Simulating and Preventing COVID-19 Using Epidemiological Models

Introduction

The whole world has been facing the biggest risk in the shape of COVID-19 global pandemic. The increasing number of infected and deceased patients makes a huge impact on the society. It is urgent to uncover the natural progression of the novel coronavirus. Generally, a disease follows the host formation and progression, such as exposure to the infection, host formation, and the spread of the infection. As an infectious disease, the cause of COVID-19 can be defined as an epidemiological triad, which is a traditional model involved three components: the agent, the host, and the environment. The agent carries the infection that is transmitted to the host under a certain environment. Cutting off the connection between those factors can disrupt the proliferation of COVID-19 effectively. Interrupting factors, such as agent-host, environment-host, and agent-environment, can be conceptualized into three scenarios: community, hospital, and aerosol-generating medical procedure (Tsui et al., 2020). In this scenario, prediction tools can serve to determine different objectives such as the pandemic trend, the medical equipment supplies and distributions, and the degrees of policy execution (i.e. quarantine regulations, lockdown orders, travel restriction policies). Strong policies are needed to be administered and executed in order to control the pandemic. On the other hand, the disease control policy requires rationality and reliability. Data-driven approaches are helpful for the policy-making process in terms of accurate parameter estimations and mathematical simulations. Further, policy-makers need to rebuild the infrastructure in terms of a quick and accurate responses, which is an important component of the smart healthcare system. Data mining methods along with the epidemiological models always make the contribution to the smart healthcare system (Jain & Bhatnagar, 2017).

Responses from a smart healthcare system require formal procedures for measuring and tracking the outbreak of a new disease. Epidemiological models with mathematical simulations can be served to manage the impacts and reduce the risk. A successful simulation analysis for an infectious disease relies on measuring influential factors including the infectious duration, the opportunity of contact, the transmission probability, and the susceptibility. (Kucharski, 2020). The new virus will die off after major actions have been taken for susceptible carries, otherwise, the disease may eventually become an epidemic. Relationships between susceptible, infected, and recovered population are important to uncover the transmission pattern of an infectious disease (Hethcote, 2000). The susceptible-infected-removed (SIR) model has been considered as the most popular stochastic simulations in the field of epidemiology because of its efficiency and simplicity. Firstly, it can predict the number of susceptible, infected, and recovered individuals at any given time. Secondly, its simplicity allows the computational process easier by estimating a small number of parameters. Various SIR models have been used to reveal the outbreaks’ pattern of other diseases such as SARS, H1N1, and MERS (Zhang, 2007; Coburn et al., 2009; Kwon & Jung, 2016).

Motivated by the current urgent demand of epidemiological simulation and prediction, this chapter presents how SIR-based models work with stochastic simulations for the disease control in the context of the COVID-19 pandemic. A brief introduction of SIR family models will be given, followed by an exploratory analysis of the U.S. data from the Johns Hopkins University. Case studies will be conducted to illustrate model usages in terms of parameter estimations and stochastic simulations for the disease control measures. The objectives of this chapter are listed as follows:

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  reviewing the most recent studies and applications for COVID-19 predictions and simulations based on the SIR family of models.

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  illustrating several SIR-based models, such as the basic SIR, SIR-D, SIR-F, SEIR, and eSIR, in terms of model structures and ordinary differential equations.

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  providing a real-world case study in regards to estimate parameters with trend analysis using SIR, SIR-D, and SIR-F.

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  simulating future situations in the U.S. under different scenarios and effects, including the no-actions scenario, the effect under new medicines, the effect under vaccinations, and the effect under lockdowns.

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  discussing potential solutions that can be adopted for SIR-based predictions and simulations, i.e. the mixed model approach.