Dose-dependent infection rates of parasites produce the Allee effect in epidemiology

Area of Science:

• Epidemiology
• Mathematical Biology
• Parasitology

Background:

• Standard epidemiological models often assume mass-action principles for microparasitic infections.
• These models typically consider constant infection rates, parasite virulence, and reproduction rates, independent of parasite dose.
• Empirical evidence suggests infection rates are sigmoidal, and host lifespan/parasite reproduction correlate negatively with parasite dose.

Purpose of the Study:

• To incorporate dose-dependent relationships into standard microparasitic infection models.
• To investigate the impact of these dose dependences on infection dynamics and parasite invasion.
• To determine the conditions required for parasite establishment in the presence of dose-dependent effects.

Main Methods:

• Development of a modified epidemiological model incorporating sigmoidal infection rates.
• Inclusion of negative correlations between parasite dose, host lifespan, and parasite reproduction rate.
• Analysis of the model to identify invasion thresholds and conditions for parasite establishment.

Main Results:

• The modified model exhibits an Allee effect, characterized by a critical invasion threshold for the parasite.
• Parasite strains require a basic reproductive rate substantially greater than 1 to establish infection, stricter than mass-action models.
• Negative correlations between parasite dose and host lifespan/parasite reproduction can facilitate parasite invasion by overcoming Allee dynamics.

Conclusions:

• Dose-dependent factors significantly alter microparasitic infection dynamics, leading to more restrictive invasion conditions.
• The Allee effect highlights the importance of initial parasite numbers or transmission rates for successful infection establishment.
• Understanding these dose-response relationships is crucial for accurate prediction and control of microparasitic diseases.