ABSTRACT 23 In social species where offspring are reared together in communal burrows or similar 24 structures, young animals typically do not engage in between-group contact during their 25 developmenta behavioural trait we call 'offspring with restricted between-group contact' 26 (ORC). The impact of this trait on the persistence of contagious pathogens that generate 27 lifelong immunity in their hosts is currently unclear. We hypothesize that in populations with 28 ORC, the formation, in groups, of a 'protective barrier' of only recovered adults, prevents the 29 transmission of this type of pathogens to the new susceptible hosts (i.e. young animals), 30 thereby increasing the probability of epidemic fade-out. We implement a spatially implicit 31 individual-based Susceptible-Infected-Recovered (SIR) model for a large range of host and 32 pathogen traits and show that the epidemic fade-out probability is consistently higher in 33 populations with ORC, especially when disease spread is fast (high basic reproduction 34 number R0). We also show that ORC can counteract the cost of group-living in terms of 35 disease risk to a greater extent than variation in other traits. We discuss our findings in 36 relation to herd immunity and outline how they could be used to implement efficient 37 management measures such as vaccinations. . 53 A social network can further be characterized by its modularity, that is, its degree of division 54 into modules such as social groups (e.g. clans, prides or troops) or subgroups (e.g. age classes 55 in the case of eusocial insects, Stroeymeyt et al. 2018 , also see Griffin and Nunn 2012, Sah et 56 al. 2017). Generally, a social network is considered to be highly modular, or to have a high 57 'community structure' (White et al. 2017 ) when individuals within one module are more 58 connected to each other than they are to individuals in other modules (Newman 2006 ). It has 59 been hypothesized that a highly modular social network can generally reduce disease risk in 60 group-living animals (Griffin and Nunn 2012, Nunn et al. 2015 ). Yet this view has been 61 recently challenged by a study which found that the beneficial effects of modularity on 62 disease fade-out are restricted to extreme cases of exceptionally high modularity, which are 63 rarely observed in natural systems (Sah et al. 2017) . 64 Here we investigate how highly modular social networks characterized by age-dependent 65 between-group contact affect pathogen spread and persistence. We focus specifically on 66 networks where young animals have no contact with members of other groups, and term this 67 life history trait 'offspring with restricted between-group contact' (ORC). 68 In contrast to most ungulate species for instance, in which precocial young follow their 69 mother shortly after birth (Lent 1974) , several group-living species rear their offspring in 70 communal burrows, nurseries, crèches or family groups within group territories or home 71 ranges for extended periods of time, during which time young rarely if ever contact 72 individuals of other groups. This includes for instance spotted hyenas Crocuta crocuta 73 (Kruuk 1972), African lions Panthera leo (Schaller 1972) transmission is frequency or density-dependent. For each specific combination of parameters, 105 we investigated two scenarios. First, we set up a baseline scenario in which rates of between-106 group contact were identical for individuals of all ages. Second, we investigated an ORC 107 scenario in which individuals below a given age-threshold could not contact members of 108 other groups, i.e. their rates of between-group contact were set to zero. This is simulating the 109 legal requirements of confinement put into action by authorities to limit the spread of 110 pandemics, e.g. during the COVID-19 pandemic; the closure of schools and prevention of 111 contact between young and elderly people, including within households (e.g. Anderson et al. 112 2020, Kelvin and Halperin 2020). Because ORC decreases R0, we adjusted the infection rate 113 in the baseline scenario such that the value of R0 was always identical in both scenarios to 114 insure that the emergence of a more efficient immunity barrier are directly related to the ORC 115 trait, and not to its mediated effect on R0. We discuss our results in relation to behavioural 116 mechanisms yielding herd immunity as well as the likely outcomes of altering social network 117 modularity through management measures.
Model description 120 The model description followed the ODD (Overview, Design concepts, Details) protocol for Table 1, where their   168 simulation values are also provided. 169 In the first process (pathogen transmission), the force of infection was influenced by i) the 170 age at first between-group contact, Age-contact, ii) the number (for density-dependent The second process (death) included two forms of mortality: the host intrinsic mortality (1-, 188 with  being the weekly survival probability) and the host mortality induced by the pathogen 189 (virulence ). Individuals who survived over the maximum infection length (IL) gained 190 immunity for the rest of their lives. 191 The third process (reproduction) was regulated by the carrying capacity of the host K. Births 192 occurred only in groups that were below a local breeding capacity, which was defined by the 193 maximum group size. The probability that an individual at a reproductive age of 2 years and 194 more (Age-repro ≥ 104 weeks) gave birth to one offspring was given by fage. and 195 corresponded to approximately 1 -3 offspring per year. 196 The fourth process (dispersal) described individuals which left their natal group as they 197 became reproductively mature. 198 In the last process (ageing), we updated the individual's state variable age as well as the time-199 span-infected counter. The initialization of the age of individuals was determined by a random exponential 202 distribution with a mean set at the age at first reproduction (Age-repro = 104 weeks, Table   203 1). All groups were set with a certain size and all individuals were set as susceptible, except 204 one who was set as infected. Pathogen invasion started stochastically with this one infected 205 individual chosen randomly in the initial population. The total population was at a carrying 206 capacity of 1000 individuals at the beginning of the simulations to make simulation runs 207 comparable, but the number of groups was given depending on the initialized number of 208 individuals per group (see also Table 1 ). (3) Reproduction 257 We assumed density-dependent reproduction. Reproduction only occurred if the group size 258 was below the carrying capacity of groups, i.e. the Group.size threshold (Table 1) . If 259 reproduction occurred, then every week, each adult which was older than Age-repro gave birth 260 to a single offspring with a probability fage. All individuals were born as susceptible, 261 independently of the infection status of their parent; hence, we did not consider vertical 262 transmission or immunity due to the transmission of (maternal) antibodies to offspring 263 (through e.g. milk) for a short period after birth. (Table   281 1). We also considered variation in the simulation values for the parameters characterizing 
Effects of restricting offspring between-group contact on epidemic fade-out probability 309 As theory predicts, epidemics faded-out at a R0 < 1, and did so regardless of the type of Table 2 for other examples). Our 427 results might also be applicable to cases where offspring are not stationary yet potentially 428 protected from between-group contacts by other types of 'barriers', such as behavioural ones. 429 This might include territorial space use of adults, e.g. troop formation in gorillas Gorilla g. . This is often difficult to verify in wild, free-ranging populations, as it requires 452 repeated serological samples to measure antibody levels even in old animals. Even so, we 453 expect our results to hold if immunity against the pathogen is maintained for several years. 454 The impact of the length of the protective period of immunization (lifelong or less) could also 455 be tested specifically with our model. branches: the left one corresponds to R0 < 7.5 and the right branch corresponds to R0 ≥ 7.5. 698 The values at the terminal nodes indicate differences in epidemic fade-out probabilities. 