Understanding the implications of under-reporting, vaccine efficiency and social behavior on the post-pandemic spread using physics informed neural networks: A case study of China

PLOS ONE RESEARCH ARTICLE Understanding the implications of underreporting, vaccine efficiency and social behavior on the post-pandemic spread using physics informed neural networks: A case study of China Samiran Ghosh1, Alonso Ogueda-Oliva2, Aditi Ghosh ID3*, Malay Banerjee ID1, Padmanabhan Seshaiyer2 a1111111111 a1111111111 a1111111111 a1111111111 a1111111111 1 Indian Institute of Technology Kanpur, Kanpur, India, 2 George Mason University, Fairfax, VA, United States of America, 3 Texas A&M University-Commerce, Commerce, TX, United States of America * Abstract OPEN ACCESS Citation: Ghosh S, Ogueda-Oliva A, Ghosh A, Banerjee M, Seshaiyer P (2023) Understanding the implications of under-reporting, vaccine efficiency and social behavior on the post-pandemic spread using physics informed neural networks: A case study of China. PLoS ONE 18(11): e0290368. https://doi.org/10.1371/journal.pone.0290368 Editor: Rajnesh Lal, Fiji National University, FIJI Received: August 6, 2023 Accepted: October 25, 2023 Published: November 16, 2023 Copyright: © 2023 Ghosh et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: The underlying data set can be found here: https://github.com/ aoguedao/understanding-post-pandemic-mathmodeling. Funding: This work is supported in part by the last author’s grant from the National Science Foundation DMS 2232739 and DMS 2230117. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. In late 2019, the emergence of COVID-19 in Wuhan, China, led to the implementation of stringent measures forming the zero-COVID policy aimed at eliminating transmission. ZeroCOVID policy basically aimed at completely eliminating the transmission of COVID-19. However, the relaxation of this policy in late 2022 reportedly resulted in a rapid surge of COVID-19 cases. The aim of this work is to investigate the factors contributing to this outbreak using a new SEIR-type epidemic model with time-dependent level of immunity. Our model incorporates a time-dependent level of immunity considering vaccine doses administered and time-post-vaccination dependent vaccine efficacy. We find that vaccine efficacy plays a significant role in determining the outbreak size and maximum number of daily infected. Additionally, our model considers under-reporting in daily cases and deaths, revealing their combined effects on the outbreak magnitude. We also introduce a novel Physics Informed Neural Networks (PINNs) approach which is extremely useful in estimating critical parameters and helps in evaluating the predictive capability of our model. 1 Introduction COVID-19, caused by the novel coronavirus SARS-CoV-2, first emerged in Wuhan, Hubei province, China, in late 2019. As the virus continued to spread, China implemented stringent measures to control its transmission. Since then, China continued with the same methods, making them part of its zero-COVID policy, even after the availability of vaccines. ZeroCOVID policy refers to an approach aimed at completely eliminating the transmission of COVID-19 within a specific region or country. This approach typically involves strict measures such as extensive testing, contact tracing, quarantine, travel restrictions and lockdowns to prevent the spread of the virus. PLOS ONE | https://doi.org/10.1371/journal.pone.0290368 November 16, 2023 1 / 27 PLOS ONE Competing interests: The authors have declared that no competing interests exist. Understanding the implications of under-reporting, vaccine efficiency and social behavior The zero-COVID policy in China has both positive and negative aspects. It aims to control the disease, protect public health, prevent healthcare system overload, and maintain economic stability. However, it also leads to economic disruptions, social and mental health impacts, potential human rights concerns, and faced challenges in feasibility and sustainability [1]. At the end of 2022, when the zero-COVID policy was relaxed gradually in China, it faced a rapid spread of the infection [2]. While we do not have access to official real-time data, there have been reports in the media suggesting a significant increase in daily COVID-19 cases in China after the relaxation of their zero-COVID policy [3–6]. According to these sources, the number of cases has allegedly surged to the magnitude of approximately ten millions per day [3, 4]. This sudden surge in epidemic progression forced researchers to think about the possible reasons behind it. The implementation of a zero-COVID policy aims to eliminate the transmission of COVID-19, resulting in fewer infections. However, this approach may limit the development of acquired immunity in the population, leaving a significant portion susceptible to the infection. An increase in the total level of immunity within a population results in a reduction of the proportion of individuals who are susceptible to the disease. The total level of immunity in a population comes from two sources: 1. Vaccine induced immunity: Immunity obtained through vaccination of the individuals. 2. Acquired Immunity: ‘Acquired immunity’ refers to the adaptive immunity developed within a recovered individual after recovery from the infection. Since, zero-COVID policy resulted in a fewer infections, the contribution of the acquired immunity in the total level of immunity is negligible. Consequently, the proportion of susceptible individuals is comparatively high. The vaccine induced immunity is the major contributor to reduce the proportion of susceptible population. However, the waning of immunity can increase the proportion of susceptibility over the time. This waning of immunity solely depends upon the efficacy of the vaccine. In the context of COVID-19, the level of immunity acquired through prior infection is long lasting compared to the immunity obtained through vaccination. Vaccine efficacy refers to the effectiveness of a vaccine in preventing a disease. It is typically expressed as a percentage and represent the reduction in disease incidence among vaccinated individuals compared to a similar group of unvaccinated individuals. In the context of COVID-19, multiple vaccines have been developed in different countries by different manufacturers. Different COVID-19 vaccines employ different mechanisms to trigger an immune response. For example, mRNA based vaccines, such as those developed by Pfizer-BioNTech and Moderna, introduce genetic material into cells to produce viral proteins. In contrast, vector-based vaccines like the AstraZenca and Johnson & Johnson vaccines use weakened viruses to deliver viral proteins. These variations in vaccine mechanisms can lead to different types of vaccine efficacies [7, 8]. There were several (...truncated)