was 100%, the number of existing cases would reach a peak of 529,723 cases on the 52nd day. Conclusion: Effective quarantine measures and COVID-19 vaccination from ocial are critical prevention measures to help end the COVID-19 pandemic. Introduction The Coronavirus disease 2019 (COVID-19) is a new respiratory infectious disease caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Since early December 2019, COVID-19 infections have occurred in many countries, and the number of COVID-19 cases has increased dramatically. On March 22, 2020, the World Health Organization declared a world pandemic [1]. Due to the lack of effective vaccines and therapeutic drug, governments have taken a series of measures to delay the transmission of COVID- 19, including case isolation and travel restrictions. These measures have helped several Asian countries represented by China achieve signicant progress in the early stages of the epidemic [2]. As a vast and densely populated country, India is facing greater challenges in coping with the COVID-19 due to the inadequate and inconsistent federal public health infrastructure. In response to the COVID-19 pandemic, the Indian government implemented a nationwide quarantine measure. Due to the timely strictly implementation of quarantine measures by the government, the total number of early infections in India was lower than that in other countries [3]. However, there were still many problems in the isolation measure. For example, people's awareness of the seriousness of the disease was insucient and the Page 3/17 government supervision was not strict. Therefore, the situation in India further deteriorated after the lifting of the quarantine measures on May 3, 2020. In early March 2021, India broke out the second COVID-19 epidemic, which was caused by the Delta variant of COVID-19 [4]. The infectivity and mortality of the Delta variant are higher than that of the common COVID-19 virus, and the transmission speed is faster at higher temperature [5]. Within two months, the continuous COVID-19 epidemic resulted in more than 60,000 deaths in India, and has plunged the society into chaos and panic. Currently, the epidemic characteristics and transmission mechanism of the mutant virus remained poorly understood, and how to deal with mutant virus is still an urgent problem to be solved. The Susceptible-Infected-Removed (SIR) model is a classic mathematical modeling which was frequently used to simulate the dynamic mechanism of infectious diseases [7]. However, the classic SIR model only takes three compartments into consideration. In this study, we used the extended SIR models, SEIR [8], SEIRQ and SEIRM, to simulate the second epidemic in India, which has taken isolation and vaccine factor into consideration, to explore whether the epidemic trend will change after effective isolation measures are taken and what is the minimum number of people who need different vaccines to end the epidemic. Material And Methods Formulation of SEIR model The SEIR model provides a practical quantitative research method for the analysis of the epidemiological characteristics of infectious diseases. The model was constructed based on the following assumptions. (1) The asymptomatic infected persons were not considered. (2) No consideration for reinfection. (3) The impacts of birth rate, death rate and immigration were not considered. (4) The model only considered the propagation dynamics in the natural state. In this model, the target population is divided into four compartments, including Susceptible (S), Exposed (E), Infected (I) and Removed (R). Individuals in SEIR move from one compartment to another based on basic parameters, simulating the spread of the disease through the population [9]. In the SEIR model (Fig. 1a), where N is the population size, β is the infection rate, γ is the removed rate, and σ is the incidence rate. Eq. 1 shows the system of ordinary different equations used to determine how much of the population is within each group at a specic time for the model. Equation 1 Page 4/17 Formulation of SEIRQ model In the absence of effective vaccines during the epidemic period, isolation measure was an effective measure to control the spread of infectious diseases. Therefore, the isolation factor was included in the model to analyze the trend of the epidemic in India under the implementation of effective isolation measures. In the SEIRQ model (Fig. 1b), Q represents the population isolated after illness, α is the isolation rate, ω represents the probability that an isolated person will recover or die. Eq. 2 shows the system of ordinary different equations used to determine how much of the population is within each group at a specic time for the model. Equation 2 Page 5/17 Formulation of SEIRM model Vaccination was the most effective means of prevention and control of the COVID-19 epidemic. The vaccine factor was included in the model to analyze what was the minimum number of people who need to be vaccinated with different vaccines to end the epidemic. In the SEIRM model (Fig. 1c), M represents the population with effective antibodies after vaccination, λ is the average daily vaccination rate within 70 days of vaccination (According to reports, the number of single-day vaccination in China could reach up to 20 million. With reference to this vaccination rate, it was estimated that the full vaccination in India would be completed within 70 days), µ is the effective rate. Eq. 3 shows the system of ordinary different equations used to determine how much of the population is within each group at a specic time for the model. Equation 3 Page 6/17 Main parameter settings and descriptions Due to the lack of data on the second wave in India, we referred to the literature on the epidemic in India in 2020 and combined it with actual case data for parameter estimation. The main parameter settings and detailed descriptions of each parameter were shown in Table 1. Page 7/17 Table 1 The main parameter settings Parameters Description Parameter Parameters values of the source S (0) The initial susceptible population 1353713978 actual data 1 E (0) The initial exposed population 156008 data tting I (0) The initial infected population 181868 actual data 2 R (0) The initial removed population 0 actual data 3 N The total population 1354051854 actual data 4 Q (0) The initial isolated after illness population 0 model assumption M (0) The initial population with antibodies after vaccination 0 model in a susceptible population assumption β The probability that a susceptible person would 0.6537 data tting become ill after coming into contact with an infected person σ The probability that the latent patient developed 0.1294 data tting symptoms and became the infected person γ The probability that an infected person would recover 0.3485 data tting or die α The isolation rate 1; 0.5; 0.3; model 0.1 assumption ω The probability that an isolated person would recover 0.3491 data tting or die λ The average daily vaccination rate within 70 days of 1/70; 1/100; model vaccination in the susceptible population 1/140 assumption µ The effective rate of producing effective antibodies 0.9; 0.7; 0.5 model after vaccination assumption Notes: 123: Data was collected from WHO daily updates;4Data was collected from World Bank Demographics. Model analysis Page 8/17 First, the SEIR model was formulated to simulate the number of daily infections and then compared with the actual number of infections. The average percentage error (APE) was used to evaluate the accuracy of the model, the smaller the APE value, the better the model t. An APE value0.3 is generally considered a good tting effect.
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