Infection-induced increases to population size during cycles in a discrete-time epidemic model
Laura F Strube1,2,3, Shoshana Elgart4, Lauren M Childs5
1Department of Mathematics, Virginia Tech, 225 Stanger St, Blacksburg, VA, 24061, USA.
Journal of Mathematical Biology
|April 10, 2024
Summary
Introducing infection into population models can alter dynamics, creating different bifurcation structures and even causing population increases, known as the hydra effect, especially when the disease-free population cycles.
Area of Science:
- Ecology
- Mathematical Biology
- Epidemiology
Background:
- One-dimensional discrete-time population models (e.g., Logistic, Ricker) exhibit complex dynamics like periodicity and chaos.
- Incorporating epidemiological interactions into population models introduces novel and complex behaviors.
Purpose of the Study:
- To examine a discrete-time two-dimensional susceptible-infectious (SI) model with Ricker growth.
- To investigate how infection influences bifurcation structures and population dynamics.
- To analyze the occurrence of the 'hydra effect' in this SI model.
Main Methods:
- Numerical bifurcation analysis was employed.
- The study analyzed a two-dimensional discrete-time SI model with Ricker growth dynamics.
- Investigated the impact of infection on fecundity and mortality parameters.
Main Results:
- Infection introduction leads to distinct bifurcation structures compared to disease-free systems.
- The SI model can exhibit counter-intuitive increases in total population size (hydra effect).
- The hydra effect is observed even when infection alters fecundity or mortality, particularly when the disease-free population is in a cycle.
Conclusions:
- Discrete-time SI models with Ricker growth display complex dynamics influenced by infection.
- Infection can significantly alter population dynamics, leading to unexpected outcomes like the hydra effect.
- The study highlights the importance of considering epidemiological factors in population modeling to understand emergent behaviors.
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