Mathematical Modeling, Simulations, and AI for Emergent Pandemic Diseases: Lessons Learned From COVID-19

By Esteban A. Hernandez-Vargas

Mathematical Modeling, Simulations, and Artificial Intelligence for Emergent Pandemic Diseases: Lessons Learned from COVID-19 includes new research, models and simulations developed during the COVID-19 pandemic into how mathematical methods and practice can impact future response. Chapters go beyond forecasting COVID-19, bringing different scale angles and mathematical techniques (e.g., ordinary differential and difference equations, agent-based models, artificial intelligence, and complex networks) which could have potential use in modeling other emergent pandemic diseases. A major part of the book focuses on preparing the scientific community for the next pandemic, particularly the application of mathematical modeling in ecology, economics and epidemiology.

Readers will benefit from learning how to apply advanced mathematical modeling to a variety of topics of practical interest, including optimal allocations of masks and vaccines but also more theoretical problems such as the evolution of viral variants.

• Provides a comprehensive overview of the state-of-the-art in mathematical modeling and computational simulations for emerging pandemics
• Presents modeling techniques that go beyond COVID-19, and that can be applied to tailoring interventions to attenuate high death tolls
• Includes illustrations, tables and dialog boxes to explain highly specialized concepts and insights with complex algorithms, along with links to programming code

• Language: English
• Publisher: Academic Press
• Release date: Mar 21, 2023
• ISBN: 9780323950657

Book preview

1: Modeling during an unprecedented pandemic

Esteban A. Hernandez-Vargasa,b    a Department of Mathematics and Statistical Science, University of Idaho, Moscow, ID, United States

b Institute for Modeling Collaboration and Innovation, University of Idaho, Moscow, ID, United States

Abstract

Emerging and reemerging pathogens are latent threats in our society with the risk of killing millions of people worldwide, without forgetting the severe economic and educational backlogs. The spread of pathogens from one individual to another can be abstract in mathematical terms, helping public health agencies with predictions of the pandemic and evaluating possible scenarios. Nevertheless, modeling disease transmission is a central vexation for the scientific community—this involves several complex and dynamic processes. The emerging pathogen SARS-CoV-2 has led us to long terms of confinement and social isolation. Many lessons have been learned during COVID-19; a very important one is that mathematics is a central tool to follow uncharted territories during pandemics.

This chapter aims to put in perspective the subsequent chapters presented in this book, which are a collection of mathematical models, computational simulations, and artificial intelligence approaches that were employed during the COVID-19 pandemic.

Keywords

Mathematical modeling; AI; Simulations; Emergent diseases; COVID-19

1: Modeling epidemics

Infectious diseases can cause the invasion of an individual by pathogens whose activities can highly harm the host's tissues while transmitting to other individuals. Infectious diseases can be divided into acute or chronic infections. Examples of infectious diseases in history are many; for instance, the year 1918 saw the deadliest pandemic reported in history named the 1918 flu pandemic, killing about 50 million people. In 2009, the H1N1 influenza pandemic globally caused between 100,000 and 400,000 deaths in the first year. The magnitude of the threat represented by emerging virus diseases is immense; for example, HIV/AIDS has resulted in more than 30 million deaths from all socioeconomic backgrounds [1]. Furthermore, reemerging viruses like Ebola in 2014 and Zika in 2016 have baffled us with their threat to humans and healthcare systems around the globe. Nowadays, we all experience the consequences of the COVID-19 pandemic, which has spread across borders, affecting several nations simultaneously and having a considerable economic and social impact worldwide.

An emerging infectious disease is defined as a disease that has newly appeared in a population or has existed but is rapidly increasing in incidence [2]. The National Institute of Allergy and Infectious Diseases (NIAID) has defined three categories of priority [2]. Pathogens in the first category A are those that pose the highest risk to national security and public health because they can be quickly disseminated or transmitted from person to person, for example, Yersinia pestis (plague), Bacillus anthracis (anthrax), dengue, and ebola [2]. The second category B is composed of pathogens that are moderately easy to disseminate and may result in moderate morbidity rates and low mortality rates; examples are Hepatitis A, Salmonella, Yellow fever virus, Chikungunya virus, and Zika virus, among many others. The third category C includes emerging pathogens that could be engineered for mass dissemination in the future because of the availability and ease of production and dissemination; examples are tuberculosis, influenza viruses, SARS-CoV, and Rabies virus, among others [2].

The causes and sources of disease are very difficult to identify at the early stages of an outbreak. Surveillance, monitoring, and preparedness remain the main counterattack against infections—and consequently require constant improvements at the local, regional, and national levels [3]. In the past 60 years, in particular the last months, the study of infectious diseases has matured into a multidisciplinary field at the intersection of epidemiology, mathematics, artificial intelligence, ecology, sociology, immunology, and public health.

Mathematical modeling is an abstraction of a system based on mathematical terms to study the effects of different components and consequently to make predictions [4]. Mathematical models for the spread of diseases have played a central role in epidemics, providing a cost-effective way of assessing disease transmission, targets for preventing disease, and control [5]. Mathematical modeling was pivotal in suggesting new vaccination strategies to protect against influenza infection [6]; support public health strategies for containing SARS-CoV-2 [7–9]; or for the use of antiretroviral treatment for HIV-infected patients as a prevention measure [10].

During the COVID-19 pandemic, the Kermack-McKendrick model of Susceptible-Infectious-Recovered [11] (SIR or compartmental model) was used to derive an overwhelming amount of research in different countries. However, Kermack-McKendrick’s models often overlook population heterogeneity. These models typically assume that the population of interest is well mixed: every individual has the same chance to get the disease from an infected case [5]. This simplification makes the SIR model analytically tractable, but at the same time leads to less accurate evaluations of the disease spread [12]. Classifying the population into homogeneous subgroups concerning the disease of interest can increase the model representativeness [13] but also quickly increase the model complexity. Nevertheless, even in these cases, the homogeneous assumption remains [12].

Modeling during an unprecedented pandemic such as COVID-19 waschallenging and chaotic. Uncertainties about the transmission of the virus were debated in the scientific community and public news. Massive sampling for detecting infected individuals was too challenging in developed countries, while in developing countries, it was not even envisaged. Confinement strategies in different countries were not popular but necessary, resulting in millions of students taking lectures online while millions of workers doing home office. Regarding the scientific community, thousands of scientists did try to contribute to the pandemic with their respective expertise in different fields, while many other scientists without any background in infectious diseases were finding the opportunity to become famous. Governmental institutions were not prepared worldwide. Thus, in many countries, public health policies were misleading and confusing their citizens, which derived in a lack of credibility just after a few months of pandemics. Indeed, there are many lessons that we can learn from COVID-19. As we enter the fourth year of the COVID-19 pandemic, this book brings back an effort to recapitulate major mathematical modeling efforts from different angles, discussing what was done, what needed to be done, and what type of efforts should be ready for the next pandemic.

2: Book overview

This book consists of 15 chapters that provide an effort with different mathematical techniques to tackle the COVID-19 pandemic. Leveraging different kinds of data through novel quantitative approaches will guide public health policies in decision-making in the following decades. More importantly, this book ends each chapter with the lessons learned from COVID-19. The authors addressed central problems during the COVID-19 pandemic, which will remain as critical documentation for future pandemics.

Chapter 2 provides a global overview of the COVID-19 pandemic with the cumulative SARS-CoV-2 incidence rate (weekly cases per 100,000 inhabitants) by continent as well as a list of countries with the lower COVID-19 mortality excess rate per 100,000 inhabitants. Other fundamental aspects of the COVID-19 pandemics are discussed in this chapter, such as reinfections and the emergence of variations of SARS-CoV-2.

Chapter 3 explores how the evolution of COVID-19 disease has been changing since the beginning of the pandemic as well as the mathematical models used to answer questions such as: when the first case will be reported in a certain region? How fast the disease will spread? How local transmission dynamics could develop? How effective were the mitigation measures? What would be the best vaccination strategy? How would vaccination impact the transmission dynamics? The authors emphasize the limitations of mathematical modeling that appeared in COVID-19, and whenever possible, strategies will be proposed to address these limitations.

Chapter 4 aims to consider regional differences and discover dominant patterns in the profiles of the COVID-19 incidence rate curves across regions. This introduced geometrical methods to analyze the shapes of local curves and statistically group them into distinct clusters, according to their shapes. This information derives the so-called shape averages of curves within these clusters, which represent a better characterization of a pandemic's trajectory. The authors apply this methodology to data for two geographic areas: a state-level analysis within the United States and a country-level analysis within Europe.

Chapter 5 brings to discussion the tremendous inequality in vaccine supply; some regions of the world continue to hoard surpluses of the vaccine while other regions still have very limited access to vaccines. Isolationism (and vaccine nationalism) is a more obvious way to achieve self-preservation than solidarity (and vaccine globalism). The central question addressed in this chapter is which of these two strategies more effectively achieves national self-protection? Simulations show that tightening borders is extraordinarily costly and ineffective. In addition, the findings also show that highly granular vaccine disparities promote the evolution of vaccine escape.

Chapter 6 introduces a network-guided contact tracing strategy based on the heterogeneity of contact networks in metropolitan areas such as Mexico City. Two contact tracing scenarios were simulated: one in which secondary contacts are randomly identified and the other one in which secondary contacts are identified by a biased sampling caused by the heterogeneous network. The results show that this second strategy can identify a larger number of infected individuals by using the same resources.

Chapter 7 considers deep learning in forecasting the COVID-19 pandemic and county-level risk warnings. The authors showed that a physics-hybrid deep learning framework on county-level predictions can predict the prevalence of multiscale COVID-19 in all 412 counties in Germany. It can also be naturally extended to multinational or transnational analyses. Based on this framework, the authors also discuss the possible extensions of introducing vaccination rates and virus variants into their methods. This chapter highlights the importance of combing epidemiological models with deep learning methods for the inherent stability and generalization ability.

Chapter 8 introduces an approach that considers the an epidemiological model, neural networks, control theory, and complex systems. A controller for the vaccine application strategy is designed using impulse control. The behavior of the dynamics of the model with this type of control is very interesting since in all the classes the dynamics start faster. The authors observe that this control design can stabilize the system; with this, we can achieve a balance in the transmission of the disease.

Chapter 9 discusses the normalization of the home office as a work scheme that has caused collateral effects on the well-being of workers derived from isolation and lack of socialization. The authors developed an agent-based model for COVID-19 to include the application of vaccines, social phenomena related to human interactions, anxiety in workers, and communication technologies to facilitate reintegration. Numerical results showed that anxiety levels and the basic reproduction number decreased from the scenario without interventions to vaccination, and the activities carried out increased, allowing workers to reintegrate and face anxiety.

Chapter 10 presents the implementation of mitigation measures and modeling of in-hospital dynamics depending on the COVID-19 infection status. Patients are considered from their entry until their discharge or death, thus predicting the total number of individuals in hospital beds and the intensive care unit for each healthcare unit. Consequently, this model was to establish which combination of several quarantine scenarios and other policies was best at what time.

Chapter 11 presents a very debatable aspect of COVID-19, the reopening of schools, which has not been an easy decision to make, because this implies an increase in mobility, as well as in contact with the population and therefore in the number of cases. In this chapter, the authors explored mathematical compartmental models to analyze possible scenarios after the reopening of schools, within a campus college in Mexico. The proposed model is based on the Paltiel model and the Reed Frost model, considering the daily screening in the population, as well as parameters and probability densities based on the official public data on COVID-19 in Mexico.

Chapter 12 considers a mathematical assessment of the role of vaccination against COVID-19 in the United States. Simulations show that vaccine-derived herd immunity can be achieved in the United States using Pfizer or Moderna vaccine if at least 78% of the populace is fully vaccinated. The herd immunity threshold decreases if the vaccination program is combined with other NPIs, such as face mask usage (at increased coverage and effectiveness, in comparison to their baseline values during the third wave of the pandemic). It is shown that although the use of low to moderately effective face masks (such as cloth and surgical masks) alone might not be sufficient to contain the COVID-19 pandemic even at full coverage, the use of masks or the Pfizer or Moderna vaccine alone may be sufficient to lead to the elimination of the pandemic if the coverage is moderately high enough.

Chapter 13 proposes an approach to ascertainment and biased testing rates in the surveillance of emerging infectious diseases. Epidemiological analysis showed that using passive surveillance data and discussing the following can be determined: (i) What kind of biases exists? (ii) How do biases affect epidemiological analyses? (iii) How to reduce such biases. This chapter also discusses how the contribution of an infected individual to the viral load in wastewater may depend on the severity of the symptoms.

Chapter 14 focuses on SARS-CoV-2 at the within-host level. The authors fully characterize the dynamical behavior of the target-cell models under treatment actions. Based on the concept of virus spreadability, antiviral effectiveness thresholds are determined to establish whether a given treatment can clear the infection without secondary effects. Also, it is shown how to simultaneously minimize the total fraction of infected cells while maintaining the virus load under a given level, through an optimal control strategy.

Chapter 15 presents two novel modeling ideas to describe and understand the effects and evolution of the COVID-19 pandemic in Mexico. The first idea is to model epidemic curves assuming that the times when a certain number of infected individuals are observed have been censored but follow a known probability distribution; the censorship point is the most recent date for which a record is available. The second idea exploits the information of patients identified as SARS-CoV-2 positive in Mexico to understand the relationship between comorbidities, symptoms, hospitalizations, and deaths due to the COVID-19 disease.

Chapter 16 wraps up the book by presenting the crucial topics by late 2022, for the mitigation and control of the SARS-CoV-2 pandemic. This chapter reviews important factors related to the evolution of the epidemic, such as nonpharmaceutical interventions, vaccination rates, coverage, the evolution of SARS-CoV-2 variants, and their impact on the control of the epidemic. Ultimately, this chapter presents the notable successes in the application of mathematical models to understand different factors, scales, and behaviors of the epidemic, but likewise there have been failures, many arising from the political use of model outputs but others having their roots on the incomplete knowledge of the basic theory of the biology of the virus and the epidemic.

References

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[2] NIAID. NIAID Emerging Infectious Diseases/Pathogens. NIH: National Institute of Allergy and Infectious Diseases; 2022. Available at: https://www.niaid.nih.gov/research/emerging-infectious-diseases-pathogens (Accessed 7 July 2022).

[3] Grundmann O. The current state of bioterrorist attack surveillance and preparedness in the US. Risk Manag. Healthc. Policy. 2014;7:177–187.

[4] Hernandez-Vargas E.A. Modeling and Control of Infectious Diseases: With MATLAB and R. Elsevier Academic Press; 2019.

[5] Heesterbeek H., et al. Modeling infectious disease dynamics in the complex landscape of global health. Science. 2015;347:aaa4339.

[6] Rose M.A., et al. The epidemiological impact of childhood influenza vaccination using live-attenuated influenza vaccine (LAIV) in Germany: predictions of a simulation study. BMC Infect. Dis. 2014;14:40.

[7] Mejia-Hernandez G., Hernandez-Vargas E.A. When is SARS-CoV-2 in your shopping list?. Math. Biosci. 2020;328:1–7.

[8] Ravichandran S., et al. Antibody signature induced by SARS-CoV-2 spike protein immunogens in rabbits. Sci. Transl. Med. 2020;12:1–9.

[9] Weitz J.S., et al. Intervention serology and interaction substitution: exploring the role of ‘immune shielding’ in reducing COVID-19 epidemic spread. Nat. Med. 2020;26:849–854.

[10] Tanser F., Baernighausen T., Graspa E., Zaidi J., Newell M.-L. High coverage of ART associated with. Science. 2013;339:966–972.

[11] Kermack W.O., McKendrick A.G. A contribution to the mathematical theory of epidemics. Proc. R. Soc. A Math. Phys. Eng. Sci. 1927;115(772):700–721.

[12] Bansal S., Grenfell B.T., Meyers L.A. When individual behaviour matters: homogeneous and network models in epidemiology. J. R. Soc. Interface. 2007;4:879–891.

[13] Nishiura H., Oshitani H. Household transmission of influenza (H1N1-2009) in Japan: age-specificity and reduction of household transmission risk by zanamivir treatment. J. Int. Med. Res. 2011;39:619–628.

2: Global epidemiology and impact of the SARS-CoV-2 pandemic

Sofia Bernal-Silvaa; Angélica Torres-Díazb,c; Andreu Comas-Garcíaa    a School of Medicine, Autonomous University of San Luis Potosi, San Luis Potosi, Mexico

b Division of Higher Studies for Equity, School of Medicine, Autonomous University of San Luis Potosi, San Luis Potosi, Mexico

c Organization to Restore the Environment and Social Harmony (ORMA, A.C.), San Luis Potosi, Mexico

Abstract

In this chapter, we evaluated the development and impact of the SARS-CoV-2 pandemic. The evaluation was performed by continent and country. The structure of the weekly mortality curves on all continents is very different from the weekly incidence rate. With the data from the Johns Hopkins University Coronavirus Resource Center and the Institute of Health Metrics and Evaluation published in The Lancet, we have calculated the COVID-19 directed and associated mortality rate for 181 countries. Despite the structural similarity between the second, third, and fourth waves being similar, the weekly mortality rate intensity of the four waves was very asynchronous among all the countries. One of the primary consequences of this pandemic is orphanhood. Recently, the Imperial College of London has published a webpage that calculates the number of orphans generated by the COVID-19 pandemic. Despite the fact that before the SARS-CoV-2 outbreak there was plenty of scientific evidence about how to handle and/or mitigate a pandemic, almost every government adopted different policies with different anti-epidemic effects and impacts.

Keywords

Epidemiology; SARS-CoV-2; Incidence; Morality; Lethality; Orphanhood; Public policies

1: Introduction

The enveloped RNA viruses with the largest known genome coronaviruses have a high capacity for genomic recombination infecting mammals, birds, and humans and causing respiratory, enteric, hepatic, and neurological diseases. One of the most frequent agents that cause common colds are zoonotic viruses whose wide distribution means that the interaction between humans and wild animals increases the probability of the emergence of new coronavirus species or strains. In humans, four seasonal coronaviruses frequently cause common colds but rarely cause pneumonia (hCoV-229E, -OC43, -NL63, and -HKU1), while, prior to 2019, only two types of coronaviruses had caused major outbreaks of severe respiratory infection: SARS-CoV occurred in 2002–03 in China and MERS-Co occurred in 2012 in the Middle East [1,2].

In late December 2019, a new cluster of patients presenting a severe acute respiratory syndrome (SARS) of unknown cause was detected in the City of Wuhan, in the province of Hubei, China. At the beginning of the outbreak, the Chinese Government expressed serious doubts about the possibility of person-to-person transmission. However, on January 24, 2020, the first report of a family cluster presenting verified person-to-person transmission was published. By March 12, almost 3 months after the outbreak began, when the World Health Organization (WHO) declared the SARS-CoV-2 outbreak a pandemic, SARS-CoV-2 was present in 114 countries, with more than 132,496 infections and 4917 deaths recorded. On May 15, the first chain of multiple human-to-human transmission outside Asia was documented. By June 1, 2022, 531,567,231 cases had been reported in 191 countries or territories, 6,297,253 deaths had been registered, and 11,653,556,780 doses of COVID-19 vaccine had been administered [1–5]. While SARS-CoV-2 infection mainly occurs via airborne transmission, the infection can also occur via close interpersonal contact.

The recent finding that the virus can also be detected in feces and wastewater samples 6,7 has the potential to diversify and improve both the epidemiological surveillance measures employed to track the pandemic and the strategies for controlling/mitigating it. The sampling of wastewater could be applied on a mass scale as a novel public health strategy that could enable the genomic surveillance of the virus without the need for human testing.

2: Global epidemiology

The SARS-CoV-2 pandemic has been characterized by repeated waves, approximately two per year, of cases driven by the emergence of new variants of concern (VOC). Until now, each new VOC presented enhanced fitness that affects its growth rate and basic reproduction number (R0) and results in a higher immune-evasion rate/higher rate of immune escape and a shorter generation time [8].

In general, while several SARS-CoV-2 waves have been observed in all continents and countries, the ongoing transmission of the virus has at no point been arrested. Therefore, rather than waves, this behavior could be considered, in epidemiological terms, a serial recrudescence phenomenon comprising transmission, the presentation of cases, and death. Nonetheless, in this chapter, we will continue to use the term waves. Fig. 1 shows the weekly incidence rate per continent, while Fig. 2 shows the cumulative incidence rate for each continent and Table A.1 compares the incidence, mortality, and lethality of the virus among the continents.

Fig. 1

Fig. 1 Weekly SARS-CoV-2 incidence rate (weekly cases per 100,000 inhabitants) by continent. Data from Johns Hopkins University of Medicine, Coronavirus Resource Centre. https://coronavirus.jhu.edu/map.html.

Fig. 2

Fig. 2 Cumulative SARS-CoV-2 incidence rate (weekly cases per 100,000 inhabitants) by continent. Data from Johns Hopkins University of Medicine, Coronavirus Resource Centre. https://coronavirus.jhu.edu/map.html.

The weekly incidence rate in Africa shows four waves, each of which presents a trend of continuous increase (Fig. 1), which could be a consequence of not only VOC (beta, delta, and omicron) circulation but also the increased testing rate. It should be noted that the peak of the fourth wave was 2.5 times higher than the peak of the third. While the cumulative incidence rate recorded in Africa was 2.8, 3.0, 9.5, and 33.6 times lower than that observed in America, Asia, Europe, and the rest of the world, respectively, it was 1.6 times higher than that observed in Oceania (Fig. 2). The intensity of the weekly incidence rate for the first three waves among all countries was asynchronous, while the fourth wave occurred almost at the same time throughout the African continent (Fig. 3A).

Fig. 3

Fig. 3 Weekly SARS-CoV-2 incidence rate intensity per country. (A) Africa, (B) America, (C) Asia, (D) Europe, and (E) Oceania. The incidence rate was adjusted from 0 to 1, and was represented in color. Data from Johns Hopkins University of Medicine, Coronavirus Resource Centre. https://coronavirus.jhu.edu/map.html.

America presents five waves, the smallest of which was the first, to which the next three were very similar, while the fifth was the largest, with a peak 3.7 times higher than the peak of the fourth wave (Fig. 1). The cumulative incidence rate observed for America was 1.1, 3.5, and 12.3 times lower than that observed for Asia, Europe, and the rest of the world, respectively, but 2.7 and 4.3 times higher than that observed for Africa and Oceania, respectively (Fig. 2). In the case of America, the first wave was the smallest, the next three were very similar, and the fourth was the largest. The heat map for the intensity of the incidence rates (Fig. 3B) shows an asynchrony of incidence patterns between countries, although continuous transmission is clearly observed for all. In contrast with the first four waves, the fifth is very short and synchronic among all