TY - JOUR
T1 - Separate seasons of infection and reproduction can lead to multi-year population cycles
AU - Hilker, F. M.
AU - Sun, T. A.
AU - Allen, L. J.S.
AU - Hamelin, F. M.
N1 - Publisher Copyright:
© 2020 Elsevier Ltd
PY - 2020/3/21
Y1 - 2020/3/21
N2 - Many host–pathogen systems are characterized by a temporal order of disease transmission and host reproduction. For example, this can be due to pathogens infecting certain life cycle stages of insect hosts; transmission occurring during the aggregation of migratory birds; or plant diseases spreading between planting seasons. We develop a simple discrete-time epidemic model with density-dependent transmission and disease affecting host fecundity and survival. The model shows sustained multi-annual cycles in host population abundance and disease prevalence, both in the presence and absence of density dependence in host reproduction, for large horizontal transmissibility, imperfect vertical transmission, high virulence, and high reproductive capability. The multi-annual cycles emerge as invariant curves in a Neimark–Sacker bifurcation. They are caused by a carry-over effect, because the reproductive fitness of an individual can be reduced by virulent effects due to infection in an earlier season. As the infection process is density-dependent but shows an effect only in a later season, this produces delayed density dependence typical for second-order oscillations. The temporal separation between the infection and reproduction season is crucial in driving the cycles; if these processes occur simultaneously as in differential equation models, there are no sustained oscillations. Our model highlights the destabilizing effects of inter-seasonal feedbacks and is one of the simplest epidemic models that can generate population cycles.
AB - Many host–pathogen systems are characterized by a temporal order of disease transmission and host reproduction. For example, this can be due to pathogens infecting certain life cycle stages of insect hosts; transmission occurring during the aggregation of migratory birds; or plant diseases spreading between planting seasons. We develop a simple discrete-time epidemic model with density-dependent transmission and disease affecting host fecundity and survival. The model shows sustained multi-annual cycles in host population abundance and disease prevalence, both in the presence and absence of density dependence in host reproduction, for large horizontal transmissibility, imperfect vertical transmission, high virulence, and high reproductive capability. The multi-annual cycles emerge as invariant curves in a Neimark–Sacker bifurcation. They are caused by a carry-over effect, because the reproductive fitness of an individual can be reduced by virulent effects due to infection in an earlier season. As the infection process is density-dependent but shows an effect only in a later season, this produces delayed density dependence typical for second-order oscillations. The temporal separation between the infection and reproduction season is crucial in driving the cycles; if these processes occur simultaneously as in differential equation models, there are no sustained oscillations. Our model highlights the destabilizing effects of inter-seasonal feedbacks and is one of the simplest epidemic models that can generate population cycles.
KW - Difference equations
KW - Host–pathogen dynamics
KW - Neimark-Sacker bifurcation
KW - Pathogen-driven outbreak
KW - Quasi-periodic oscillation
KW - SI model
KW - Seasonal population dynamics
UR - http://www.scopus.com/inward/record.url?scp=85078134926&partnerID=8YFLogxK
U2 - 10.1016/j.jtbi.2020.110158
DO - 10.1016/j.jtbi.2020.110158
M3 - Article
C2 - 31926973
AN - SCOPUS:85078134926
SN - 0022-5193
VL - 489
JO - Journal of Theoretical Biology
JF - Journal of Theoretical Biology
M1 - 110158
ER -