"Right off the bat, let me say that I really enjoyed Kuhl's book. It is beautifully written, very engaging, and the topics and examples are thoughtfully chosen. ... This is a timely and truly wonderful book." (Anita T. Layton, SIAM Review, Vol. 64 (3), September, 2022)
"This is a very ambitious book. ... Every chapter has a collection of very good problems. ... the many examples using real data make the book a valuable resource. Overall the book presents a number of important ideas and offers some significant new approaches for modeling real and complicated epidemics. It's a great place to begin to understand where mathematical epidemiology is now and where it has to go." (Bill Satzer, MAA Reviews, May 9, 2022)

table of contents

introduction

overview

I. infectious diseases

a brief history of infectious diseases

classical infectious diseases smallpox, polio, measles, rubella, influenza

corona virus type diseases SARS, MERS, COVID-19

statistic vs. mechanistic modeling

data science vs. data-driven modeling

examples: the measles

reading: bar-on et al., SARS-CoV-2 (COVID-19) by the numbers, elife 9 (2020) e57309.

II. mathematical epidemiology

II.1. introduction to compartment modeling

concept of compartment modeling

the kermack-mc kendrick theory

the classical S,I,R model

SIR model with and without vital dynamics

examples: the plaque

reading: bauer f, compartment models in epidemiology, mathematical epidemiology (2008) 19-79.

II.2. compartment modeling of epidemiology

overview of compartment models

the M, S, E, I, R, D compartments

SIR, SIS, SIRD, MSIR, SEIR, MSEIR, MSEIRS models

latent, contact, and infectious periods

examples: the measles

reading: hethcode hw, the mathematics of infectious disease, siam review 42 (2020) 599-653.

II.3. concepts of endemic disease modeling

concept of basic reproduction number

endemic equilibrium

herd immunity

eradicating disease through vaccination

examples: measles

reading: dietz k, the estimation of the basic reproduction number for infectious diseases, stat meth med res 2 (1993) 23-41.

III. data-driven modeling in epidemiology

III.1. compartment modeling of COVID19

characteristic timeline of COVID-19

SIR and SEIR models for COVID-19

susceptible, exposed, infectious, and recovered populations

latent, contact, and infectious periods of COVID-19

examples: sensitivity analysis for COVID-19

reading: peirlinck m, et al. outbreak dynamics of COVID-19 in china and the united states. biomech model mechanobio 19 (2020) 2179-2193.

III.2. early outbreak dynamics of COVID-19

basic reproduction number of COVID-19

SEIR model and parameter identification of Ro

comparison with other infectious diseases and with directly measured Ro

implications for exponential growth and herd immunity

examples: parameter identification for china and the united states

reading: park et al., reconciling early-outbreak estimates of the basic reproduction number and its uncertainty. j royal soc interface 17 (2020) 20200144.

III.3. asymptomatic transmission of COVID-19

concept of asymptomatic transmission

SEIIR model

antibody seroprevalence studies

undercount and its implications on herd immunity

examples: santa clara county, new york city, heinsberg

reading: ioannis j, the invection fatality rate of COVID-19 inferred from seroprevalence data, medRxiv, doi:10.1101/2020.05.13.20101253

III.4. inferring outbreak dynamics of COVID-19

concept of data-driven modeling

bayesian SEIIR model

machine learning and bayesian methods

uncertainty quantification

inferring the beginning of the outbreak

examples: santa clara county

reading: peirlinck m et al., visualizing the invisible: the effect of asymptomatic transmission. comp meth appl mech eng. 372 (2020) 113410.

IV. modeling outbreak control

IV.1. managing infectious diseases

overview of community mitigation strategies

ethical implications of political countermeasures

concept of nowcasting

basic and effective reproduction numbers Ro and Rt

examples: china, europe, united states

reading: wilder-smith a, freedman do. isolation, quarantine, social distancing and community containment, j travel med (2020) 1-4.

IV.2. change-point modeling of COVID-19

concept of change points

interval-type compartment models for COVID-19

discretely vs continuously changing transition rates

learning change points

examples: COVID-19 dynamics in germany

reading: dehning et al., inferring change points in the spread of COVID-19 reveals the effectiveness of interventions, science doi:10.1126/science.abb9789

IV.3. dynamic compartment modeling of COVID-19

concept of flattening the curve

bayesian dynamic SEIR model

time-dependent contact rate, hyperbolic tangent vs. random walk

learning the time-varying effective reproduction number Rt

examples: Ro and Rt in europe

reading: linka et al., the reproduction number of COVID-19 and its correlation with public health interventions, comp mech. 66 (2020) 1035-1050.

V. network modeling of epidemiology

V.1. network modeling of epidemic processes

concept of network modeling

directed graphs, shortest path, small world networks

adjacency, degree, graph Laplacian

network modeling of epidemiology

examples: network models of europe and the united states

reading: pastor-satorras r et al., epidemic processes in complex networks, rev mod phys 87 (2015) 926-973.

V.2. network modeling of COVID-19

concept of reaction-diffusion modeling

network SEIR model for COVID-19

network vs. continuum modeling of COVID-19 spread

air traffic mobility networks and spreading patterns

examples: early COVID-19 spreading across the european union

reading: linka k et al. outbreak dynamics of COVID-19 in europe and the effect of travel restrictions. comp meth biomech biomed eng; 2020; 23:710-717.

V.3. dynamic network modeling of COVID-19

concept of disease management via constrained mobility

dynamic network SEIR model for COVID-19

mobility networks of walking, car, transit, air traffic

correlating mobility and reproduction

examples: mobility and reproduction number in the european union

reading: linka k et al. global and local mobility as a barometer for COVID-19 dynamics. biomech model mechanobio (2020) doi:10.1007/s10237-020-01408-2.

VI. informing political decision making through modeling

VI.1 exit strategies from lockdown

concept of travel restrictions

dynamic network mobility SEIR model

travel bubbles to safely lift travel bans

restricted travel vs. quarantine

example: newfoundland, canada, north america

reading: linka k et al. is it safe to lift COVID-19 travel bans. the newfoundland story. comp mech. 66 (2020) 1081–1092.

VI.2. vaccination strategies

concept of vaccination towards herd immunity or eradication

SEIR model for COVID-19 vaccination

strategies of test-trace-isolate

estimating herd immunity and tracing thresholds for COVID-19

example: learning from eradicating smallpox

reading: anderson rm, may rm, directly transmitted infectious diseases: control by vaccination, science 215 (1982) 1053-1060.

VI.3. the second wave

concept of seasonality

seasonal SEIR model

basic reproduction number of seasonal infectious disease

seasonality of mobility, seasonal workers, tourism, behavioral changes

example: seasonality of COVID-19

reading: grassly nc, fraser c, seasonal infectious disease epidemiology, proc royal soc b 273 (2006) 2541-2550.

lessons learned

COVID-19 is spreads exponentially if uncontrolled

COVID-19 is as contagious as previous coronaviruses

without vaccination, COVID-19 will be with us for a long time

we can flatten the curve and model it

constraining mobility is drastic but effective

reproduction is correlated to mobility with a delay of two weeks

most COVID-19 cases are asymptomatic and unreported

COVID-19 generates a ton of data, but not always suited for models

selective reopening can be more effective than quarantine

testing is critical for safe reopening

reading: kuhl e. data-driven modeling of COVID-19 - lessons learned. extr mech lett. 40 (2020) 100921.

potentially additional topics

superspreading

concept of heterogeneity

dispersion parameter k

superspreading events of COVID-19

implications for outbreak control

example: superspreading events in churches and meat factories

reading: lloyd-smith jo et al., superspreading and the effect of individual variation on disease emergence, nature 438 (2005) 355-359.

heterogeneous mixing

concept of population heterogeneity

SEIR model of mixing

age-specific modeling

implications for outbreak control

example: role of children in COVID-19 transmission

reading: britton t et al., mathematical model reveals the influence of population heterogeneity on herd immunity to SARS-CoV-2, science 369 (2020) 846-849.

Ellen Kuhl is the Walter B. Reinhold Professor in the School of Engineering and Robert Bosch Chair of Mechanical Engineering at Stanford University. She is a Professor of Mechanical Engineering and, by courtesy, Bioengineering. She received her PhD from the University of Stuttgart in 2000 and her Habilitation from the University of Kaiserslautern in 2004. Her area of expertise is Living Matter Physics, the design of theoretical and computational models to simulate and predict the behavior of living systems. Ellen has published more than 200 peer-reviewed journal articles and edited two books; she is an active reviewer for more than 20 journals at the interface of engineering and medicine and an editorial board member of seven international journals in her field. She is a founding member of the Living Heart Project, a translational research initiative to revolutionize cardiovascular science through realistic simulation with 400 participants from research, industry, and medicine from 24 countries. Ellen is the current Chair of the US National Committee on Biomechanics and a Member-Elect of the World Council of Biomechanics. She is a Fellow of the American Society of Mechanical Engineers and of the American Institute for Mechanical and Biological Engineering. She received the National Science Foundation Career Award in 2010, was selected as Midwest Mechanics Seminar Speaker in 2014,

and received the Humboldt Research Award in 2016 and the ASME Ted Belytschko Applied Mechanics Award in 2021. Ellen is an All American triathlete on the Wattie Ink. Elite Team, a multiple Boston, Chicago, and New York marathon runner, and a Kona Ironman World Championship finisher.

This innovative textbook brings together modern concepts in mathematical epidemiology, computational modeling, physics-based simulation, data science, and machine learning to understand one of the most significant problems of our current time, the outbreak dynamics and outbreak control of COVID-19. It teaches the relevant tools to model and simulate nonlinear dynamic systems in view of a global pandemic that is acutely relevant to human health.

If you are a student, educator, basic scientist, or medical researcher in the natural or social sciences, or someone passionate about big data and human health: This book is for you! It serves as a textbook for undergraduates and graduate students, and a monograph for researchers and scientists. It can be used in the mathematical life sciences suitable for courses in applied mathematics, biomedical engineering, biostatistics, computer science, data science, epidemiology, health sciences, machine learning, mathematical biology, numerical methods, and probabilistic programming. This book is a personal reflection on the role of data-driven modeling during the COVID-19 pandemic, motivated by the curiosity to understand it.

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