Passive and active field theories for disease spreading

Introduction to the show: ident: Genomics Radio. Generated commentary on the latest computational biology and genomics papers.

Ines: Hi, I'm Ines.

Marcus: And I'm Marcus, here with Yuki.

Ines: We're looking at the paper: "Passive and active field theories for disease spreading".

Marcus: Here's the gist of the paper. The SIR-DDFT model is an extension combining epidemiological compartmental models with dynamical density functional theory to explicitly account for social distancing in disease spreading, which allows researchers to investigate how non-reciprocal interactions affect epidemic dynamics in soft matter physics.

Ines: The gist The SIR-DDFT model is a combination of the susceptible-infected-recovered (SIR) model from epidemiology with dynamical density functional theory (DDFT) from nonequilibrium soft matter physics, which allows for an explicit modeling of social distancing Model Foundation The starting point is the very well-known SIR model developed in Ref.

22: (based on earlier work

51, 52: ) which describes the time evolution of the total number of susceptible (S¯), infected (¯I), and recovered (R¯) persons Incorporating Social Distancing via DDFT To tackle the problem where all particles diffuse freely without affecting each other in a human society due to social distancing being a repulsive interaction This leads to an RDDFT model capable of describing epidemic spreading The free energy functional F is given by F = Fid + Fexc + Fext (8) In the present context, repulsive interactions represent the effects of social distancing and isolation This is represented by including a contribution for social distancing Fsd and a contribution for self-isolation Fsi The excess free energy then reads Fexc = Fsd + Fsi (11) Epidemiological Extensions The SIR-DDFT model allows for several extensions motivated by epidemiological considerations 1.

Ines: Governmental interventions: This involves adding dynamic equations for the coefficients Csd and Csi based on the rectangular hysteresis model The physical idea is that the start and end of a shutdown is triggered if the number of infected persons ¯I passes threshold values ¯Istart and ¯Istop, respectively 2.

Paper summary: Ines: So we're looking at this paper "Passive and active field theories for disease spreading". It combines epidemiology with soft matter physics to model things like social distancing.

Marcus: Right. The main point is using a SIR-DDFT model, which takes the standard SIR model and adds dynamical density functional theory to explicitly include social distancing.

Yuki: What this means for us is that we can look at how non-reciprocal interactions affect disease spread through the lens of soft matter physics, which is usually about colloids and polymers.

Ines: The paper claims they extend this SIR-DDFT model both epidemiologically by adding things like vaccines, asymptomatic cases, reinfections, and mutations.

Marcus: And from the soft matter side, they incorporate noise and self-propulsion to make it a more active system. They even derive a phase field crystal model for a simpler description.

Ines: The simulation part is interesting because they look at how these epidemiological models are affected by non-reciprocal interactions using computer simulations of a zombie outbreak.

Marcus: That's what they did in Section V, showing the results of numerical simulations on that zombie outbreak scenario described by equations sixty and sixty-one <ref:2307.00437#pg2,the results of numerical simulations>.

Yuki: I wonder if this framework helps us understand how population genetics or community structure influences these spreading dynamics in a more physical way.

Ines: The paper focuses on modeling the dynamics of susceptible, infected, and recovered populations spatially rather than just total numbers. They use density fields S, I, and R to capture that distribution.

Marcus: They start with the standard SIR model where susceptibles get infected at a rate ceff times I with an effective contact rate ceff, and infected people recover at a rate w and die at a rate m <ref:2307.00437#pg2>.

Yuki: But the spatial distribution matters because it dictates how interactions happen locally. How does this spatial aspect change what we can infer about disease spread in a real population?

Ines: It means we're not just looking at aggregate numbers anymore; we're modeling where the people are, which directly affects contact rates. The paper introduces the free energy functional F, which includes terms for social distancing and self-isolation.

Marcus: They define this excess free energy as Fexc = Fsd plus Fsi, which represents the effects of social distancing and self-isolation in the system <ref:2307.00437#pg2>.

Yuki: So, when we talk about social distancing as a repulsive interaction in soft matter physics, what are we really trying to capture about human behavior?

Ines: They incorporate governmental interventions by adding dynamic equations for coefficients Csd and Csi based on the rectangular hysteresis model. This means contact restrictions aren't constant; they switch on and off depending on whether the infection number crosses certain thresholds <ref:2307.00437#pg3>.

Marcus: That transition logic, using those threshold values like Istart and Istop, is a physical way to model how interventions are imposed and lifted over time. It's not just a simple switch.

Paper summary: Yuki: And then there's the extension for vaccination, which moves people from the susceptible compartment to the recovered one in this model <ref:2307.00437#pg3>. How does that fit into tracking population immunity?

Ines: It also allows for reinfections by introducing a constant reinfection rate cR, where recovered persons can get infected again when they encounter an infected individual <ref:2307.00437#pg3>.

Marcus: They also extend this with fields for exposed and asymptomatic persons, E and A, which adds the incubation period and accounts for people who are infected but not showing symptoms <ref:2307.00437#pg3>.

Yuki: If we look at the mutation extension they include, IM and RM fields. Does this suggest that genetic drift or selective pressures play a role in how these new variants spread through the modeled environment?

Ines: Yes, they add equations for those fields like ∂tIM = ΓIM ∇ · ⃗ IM∇⃗ δF/δIM + cMSIM + cMRRIM − wMIM − mMIM <ref:2307.00437#pg3>.

Marcus: And then they layer in the soft matter physics stuff, adding noise terms to make it stochastic, and active matter where motion depends on an orientation vector that describes self-propulsion <ref:2307.00437#pg2>.

Yuki: That active matter part is interesting because it treats humans as self-propelled particles, which connects the epidemiology directly to physical properties of the material.

Ines: They even simplify things by proposing an SIR-PFC model, replacing the complex DDFT equations with a reference density ρ hat for a phase field crystal <ref:2307.00437#pg3>.

Marcus: So, when they ran those computer simulations on the zombie outbreak described by SZ-DDFT model equations sixty and sixty-one what did they find about the influence of Csz <ref:2307.00437#pg2>?

Ines: They found that Csz has no influence on the final number of susceptibles or zombies at all. What really matters in that simulation is only the kill rate kappa <ref:2307.00437#pg2>.

Yuki: That's a bit surprising, since they built up such a complex model involving many interactions and fields before finding that one parameter dominates the outcome so strongly.

Marcus: Yeah, it means for ending the outbreak, whether kappa is smaller or larger than five determines the result <ref:2307.00437#pg2>. It simplifies the massive model down to a very basic comparison between two numbers.

Ines: The paper shows that passive and active field theories can provide a way to see how these different physical concepts interact in disease spreading, even when we look at complex scenarios like zombie outbreaks <ref:2307.00437#pg2>.

Marcus: It suggests that the mathematical structure of the model itself, incorporating these non-reciprocal interactions, is what drives the outcome more than some of the finer details they added.

Yuki: For someone who only listens to this show, it means we can use physics concepts from soft matter to analyze complex epidemiological dynamics in a way that goes beyond just counting individuals in compartments.

Ines: This work, "Passive and active field theories for disease spreading", suggests that bridging the gap between epidemiology and soft matter physics opens up new ways to model dynamic spreading processes.

Conclusion: Ines: So this paper, "Passive and active field theories for disease spreading," takes the idea of describing how things spread through space, like germs, and puts it into a framework using soft matter physics concepts.

Marcus: Yeah, they're combining epidemiological models with density functional theory to explicitly model social distancing and other complex behaviors in disease dynamics.

Yuki: From a population genetics standpoint, I’m interested in how this spatial modeling of interactions fits into the larger picture of how disease spreads through human communities over time.

Ines: What the authors are doing is extending these models by adding things like vaccines, asymptomatic cases, reinfections, and even mutations to see how those factors play out spatially.

Marcus: And on the physics side they’re adding noise and self-propulsion to treat humans like active particles moving around, which makes the model more dynamic than just a static density field.

Yuki: So it's not just about counting people in compartments anymore; it's about modeling how movement and physical interactions shape the spread of an infection across a landscape.

Ines: They even simplify things by using a phase field crystal model, which is like taking a complex set of equations and turning them into something easier to compute for simulations.

Marcus: The simulation results on that zombie outbreak were pretty telling because they showed that the final outcome really depends on one thing—the kill rate kappa—not all those other interaction terms.

Yuki: That’s interesting because it suggests that for a massive event, the basic killing power is more important than the fine details of how people are interacting or what specific social distancing rules you have.

Ines: It points toward a focus on fundamental parameters like transmission rates and mortality in these complex systems, which is something we need to keep in mind when analyzing any disease model.

Marcus: It also shows that bridging those two fields—epidemiology and soft matter—can give us new ways to look at the underlying physical mechanisms driving these spreading processes.

Yuki: That connection between how particles move and how diseases spread could open up new avenues for understanding population health dynamics in a much more detailed way.

Ines: So this work suggests that using these field theories allows us to study disease spreading not just as a sequence of events, but as a physical process happening in space and time.