A Stochastic Tick-Borne Disease Model: Exploring the Probability of Pathogen Persistence

Area of Science:

• Epidemiology
• Mathematical Biology
• Ecology

Background:

• Tick-borne diseases pose significant public health and ecological challenges.
• Existing deterministic models may not fully capture the inherent randomness in disease transmission dynamics.
• Understanding the role of host movement is crucial for predicting disease spread.

Purpose of the Study:

• To formulate and analyze a stochastic epidemic model for tick-borne disease transmission.
• To compare the dynamics predicted by stochastic and deterministic models.
• To assess the impact of randomness and host introduction pathways on disease outbreak probabilities.

Main Methods:

• Utilized a continuous-time Markov chain approach to develop a stochastic model.
• Based the stochastic model on an existing deterministic metapopulation model.
• Employed multitype Galton-Watson branching processes and numerical simulations for analysis.

Main Results:

• Significant differences were observed between stochastic and deterministic model predictions.
• A disease outbreak is more probable when introduced by infected deer compared to infected ticks.
• Stochasticity introduces variability not captured by deterministic approaches.

Conclusions:

• Stochastic modeling provides crucial insights into tick-borne disease dynamics.
• Host movement, particularly by infected deer, plays a critical role in disease expansion.
• These findings underscore the importance of considering host behavior in disease control and prevention efforts.