Disease spread in age structured populations with maternal age effects

Abstract

Fundamental ecological processes, such as extrinsic mortality, determine population age structure. This influences disease spread when individuals of different ages differ in susceptibility or when maternal age determines offspring susceptibility. We show that Daphnia magna offspring born to young mothers are more susceptible than those born to older mothers, and consider this alongside previous observations that susceptibility declines with age in this system. We used a susceptible-infected compartmental model to investigate how age-specific susceptibility and maternal age effects on offspring susceptibility interact with demographic factors affecting disease spread. Our results show a scenario where an increase in extrinsic mortality drives an increase in transmission potential. Thus, we identify a realistic context in which age effects and maternal effects produce conditions favouring disease transmission.

Keywords: Daphnia; Age; demography; ecology; epidemiology; evolution; immunity; maternal effects; modelling; senescence.

Figure 1

Both the original experiment (shown in black) and independent replication of the experiment (shown in grey) showing (a), proportion of infections resulting from exposure of the treatments groups from clutches 1, 2, 3 and 5, (b) reproductive output and (c) the effect of clutch number (maternal age at reproduction) on offspring body size.

Figure 2

The compartmental model with uninfected and infected groups of four age classes. UY;Y – young individuals with a young mother. UY;O – young individuals with an old mother. UO;Y– old individuals with a young mother. UO;O – old individuals with an old mother. m is the rate at which an individual goes from being a young individual to an old individual. b is the rate of transmission. d is the baseline death rate, with d +a representing baseline death rate plus a measure of virulence. Other parameters are r – maximum reproduction; K – carrying capacity; N – total population number; p ‐ the probability that non‐pathogen induced death of an infected individual will lead to transmission. As p. ramosa is only transmitted upon host death, death rates are included in the transmission terms.

Figure 3

Showing the changes in total population density with increased mortality (purple line). This is broken down into the age classes showing density of young individuals with young mothers (red line), young individuals with old mothers (yellow line), old individuals with young mothers (blue line) and old individuals with old mothers (green line). Due to parameterization of the model, the yellow and blue lines trace one another. Other parameters are r = 3; K = 1; m = 1/10.

Figure 4

Modelling outputs of the relationship between mortality and transmission potential ($R_0)$ with three different parameter values for p (extrinsic mortality of infected individuals contributing to transmission). p = 1 (yellow line), p = 0.5 (blue line) and p = 0 (red line). (a) No age effects or maternal age effects present, (b) Maternal age effects, (c) Age specific susceptibility, or (d) – Both maternal and age effects present. In the presence of no effects (a), the expected negative relationship between mortality and transmission potential is shown at all levels of extrinsic mortality. The presence of maternal age effects (b), age‐specific susceptibility (c) or both effects (d) within a population results in a humped relationship, where an increase in mortality initially increases transmission, due to the shift in density of susceptible individuals. This positive relationship between mortality and transmission potential is most pronounced at all levels of extrinsic mortality when both effects are present. Other parameters are: r = 3; K = 1; a = 1/5; m = 1/10; ${\mathrm{\beta }}_{Y,Y}$  = 3.5.