Relation of seasonal birth pulses and maternal immunity with viral invasion and persistence: A case study of Hendra virus infection in a population of black flying foxes (Pteropus alecto)

Increasing outbreaks of emerging infectious diseases, originating from wildlife, has intensified interest in understanding the dynamics of these diseases in their wildlife reservoir hosts. Until recently, the effect of seasonal birth pulses and subsequent waning of maternally derived antibodies on epidemics in a wild mammal population has received little attention and has remained obscure. In this study, we explore how population structure, influenced by seasonal breeding and maternally derived immunity, affects viral invasion and persistence, using a hypothetical system loosely based on Hendra virus infection in black flying foxes (Pteropus alecto). We used deterministic epidemic models to simulate transient epidemics, following viral introduction into an infection-free population, with a variety of timings within a year and different levels of pre-existing herd immunity. Moreover, we applied different levels of birth synchrony and different modelling methods of waning maternal immunity to examine the effect of birth pulses and maternally derived immunity, both individually and in combination. The presence of waning maternal immunity dispersed the supply time of susceptible individuals in seasonally breeding populations, hence diminishing the effect of birth pulse. Dampened epidemics, caused by waning maternal immunity, made viral invasion and persistence easier. This study enhanced our understanding of viral invasion, persistence, and timing of epidemics in wildlife populations.

A modelling approach was established to describe the infectious period by an exponential 66 distribution, which is a classical method to transfer individuals across infection stages [9] and is 67 implicit in a simple differential equation SIR (susceptible-infectious-immune) model with 68 constant rate parameters [10]. Although the exponential distribution has been used widely for 69 computational ease, efforts towards finding more realistic methods to model the infectious period 70 resulted in the development of gamma-distributed infectious periods [11]. Wearing, Rohani (12) 71 addressed the significance of modelling the infectious and latency periods in predicting the 72 impact of infectious diseases. Although maternal immune period has been modelled using a 73 conventional exponential distribution, for both infectious and latency periods, the effect of this 74 method on the model outcomes has been poorly studied. Therefore, it is worthwhile to explore 75 the mechanism of generation of different epidemic modelling outcomes by an exponential and a 76 gamma distribution. This would, in turn, help to determine whether the method of modelling 77 waning maternal immunity is an important influence on model behaviour.

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Bats (Order: Chiroptera) have been identified as natural reservoirs of many emerging 79 infectious diseases of public health concern [13, 14]. They do not appear to suffer from many of 80 these infections, especially those caused by viruses, despite the obvious exceptions of rabies and    year, the SIR model showed seasonally clustered epidemic peaks, although this feature was 279 weakened in the exponential MSIR model, and hardly observed in the gamma MSIR model (Fig.   280 3). When herd immunity was similar to herd immunity of an endemic equilibrium state in SIR 281 model, the epidemic peaks mostly appeared within one year after viral introduction in the SIR 282 model with birth pulses. However, in the exponential MSIR model, the epidemic peaks were 283 delayed compared to those in the SIR model and showed a broader spectrum of timings than in 284 the SIR model ( Supplementary Fig. S3). In the gamma MSIR model, after viral introduction, the 285 epidemics required a specific period to reach their peak, and the periods until epidemic peaks 286 were delayed compared to those in the exponential MSIR model. 287 Fig. 3. Timing of epidemic peaks. Peak of birth pulses occurred on 1st November. The colour 288 key shows the month when the epidemics reach their peaks following viral introduction into a 289 population. Layout of panels is explained in Fig. 1.

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Taken together, in the exponential MSIR model, the epidemic patterns appeared to be 291 more affected by seasonal birth pulses than by maternally derived immunity. In the exponential 292 MSIR model, we modelled the number of maternally immune bats to decrease by as much as 293 1/255 of the remaining maternally immune bats every day. As a result, most juvenile bats lost 294 their maternal immunity soon after birth, rather than 255 days after birth ( Supplementary Fig.   295 S2). When herd immunity was high and maternally immune newborns were more common than 296 susceptible newborns, the temporal trend of epidemics was expected to change noticeably at 255 297 days after a birth pulse (the period of maternally derived immunity) rather than at the birth pulse 298 (see Supplementary Fig. S4 for the number of individuals in each compartment across time).
299 However, the number of infectious individuals began to rise at the time of birth pulses, which 300 could probably be attributed to the exponential method of modelling the loss of maternally 301 derived immunity. In comparison, the gamma MSIR model showed a more enhanced effect of 302 maternally derived immunity (Error! Reference source not found.). In the gamma MSIR 303 model, loss of maternally derived immunity seemed to occur mainly at 255 days after birth.
304 Therefore, the impact of maternally derived immunity in determining epidemic pattern was much 305 higher than in the exponential MSIR model. Moreover, the two relatively separate timings 306 ensured a steady supply of susceptible individuals throughout the year, decreasing the extent of 307 seasonal clustering of epidemic peaks. Another reason for birth pulses having a stronger impact 308 on epidemics than did loss of maternally derived immunity was that the temporal synchrony of 309 birth pulses was higher than that of loss of maternally derived immunity. Although more 310 susceptible hosts were supplied from the loss of maternally derived immunity than from birth 311 pulses, the tighter span of the latter relative to the former had a high impact on epidemic patterns.
312 Figure 4. Supply of susceptible individuals from birth pulses and waning maternal immunity. 313 Layout of panels is explained in Figure 1. The number of days since the last birth pulse before 314 viral introduction until the viral introduction into a colony was 10, and herd immunity of the 315 population was 0. 360 Results of the gamma MSIR model should not be interpreted as demonstrating a more accurate 361 prediction than that by the exponential MSIR model; it merely shows that substantially different 362 modelling results can be generated depending on whether the loss of maternally-derived 363 immunity is exponentially or gamma-distributed. Therefore, appropriate modelling of when 364 maternally immune newborns lose their passive immunity, depending on species and pathogens 365 against emerging infectious diseases is expected to help improve the prediction of disease 366 outbreaks.

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Although this study modelled epidemics in a single population, the results obtained should 368 be considered in the context of metapopulation structure, since this study assumed SIR dynamics