The complexity of dynamic host networks.

Steve W. Cole

David E. Geffen School of Medicine at UCLA, the UCLA AIDS Institute,

the Norman Cousins Center, and the UCLA Molecular Biology Institute. Division of Hematology-Oncology Department of Medicine 11-934 Factor Building David Geffen School of Medicine at UCLA Los Angeles CA 90095-1678 coles@ucla.edu (310) 267-4243 To appear in T. S. Deisboeck, J. Y. Kresh, & T. Kepler (Eds.), Complex systems science in biomedicine. Published by Kluwer Academic – Plenum Publishers, New York.

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Disease is generally analyzed as a biological process, but sickness is also an experience. This chapter

analyzes the impact of that experience on the course of epidemics with an eye toward its evolutionary

significance. A large research literature has sought to understand the “lifestyle strategies” of parasites

(Dobson, 1988), but the hosts they colonize are often modeled as vacuous mobile resource patches that

incubate pathogens and disseminate them randomly throughout society before prematurely expiring. We

all have our problems, but this seems a bit severe. In reality, most organisms change their behavior during

periods of illness (Dantzer et al., 2001; Hart, 1988). These responses are often analyzed in terms of their

benefits for the afflicted, but they also have the potential to create a type of “social immune response” that

protects the healthy by altering patterns of interpersonal contact. Aggregated over large numbers of

individuals, these changes amount to transient distortions in the structure of social networks.

Disease-reactive network dynamics may stem from strategic intervention by a central authority (e.g.,

quarantine), but they can also develop as an emergent property of simple behavioral rules operating at the

individual level (e.g., avoid sick people). In fact, vertebrate biology appears to have evolved molecular

signaling pathways to generate disease-reactive behavior without any explicit reasoning by a host.

Diagnosis and treatment also change the functional connectivity of a disease transmission network, as do

variations in host resistance or pathogen virulence. In homogenous social networks, individual

disease-reactive behavior aggregates into fairly simple nonlinear feedback at the population level.

Vertebrate social structures are actually quite heterogeneous, and dynamic linkage can produce highly

complex behavior in such heavily structured systems. The present studies seek to understand how the

neural substrates of disease-reactive social behavior might have evolved in tandem with biological immune

responses to alter host population structure under the ecological press of socially transmitted disease.

The results presented here come from a series of epidemics simulated in ActiveHost – an

agent-based modeling system for analyzing interactions between biological and behavioral determinants of

health. The general architecture is summarized in the Appendix. Within each agent, sub-models represent

host-pathogen interactions at the cellular and molecular level, and multiple overlapping social networks

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structure between-agent interactions that may transmit disease, convey disease-blocking interventions, or

modify the behavioral processes that integrate activity among various networks. The system also includes a

framework for modeling evolutionary dynamics via age-dependent reproduction and noisy transmission of

physiologic and behavioral parameters from parent to child. ActiveHost was developed to model

contagious “lifestyle” diseases such as smoking-induced cancer or heart disease, but the present chapter

focuses on the simpler problem of predicting the spread of a fatal virus. Three empirical themes emerge.

First, as shown in Figure 1, the net effect of disease-reactive social and biological structures is to force

kinetically stable epidemics into highly unstable regimes (Figure 1B vs. C). This not only changes the

expected toll of an epidemic but it also expands the range of possible outcomes – not always for the better

from the host’s perspective (Figure 1D). The second generalization arises from this increased leverage as

small changes in individual behavior acquire greatly magnified significance for population survival (either

the host or pathogen population; Figure 1D). This accelerates the evolution of disease-reactive behavior at

the network level without requiring large changes at the level of individual genetics. Finally, the

combination of destabilized kinetics and accelerated adaptation leaves disease trajectories highly resistant

to analysis by conventional algebraic models (Figure 1E). In fact, the disease trajectories observed in active

host systems would be hard to predict by any means at all because they show the strong sensitivity to small

perturbations that is frequently taken as a hallmark of chaos (although these systems are not at all chaotic in

a technical sense; Figure 1F). The fundamental basis for such jumpy “catastrophic” dynamics lies in the

synergistic interactions among several simple characteristics of vertebrate social behavior and biology.

Host network structure

Most dynamic models in epidemiology implicitly assume that disease spreads within a homogenous

network of randomly linked hosts (Anderson, 1982). This approach fares reasonably well in some cases

(e.g., mosquito-borne malaria), but it fails to accurately forecast the spread of illnesses that depend on close

physical contact, such as HIV or hepatitis, or those involving a major behavioral risk component, such as

malignant melanoma or lung cancer. The AIDS epidemic in particular motivated the consideration of more

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structured social networks in which each agent is connected to only a few others (sparse connectivity) and

individuals are clustered in their pattern of social contact (blocked networks; Figure 2). Much attention has

focused on “small world” networks in which a few individuals are linked to many others, and “giant

components” can develop to virtually ensure a transmission path between any two individuals (Newman,

Watts & Strogatz, 2001; Watts & Strogatz, 1998). Other systems analyzed include “tribe” or “subculture

blocks” in which small groups of individuals are highly interconnected and only sparsely linked to other

groups, “continuous bands” in which individuals are linked within smooth adjacency neighborhoods, and

“defector blocks” in which most links are reciprocal but a limited number of infidelities connect one

member of a pair to another pair. In these structured networks, disease dissemination rates differ

substantially from those seen under random homogeneous mixing (Figure 2G vs. H-L) and are often much

more variable. The sparseness of a network itself becomes a dynamic characteristic as the development of

biological immunity or death removes individuals from the system of transmitters following a certain period

of infectiousness. As a result, epidemics can easily burn out (exhaust all locally available hosts) over large

areas of the population (Figures 1D, 2I, and 2K). How soon this actually occurs depends on small random

variations in linkage between sub-populations, and it is difficult to predict during the early phase of an

epidemic how quickly or even whether it will consume an entire host society (Figure 1D and E).

Temporal contact dynamics

The temporal dynamics generated by transient infectiousness are compounded by the fact that the

social interactions that transmit disease can also vary significantly over time. We each know hundreds of

people, but on any given day we interact with only a small number of them. The links we do realize are

clustered in both time and social space because we generally interact with a small and stable social core on

most days (e.g., family members and immediate co-workers). The vast majority of potential links are

realized only rarely. This “small world” temporal structure implies a functional decrease in network

connectivity per unit time, but it is not equivalent to removing low-frequency links because the network

retains a capacity for occasionally making big jumps in disease distribution (Figure 2H vs. I, and Figure 3 A

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vs. B). How soon this happens is again hard to predict, and the problem is compounded by the fact that the

temporally sparse areas of our personal social networks are especially reactive to illness (see below; Figure

3B vs. C).

Host behavioral dynamics

All network structural dynamics stem fundamentally from the dynamic behavior of individual hosts.

One factor that would seem to play a major role is a healthy person’s conscious avoidance of the sick, either

at the behest of health authorities or through their own spontaneous social quarantines. However, the

potential value of this mechanism is undermined by the fact that many pathogens are transmissible for days

or even years before any signs of illness emerge to provoke social withdrawal (e.g., viral upper respiratory

infections, HIV, or the “infectious” habit of smoking). Most visible symptoms are generated by the immune

response, rather than the pathogen, and thus require at least a day or two to develop. Quarantines also

demand extreme vigilance on the part of a large number of hosts if they are to effectively protect a

population, or even a specific individual. Given the high degree of clustering in social networks, A can

infect B quite certainly by transmitting disease to their mutual friends C, D, and E, no matter how studiously

B avoids A. Thus, B’s health depends on the simultaneous diligence of C, D, and E, and all require some

overt sign of disease to trigger withdrawal from A. Figure 4A shows that even when pathogens produce

instantly visible sickness, uninfected individuals must detect and avoid those who are infectious with an

extremely high rate of success to halt an epidemic.

Surprisingly, the most decisive disease-containing network dynamics do not stem from the

self-protective behavior of the healthy, but from the involuntary behavior of the sick. It has recently been

discovered that proinflammatory cytokines – the signaling molecules that initiate an immune response –

also prompt the brain to unleash an integrated package of “sickness behaviors” which immobilize us with

fatigue, malaise, and myalgia, and substantially crimp our social and reproductive motivation (Dantzer et al,

2001; Hart, 1988). Sickness behavior is typically analyzed in terms of its advantage for the recovery of the

individual, but its most significant contribution may lie in the protection of the group. Even small

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reductions in contact can substantially impede the spread of infection through a sparse network (Figure

5A-C). Self-generated quarantines are also likely to be more efficient than socially imposed ones because

we generally feel sick sooner than we look it (Figure 4B-D), and because the motivation for altered behavior

emerges from a biologically impacted person who tracks (is) the source of infection, rather than depending

upon the simultaneous conscientiousness of many potential targets who face an as yet unrealized threat.

Interestingly, sick people are more likely to defer contact with strangers or low-frequency partners than they

are to avoid their core social contacts (especially family). From an evolutionary perspective, this would

seem to set our closest genetic relatives at a competitive disadvantage. However, it also prevents large

jumps of disease through social space, and thus efficiently protects the population as a whole (Figures 5B

vs. C, and 5D). Sickness behavior and the reception of cytokine signals by the brain appear to constitute

one example in which evolution has encoded an emergent property of an entire social network in the

molecular biology of the individual.

Host resistance dynamics

In addition to changes in social behavior, internal physiologic dynamics also influence the effective

connectivity of a disease transmission network. One example involves the effects of physical or

psychological stress, which can impair biological immune function and thus render individuals more

vulnerable to infection (Ader, Cohen & Felten, 1995; Ader, Felten & Cohen, 2001; Sapolsky, 1994).

Reduced resistance is tantamount to increasing the number of exposures that can transmit full-blown

disease, and thus functionally increases the connectivity of a disease-transmission network in the vicinity of

a stressed individual (Figure 6A-D). Impaired resistance in even a small fraction of the population can

substantially accelerate the course of an epidemic throughout an entire society. An interesting variant of

this problem arises when host resistance depends upon an individual’s degree of social linkage. In addition

to pathways for disease distribution, social relationships are also major sources of sustenance, and host

resistance is known to diminish in individuals with little social contact (Cassel, 1976; House, Landis &

Umberson, 1988). Any attempt to decrease exposure to disease by reducing social interaction may thus be

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undermined by increased vulnerability to infection (Figure 6D vs. E). Contact-dependent resistance is

especially problematic in heavily clustered populations because much of one’s social network may fall ill

simultaneously. Total contact levels can be maintained by re-deploying links to new partners, but this

increases the real connectivity of the network and is especially counterproductive when the redeploying

agents are asymptomatically infected.

It should be noted that all disease-reactive network dynamics fundamentally stem from individual

biological immune responses. Inflammatory biology generates the illness signs that prompt the healthy to

withdraw from the sick, the sickness behaviors that prompt the sick to withdraw from the healthy, and the

leukocyte responses that modulate host resistance and functional connectivity. Even when the immune

response fails to save a given body from disease (e.g., Ebola virus), it may still effectively protect a

population by triggering changes in social contact. An ironic corollary is that the diseases most disastrous

for an individual are generally the least dangerous to society as a whole because their spectacular visibility

generates the most pronounced changes in network structure. A more sobering corollary suggests that

pathogens acquiring the capacity to undermine neural reception of inflammatory signals may enjoy a

powerful selective advantage.

Transmission of resistance: Multi-level networks

In addition to altering social contact with those already ill, host networks also respond to disease by

developing preventive technological or behavioral interventions (e.g., safe sex, antibiotics, and vaccines).

However, the networks distributing such interventions are often structured differently from those

distributing disease. For example, the socio-economic network that controls access to antiretroviral

medications is quite incongruent with the network that currently transmits HIV. Such misalignments can be

analyzed by superimposing a second “intervention network” upon a population of hosts already connected

by a dynamic exposure network. More realistic variants might include a host-specific proclivity to utilize

the intervention, which may in depend upon a third “media” network distributing perceived vulnerability.

Multilevel networks provide a platform for analyzing a variety of sociocultural dynamics that may impact

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physical health, including socially selective stressors, differential access to medical care, culturally

motivated avoidance of diagnosis or treatment (e.g., failure to be tested for HIV due to stigma), social

transmission of health risk behaviors (e.g., smoking), and the globalization of personal behavior (e.g.,

homogenization of health beliefs, social values, lifestyle, and behavior; Garrett, 1994). Multilevel networks

also provide a context for analyzing interactions between host behavior and the biology of developing

disease, such as gene x diet interactions in atherosclerosis or the evolution of pathogens and immune

responses within behaviorally structured niches. Evolving variants of ActiveHost, for example, mimic

observed data in developing more powerful immune systems for sexually promiscuous individuals (Nunn,

Gittleman & Antonovics, 2000). In the context of disease-reactive social behavior, evolutionary analyses

also show a strong selective pressure for the development of social norms that isolate individuals during

times of illness. These norms need to be transmissible from parent to child for population-level selection,

but they need not be genetically encoded. In fact, dissemination of such norms via superimposed

intervention networks enjoys considerable selective advantage over genetic transmission due to enhance

speed of norm dispersal.

Complexity from synergy

Disease-reactive social behavior creates a temporal sparseness to social networks that combines

with structural sparseness to create transient social firewalls at the interface between infected and

uninfected segments of society. This has the net effect of discretizing continuous disease dynamics. A

pathogen that kills all members of a subpopulation before they can convey it to the super-population does

not suffer a quantitative reduction in penetrance; it becomes extinct. Sparse dynamics can cut the other

way, of course, with a few random links carrying the potential to connect an isolated outbreak to a

system-wide giant component (the “patient zero” problem; Garrett, 1994). These quantal dynamics

constitute the primary reason that linear algebraic models have proven so poor in predicting the course of

emerging epidemics. Linear statistical models forecast the future range of an epidemic based on its past

variation, but reactive host networks show increasingly jumpy dynamics as the size of an epidemic grows

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(Figure 1E). Initially smooth disease trajectories thus provide little grounds for predicting whether host or

pathogen populations will perish first (Figure 1D). Sparsity-driven discretization represents the basic

engine of this unpredictability by generating frequent opportunities for the bifurcation of trajectories (e.g.,

Figures 1C, 3C, 4D, 5B, 6B and 6E). Even epidemics that have thoroughly “burnt into” a population can

suddenly sinter out or explode because they are maintained in a perpetual state of “knife-edge” criticality by

reactive network dynamics (Figure 1D).

Evolutionary considerations

In the context of such highly leveraged systems, weak interventions can have powerful effects

(Gladwell, 2000). The strength of an intervention is often analyzed in terms of its individual impact, but the

key to protecting a network lies in breadth and consistency. Perfect protection of an individual has little

impact on an epidemic if disease can reach the same destination through another path (recall the stringent

efficiency requirements for a successful social quarantine; Figure 4A). On the other hand, even weak

individual protection can generate strong herd immunity if it is widely enough distributed (Anderson, 1983;

Burnet & White, 1972). The pre-eminent value of consistency suggests that there should be strong selective

pressure for development of heritable genetic structures that reduce social contact during infection, even if

the individual impact is small. In fact, this is just what is seen in evolving ActiveHost models such as the

one portrayed in Figure 7. This system represents disease-reactive social behavior as the product of a

nervous system that listens in on inflammatory signals and stochastically reduces social interaction in

proportion to a heritable “receptor sensitivity” parameter. Note that this neuro-behavioral response evolves

only after strong biological inflammatory responses have emerged to provide an underlying disease-sensing

apparatus. These results are consistent with the observation that vertebrate physiology has dedicated

substantial molecular resources to communication between the disease-sensing immune system and the

behavior-controlling nervous system (Blalock, 1994; Dantzer et al., 2001; Pulandren et al, 2001). Similar

selective pressures may have structured the evolving mammalian brain to prefer small clustered social

systems rather than larger herds (Figure 2E and K). Neither structural nor temporal sparsity alone slows an

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epidemic much, but their combination can be decisive. In the model analyzed in Figure 1, for example, the

joint effects of clustered social structure and disease-reactive behavior are equivalent to a 60-fold increase

in the strength of biological immunity.

The later comparison highlights one powerful motivation for developing disease-reactive social

behavior – to protect us from our own immune systems. Biological immune responses evolve increasing

power as long as they are cost-free, but inflammatory reactions are both energetically expensive and

potentially self-destructive. Strong immune responses exact a significant toll on inclusive fitness by

increasing the incidence of autoimmune disease, septic shock, and impaired fertility as the body rejects the

“tissue graft” that is a fetus (Weiss, 2002). Costly inflammation creates a powerful selective advantage for

behavioral immune responses that respond to the same disease-sensing molecular apparatus without

directly damaging host tissue (Figure 7). The costs of this behavioral response pertain mainly to the

survival value of social contact for the afflicted individual. In this regard, the selective withdrawal of social

contact from all but the sick person’s closest genetic relatives makes sense, as it is those contacts who stand

to gain the most from nursing the sick back to health. Analyses show that any other arrangement provides a

poorer return on investment for the caregiver and creates sub-optimal selective pressure for the

amplification of disease-reactive behavior. In the sense that social immune responses spare us from having

to develop more aggressive biological immune responses, sickness behavior can be construed as evolving to

protect us from our own leukocytes when provoked by pathogens. The sick are unlikely to take much

consolation from the fact that their immune systems are synthesizing most of their suffering to protect

others. However, from an evolutionary standpoint, it is proper to consider the more malevolent immune

response they have been spared.

The present studies examine the evolution of “sickness behavior” in the context of agent-based

simulations, but illness-reactive behavior can also be analyzed in more traditional algebraic models

(Anderson, 1982). When the contact rates that mix susceptible and infected individuals vary as a function

of the number currently infected, this can damp epidemics that would otherwise oscillate, shift the basal

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prevalence of disease, or kick stable epidemics into truly chaotic behavior, all depending upon the exact

specification of the feedback function (nonlinear? time-lagged?) and whether or not it affects other

parameters in addition to the mixing rate (e.g., do falling contact rates also reduce host resistance?).

However, agent-based analyses have several advantages over purely algebraic analyses in analyzing the

emerging epidemic problem. First, complex real-world social structures are more easily encoded in explicit

interaction matrices (e.g., Figure 2) than they are in analytically tractable continuous functions that

modulate population-wide mixing rates. This is especially helpful in analyzing the impact of small

spontaneous behavior changes generated in reaction to locally available information. Agent models also

provide an opportunity to analyze network-mediated distribution of recursive operators that reshape

individual behavior, host-pathogen dynamics, or population interaction matrices depending upon the

realized course of an epidemic (e.g., dispersing and reconstituting groups). A third advantage is the natural

discreteness of agent-based models in regions of temporal-spatial sparseness. As noted above, this is key to

understanding the epidemic-extinguishing behavior of dynamic host networks, and natural discretization

reduces the likelihood that minor, seemingly ignorable boundary conditions will propagate into large

prediction errors. Figure 1D shows a prototypic example – an epidemic simultaneously subject to all of the

influences considered above, including a complex clustered social structure with a small number of

inter-block contacts, behavioral reactions to disease by both sick and uninfected individuals, heterogeneous

basal host resistance that varies as a function of social contacts. The observed disease trajectories show

knife-edge dynamics, with epidemics burning slowly through a population for a variable period of time

before either collapsing or exploding. This “time bomb” kinetic behavior is critical to recognize in public

health decision-making, but would not be readily apparent in the “expected value” disease trajectory

generated by algebraic models, which shows only slowly rising epidemic (mean trend in Figure 1D and

dashed prediction limits in Figure 1E). A simpler example is seen in the contrast between panels A and C in

Figure 1. Mean trajectories are comparable, but host populations consistently survive in panel A whereas

large segments of society are often annihilated in C. The difference is again critical from a public health

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perspective (not to mention an evolutionary one), but not particularly evident in the mean trajectories.

When multiple dynamic regimes are present, the expected value trajectory may not represent any of the

dynamic regimes actually observed (e.g., Figure 1C, 3C, and 4D). In contrast to the “mean + standard

error” prediction bands from purely algebraic models, agent-based systems have some considerable

advantages in forcing the recognition of such qualitative variability in disease kinetics.

Over the history of interactions between vertebrates and their parasites, each is believed to have

played a significant role in structuring the behavior of the other (Burnet & White, 1972; Dobson, 1988; May

& Anderson, 1983; Pulendran et al., 2001). The present studies suggest that a similar reciprocal dynamic

may have occurred in the evolution of the immune and nervous systems. As the biochemical cross-talk

between these two systems becomes increasingly appreciated, a teleologic perspective has emerged to

suggest that each system inhibits the other in an effort to maximize its own claim on organismic resources

(Hart, 1988; Sapolsky, 1994). The present analyses support an opposing view – that biologically-induced

sickness behavior creates a social immune response that works in synergy with leukocyte responses to

defend a genome at the species-wide level. From this perspective, the jaggedly unpredictable disease

trajectories seen in many of the examples above testify to a ferociously pitched battle between a socially

defended host and a socially predatory pathogen. Such battles have undoubtedly played a significant role in

shaping the evolution of human social and immune processes, and the present studies highlight the

profound selective advantage for the emergent coordination among those systems.

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Acknowledgements

This work was supported by the National Institutes of Allergy and Infectious Disease (AI49135, AI52737),

the James L. Pendelton Charitable Trust, and a visiting scholarship from the Santa Fe Institute for Complex

Systems.

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Figure Captions

Figure 1. Complex dynamics in sparse networks. Trajectories of 100 evolving epidemics are plotted as

they enter a population of 300 agents clustered in blocks of 3, with 1 agent in each block also connected to

an agent in an adjacent block. Compared to the disease kinetics observed under basal conditions (A), the

addition of a single additional random contact for every 30th individual results in substantial acceleration in

mean disease penetrance (heavy line) and the collapse of predictability (B). When disease-reactive network

dynamics are superimposed (C), mean penetrance rates return to basal levels but the dynamic regime

remains highly unstable. Three attractor trajectories emerge including (1) an explosive depletion of the

majority of hosts, (2) a slow steady burn through the population, and (3) rapid extinction of the pathogen

with survival of the vast majority of hosts. Note that the mean trajectory does not coincide with any of the

regimes actually observed. (D) “Knife-edge” dynamics emerge in the same system when sick individuals

withdraw at random from 50% of their potential contacts (instead of selectively avoiding those most distant

as in C). Host/pathogen equilibrium is virtually impossible to attain under these circumstances and one

population or the other rapidly becomes extinct. Which occurs is difficult to predict on the basis of the

epidemic’s early behavior (E). Linear statistical analyses fail to accurately forecast epidemic trajectories

due to highly unsmooth derivatives (dashed lines represent a 95% prediction interval based on ARIMA

1,1,0 time series analysis of the first 30 observations). In a plot of the number of infected hosts at time t vs.

t-1 (F), the phase space of the epidemic is neither classically chaotic (smooth-curved) nor random stochastic

(scattered), but migrates noisily around the autoregressive major diagonal. In each of these examples,

contacts are realized at an average rate of 1 per unit time with a probability inversely proportional to the

square of the social distance (summing to 100% per unit time), the agent is infectious for 1 time unit before

the appearance of illness and 3 thereafter, and network reactions to disease include sick individuals

withdrawing contact with partners more than 2 units of social space distant (i.e., outside their own block of

3) and healthy individuals avoiding overtly sick individuals with a success rate of 50%. Hosts begin with

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resistance of .2 (probability of infection given exposure) that drops to .05 individuals with no social contact

in the previous time epoch.

Figure 2. Social structure and disease propagation. Connectivity structures are plotted for a homogenous

randomly linked population (A) and several structured alternatives, including a reciprocal binary system

with defectors (B), a sparse network (C), a small-world network of one-to-many mappings (D), a block

structure with random inter-connections among blocks (E), and a continuous adjacency band (F). Points

represent contacts with the potential to transmit disease from a source (horizontal axis) to a target (vertical

axis), and all targets are connected to at least one source. Disease propagates through alternative contact

structures at very different rates despite the fact that the total number of links realized per unit time is

equivalent (1 in G-L). Thin lines represent realized mortality trajectories for each system, and heavy lines

show the average. Trajectories achieving a flat slope before 100% mortality indicate epidemics that have

burned out (pathogen extinction), whereas those reaching 100% indicate host extinction. When each host

reallocates one potential contact to a stable dyad (H) rather than a random partner (G), population survival

rates increase substantially. However, such effects are not equivalent to reducing the total number of

potential contacts (I) because the network retains the capacity for occasionally generating large leaps in

disease distribution. Even a small number of highly connected individuals can undermine a population’s

protection from disease, as in a small world network where possible contact numbers for each individual

follow a power-law distribution between 1 and 5 (J). In contrast, organization of social contacts into highly

clustered blocks can significantly retard disease propagation even when total possible links are 5-fold

greater than those of a randomly connected network (10 vs. 2 in K vs. G). Smooth adjacency networks with

the same number of links show an intermediate phenotype (L), with disease substantially decelerated

relative to a random homogenous system (G) but still marching inexorably through the population. All

results come from a population of 100 hosts initially exposed to 2 infected individuals (Source 1 and 2).

Individuals remain infectious for 2 units of time before departing the network, and all examples are based

on realizing one potentially infectious contact per unit time.

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Figure 3. Effects of temporal sparseness. Temporally sparse social contact is modeled by generating a

fixed set of possible contacts for each individual and realizing a constant number per unit time according to

a specified probability model. This has a substantial impact on disease propagation through even highly

vulnerable social structures such as the small world network (all links realized in A vs. a random 50% in B;

note difference in rates of host population extinction). Compared to a uniform probability of realizing any

possible contact (B), increased probability of realizing more proximal links results in considerably

enhanced individual survival (solid lines = mean) (C). These examples come from epidemics initiated by 3

infected individuals in the midst of a 200-host population with a small world contact distribution ranging

from 1-5 possible contacts per individual for a total of 496, and an infectious duration of 1 time unit. In (B),

each link is realized with a probability of 50% per unit time for all individuals, and in (C), the probability of

realizing each link is an average of 50% that varies between 0 and 1 depending upon the squared social

distance between source and target.

Figure 4. Social quarantine. Effects of healthy individuals’ withdrawal from sick contacts (social

quarantine) were modeled in a homogenous random network with 1 of 3 potential contacts realized at

random in each of 50 time epochs. Uninfected individuals must avoid infected individuals with high rates

of success to avoid population extinction (A; mean + standard error percentage of host populations

surviving the epidemic). Relative to a constant-contact network (B), social systems that dynamically

withdraw contact from overtly sick individuals (C) (those infected for more than 2 units of time in this

example) experience considerable population survival advantages. Social withdrawal by infected

individuals (D) is even more effective in containing an epidemic because they can typically detect illness

before signs are apparent to others (e.g., after 1 time unit of infection here). In all simulations, 2 initially

infected individuals distribute a pathogen within a population of 1000 hosts, hosts are infectious for 3 time

units, and each realizes 3 randomly assigned contacts with a probability of .25 per unit time.

Figure 5. Sickness behavior. Effects of sick individuals’ withdrawal from social contact (self-quarantine)

were modeled on a small world network in which each agent realizes a single randomly selected contact per

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unit time from a set of possible contacts numbering from 1 to 10 according to a power law. The pathogen is

infectious for 1 time unit before a stricken individual feels ill and another 3 time units subsequently, and

each of the 300 hosts has a resistance of .5 (1 - probability of infection given exposure). Disease readily

penetrates a nonreactive small world network to kill an average 94% of hosts within 50 time units (A). In

contrast, the population is significantly protected when sick individuals reduce their social contact rates by

10% for all partners (B). Protective effects are even more pronounced when sick individuals selectively

withdraw contacts from their most socially distant partners (C). The same number of links is withdrawn in

(B) vs. (C), and the only difference is the distance-dependent probability function in (C). Considerable

population survival benefits accrue even if individuals maintain contact with large number of individuals in

their vicinity (supporting survival of the afflicted) and defer contact only with quite distant interaction

partners (D). Such results imply there may be considerable selective pressure for biological mechanisms

that reduce social contact during sickness.

Figure 6. Dynamic host resistance and population protection. Dynamic host resistance is modeled by

varying the probability of infection given exposure. Compared to a population with no resistance (A), a

constant resistance of .5 (B) (50% probability of infection given exposure) substantially reduces disease

propagation. When resistance is constant across individuals, disease trajectories are often bimodal with

either hosts or pathogens going extinct quickly. When individual resistance varies randomly about the same

mean level (C) (resistance randomly realized on the uniform interval 0-1), populations are considerably less

vulnerable to extinction and epidemic trajectories vary more uniformly across the space of potential

outcomes. Under these conditions, the addition of illness-reactive link dynamics (D) (e.g., uninfected

individuals can evade one visibly sick contact per unit time) can be especially decisive. However, when

host resistance depends in part on the number of social contacts realized (E), protective effects of reducing

exposure can be offset by increased vulnerability to infection via remaining contacts (who may be

infectious but not visibly sick). Note the rapid bifurcation of disease trajectories in (E), with either host or

pathogen populations quickly proceeding to extinction. All examples come from epidemics introduced into

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a population of 100 hosts, each realizing 1 contact per unit time from a set of possible contacts defined by

clustered blocks of 10 supplemented by 3 random connections throughout the population. The pathogen is

infectious for 1 time unit prior to visible illness and victims remain infectious for 2 subsequent time units.

Figure 7. Evolution of disease-reactive social behavior. A population of 100 individuals, each randomly

linked to 5 others, is attacked at time 0 by a fatal infection that is transmissible for 2 time units prior to the

appearance of symptoms and 18 time units subsequently. The host population begins with a inflammatory

response of 0 (all exposures result in infection), and parents pass on to their progeny that resistance level

supplemented by 10% noise (i.e., progeny inflammatory response = parental response * exp(Normal(0,.1)).

Inflammation is linearly related to resistance (50% of exposures are resisted when inflammatory response =

.5) and it is costly in the sense that individual life span is shortened by its square (.5 inflammation results in

a 25% reduction in average life span). Sickness behavior is modeled as a multiplicative link between the

magnitude of the inflammatory response and the fractional reduction in social contacts realized during

inflammation (sickness behavior gain parameter = 1.0 initially for all individuals, with parental gain value

passed on to progeny with 5% noise as described above for inflammatory response). Each individual

produces 2 progeny at random times between 13 and 40 years of age and, in the absence of infection, dies of

other causes at a normally distributed age with mean 40 and SD 10. Population-wide levels of the

inflammatory parameter and the sickness behavior gain parameter are averaged over 20 simulations of 250

time units (~10 generations). The light line shows strong selective pressure for increased inflammatory

responses that begins to decelerate at ~40% resistance as the costs of septic shock, autoimmunity, and

infertility begin to outweigh the benefits of infectious disease protection. In contrast, the sickness behavior

gain parameter (dark line) shows slow initial growth that begins to accelerate as inflammatory responses

become more pronounced (the log of the mean sickness gain parameter is plotted for comparison with the

linear inflammatory parameter). During the early phase of the biological immune response’s evolution

(0-100 time units), there is little selective pressure to link social behavior to inflammatory responses.

However, once inflammatory responses begin to reach their cost-induced limits, considerable selective

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benefit accrues to those who reduce social behavior during inflammatory reactions. Interestingly, this type

of evolution shows considerable inertia. Under conditions of this simulation, the infectious pathogen was

generally forced into extinction ~150 time units after introduction. Continued increases in the mean

sickness behavior gain parameter stem from changes in the age structure of the population as the progeny of

relatively sensitive individuals represent a growing preponderance of the reproductively-aged. This

dynamic approaches an asymptote at ~250 time units, when the last of the pathogen-exposed generation die

of natural causes. Because the sickness behavior gain parameter multiples the effects of biological

inflammation, it fails to evolve in the absence of an evolving inflammatory response. In the absence of

sickness behavior, the biological immune response evolves slightly more rapidly and reaches a slightly

higher asymptotic equilibrium. Such results imply that vertebrates may have been “spared” higher rates of

inflammatory disease by the emergence of CNS-mediated behavioral responses to proinflammatory

cytokines.