• compartmental epidemiological model;
  • contamination by the ground;
  • host–virus system dynamics;
  • multi-annual cycles


  • 1
    Using field data published in the literature, we investigated pathogen dynamics and conditions of persistence in a mathematical model of the bank vole (Clethrionomys glareolus)–Puumala hantavirus system. The host population is assumed to have a 3-year periodic cycle. The duration of very low host density is critical for virus transmission and survival.
  • 2
    Field epidemiological data strongly suggested a transmission of the hantavirus by the contaminated environment. We thus studied whether this ‘indirect’ transmission affected the virus persistence in the host population.
  • 3
    The model assumptions were derived from the following conditions found in the literature: (1) there is no additional mortality nor fecundity loss due to the virus in infected hosts, thus the cyclic demographical pattern is not due to the virus; (2) no remission has been observed, thus we did not consider the existence of recovered individuals; (3) adult females are territorial and juveniles disperse to find a new territory and reach sexual maturity. A fragmented landscape was assumed to occur: individuals can live in favourable or unfavourable patches.
  • 4
    The model was a compartmental model; the population was structured into susceptible or infectious individuals. We considered two age classes, juveniles and adults, and two sites (populations) connected by juvenile dispersal.
  • 5
    Model dynamics accurately predicted the cyclic trend in disease prevalence as observed in epidemiological studies. They also showed that indirect transmission significantly increased the probability for the virus to persist during the low-density period of the host population. More precisely, even a low survival rate of the virus outside the host was sufficient to decrease extinction risk of the infection by stochastic events.
  • 6
    Elasticity analysis showed a high robustness of the model to changes in the parameters of indirect transmission but a high sensitivity to changes in adult density.