"Networks of Necessity: Simulating COVID-19 Mitigation Strategies for Disabled People and Their Caregivers"

One of my papers just came out in final form. Here are some details.

Title: Networks of Necessity: Simulating COVID-19 Mitigation Strategies for Disabled People and Their Caregivers

Authors: Thomas E. Valles, Hannah Shoenhard, Joseph Zinski, Sarah Trick, Mason A. Porter, and Michael R. Lindstrom

Abstract: A major strategy to prevent the spread of COVID-19 is the limiting of in-person contacts. However, limiting contacts is impractical or impossible for the many disabled people who do not live in care facilities but still require caregivers to assist them with activities of daily living. We seek to determine which interventions can best prevent infections of disabled people and their caregivers. To accomplish this, we simulate COVID-19 transmission with a compartmental model that includes susceptible, exposed, asymptomatic, symptomatically ill, hospitalized, and removed/recovered individuals. The networks on which we simulate disease spread incorporate heterogeneity in the risk levels of different types of interactions, time-dependent lockdown and reopening measures, and interaction distributions for four different groups (caregivers, disabled people, essential workers, and the general population). Of these groups, we find that the probability of becoming infected is largest for caregivers and second largest for disabled people. Consistent with this finding, our analysis of network structure illustrates that caregivers have the largest modal eigenvector centrality of the four groups. We find that two interventions—contact-limiting by all groups and mask-wearing by disabled people and caregivers—most reduce the number of infections in disabled and caregiver populations. We also test which group of people spreads COVID-19 most readily by seeding infections in a subset of each group and comparing the total number of infections as the disease spreads. We find that caregivers are the most potent spreaders of COVID-19, particularly to other caregivers and to disabled people. We test where to use limited infection-blocking vaccine doses most effectively and find that (1) vaccinating caregivers better protects disabled people from infection than vaccinating the general population or essential workers and that (2) vaccinating caregivers protects disabled people from infection about as effectively as vaccinating disabled people themselves. Our results highlight the potential effectiveness of mask-wearing, contact-limiting throughout society, and strategic vaccination for limiting the exposure of disabled people and their caregivers to COVID-19.

"A Multilayer Network Model of the Coevolution of the Spread of a Disease and Competing Opinions"

A new paper of mine just came out in final form. Here are some details.

Title: A Multilayer Network Model of the Coevolution of the Spread of a Disease and Competing Opinions

Authors: Kaiyan Peng, Zheng Lu, Vanessa Lin, Michael R. Lindstrom, Christian Parkinson, Chuntian Wang, Andrea L. Bertozzi, Mason A. Porter

Abstract: During the COVID-19 pandemic, conflicting opinions on physical distancing swept across social media, affecting both human behavior and the spread of COVID-19. Inspired by such phenomena, we construct a two-layer multiplex network for the coupled spread of a disease and conflicting opinions. We model each process as a contagion. On one layer, we consider the concurrent evolution of two opinions — pro-physical-distancing and anti-physical-distancing — that compete with each other and have mutual immunity to each other. The disease evolves on the other layer, and individuals are less likely (respectively, more likely) to become infected when they adopt the pro-physical-distancing (respectively, anti-physical-distancing) opinion. We develop approximations of mean-field type by generalizing monolayer pair approximations to multilayer networks; these approximations agree well with Monte Carlo simulations for a broad range of parameters and several network structures. Through numerical simulations, we illustrate the influence of opinion dynamics on the spread of the disease from complex interactions both between the two conflicting opinions and between the opinions and the disease. We find that lengthening the duration that individuals hold an opinion may help suppress disease transmission, and we demonstrate that increasing the cross-layer correlations or intra-layer correlations of node degrees may lead to fewer individuals becoming infected with the disease.

"Epidemic Thresholds of Infectious Diseases on Tie-Decay Networks"

Another paper of mine has just been published in final form. (Technically, one could say that it's almost in final form; the issue number has been determined, but its stamp is not yet on the .pdf file as I write this blog entry because some other articles from the same issue haven't yet been published.) Here are some details.

Title: "Epidemic Thresholds of Infectious Diseases on Tie-Decay Networks"

Authors: Qinyi Chen and Mason A. Porter

Abstract: In the study of infectious diseases on networks, researchers calculate epidemic thresholds to help forecast whether or not a disease will eventually infect a large fraction of a population. Because network structure typically changes with time, which fundamentally influences the dynamics of spreading processes and in turn affects epidemic thresholds for disease propagation, it is important to examine epidemic thresholds in models of disease spread on temporal networks. Most existing studies of epidemic thresholds in temporal networks have focused on models in discrete time, but most real-world networked systems evolve continuously with time. In our work, we encode the continuous time-dependence of networks in the evaluation of the epidemic threshold of a susceptible–infected–susceptible (SIS) process by studying an SIS model on tie-decay networks. We derive the epidemic-threshold condition of this model, and we perform numerical experiments to verify it. We also examine how different factors—the decay coefficients of the tie strengths in a network, the frequency of the interactions between the nodes in the network, and the sparsity of the underlying social network on which interactions occur—lead to decreases or increases of the critical values of the threshold and hence contribute to facilitating or impeding the spread of a disease. We thereby demonstrate how the features of tie-decay networks alter the outcome of disease spread.

"Disease Detectives: Using Mathematics to Forecast the Spread of Infectious Diseases"

Our article for teens and preteens about modeling the spread of infectious diseases just came out in final form. Here are some details.

Title: Disease Detectives: Using Mathematics to Forecast the Spread of Infectious Diseases

Authors: Heather Z. Brooks, Unchitta Kanjanasaratool, Yacoub H. Kureh, and Mason A. Porter

Abstract: The COVID-19 pandemic has led to significant changes in how people are currently living their lives. To determine how to best reduce the effects of the pandemic and start reopening communities, governments have used mathematical models of the spread of infectious diseases. In this article, we introduce a popular type of mathematical model of disease spread. We discuss how the results of analyzing mathematical models can influence government policies and human behavior, such as encouraging mask wearing and physical distancing to help slow the spread of a disease.

A Great 'Team' Page

The 'team' page at the Institute for Disease Modeling is spectacular!

Take a look at it for the short video clips!

(Tip of the cap to Carl Bergstrom.)

"A Two-Patch Epidemic Model with Nonlinear Relapse"

Another of my papers came out in final form today. Here are some details.

Title: A Two-Patch Epidemic Model with Nonlinear Relapse

Authors: Juan G. Calvo, Alberto Hernández, Mason A. Porter, and Fabio Sanchez

Abstract (English version): The propagation of infectious diseases and its impact on individuals play a major role in disease dynamics, and it is important to incorporate population heterogeneity into efforts to study diseases. As a simplistic but illustrative example, we examine interactions between urban and rural populations on the dynamics of disease spreading. Using a compartmental framework of susceptible–infected–susceptible (SIŜ) dynamics with some level of immunity, we formulate a model that allows nonlinear reinfection. We investigate the effects of population movement in a simple scenario: a case with two patches, which allows us to model population movement between urban and rural areas. To study the dynamics of the system, we compute a basic reproduction number for each population (urban and rural). We also compute steady states, determine the local stability of the disease-free steady state, and identify conditions for the existence of endemic steady states. From our analysis and computational experiments, we illustrate that population movement plays an important role in disease dynamics. In some cases, it can be rather beneficial, as it can enlarge the region of stability of a disease-free steady state.

Note: The published paper also has a Spanish version of the abstract.

What Happens in San José Stays in San José (2019 Edition)

I'll soon be going to San José, Costa Rica for the third time to work on a collaboration on dengue dynamics and control. I'll also be participating in a spiffy panel discussion, where I'll get to meet one of my coauthors in person for the first time.

Children to be Named Later (Best. Erratum. Ever.)

The excellent new book by Kiss, Miller, and Simon on epidemics and networks also has an erratum that is one of my all-time favorites. (See their website of errata.)

In fact, I think this error is a feature of the book, rather than a bug (especially given that I automatically think of Paul Erdős). By the way, the book itself is awesome, so go take a look at it. Here is a screenshot of the erratum.

(Tip of the cap to my Ph.D. student Yacoub Kureh for pointing this out to me in our meeting today. This erratum is an instant classic.)

What Happens in Paris Stays in Paris

I am making my first ever trip to France (aside from a few hours in an airport for a layover). I am adding a new country early in 2014, and I have at least one more new country for me on the docket for this year.

I am going to Paris to visit Vittoria Colizza at EPIcx Lab.

Epidemic Model of Zombie Outbreak

This is too good to make up.

Some mathematicians have recently published (though apparently in a non-prominent venue or at least one that is unfamiliar to me) the following epidemic model of a zombie outbreak. It uses the standard ODE compartment models used for studying disease dynamics, although they change some terminology to suit their "application". For example, the SIR model is now known as the SZR model. (The symbol "I" stands for "infected", whereas "Z" stands for zombie.)

Basically, I don't know whether to laugh or cry---well, to be honest, I'm doing a little bit of both right now. Talk about "awesome" research. Wow.

To be fair, if you take a look at the text, this paper appears to have arisen from a class project, and I bet the students involved had a lot of fun with the project and learned a lot. I think there do exist appropriate venues for publishing such papers, assuming that the paper is written in an expository manner so that, e.g., other students can benefit from it. This paper seems to have been published in a compendium about research on modelling of infectious diseases, which is not the venue where such an audience would typically look. (It would be more appropriate to write about this kind of playful "application" in a venue such as American Mathematical Monthly that university students actually read. Then I think there can be considerable benefit to such a paper, as it can suck in some of the younger crowd.)

(Tip of the hat to Mariano Beguerisse Díaz.)