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Stochastic models of a parasitic infection, exhibiting three basic reproduction ratios
1Abteilung Angewandte Mathematik, Universität Zürich, Switzerland. cl@luchsinger-mathematics.ch
Abstract:
Two closely related stochastic models of parasitic infection are investigated: a non-linear model, where density dependent constraints are included, and a linear model appropriate to the initial behaviour of an epidemic. Host-mortality is included in both models. These models are appropriate to transmission between homogeneously mixing hosts, where the amount of infection which is transferred from one host to another at a single contact depends on the number of parasites in the infecting host. In both models, the basic reproduction ratio R0 can be defined to be the lifetime expected number of offspring of an adult parasite under ideal conditions, but it does not necessarily contain the information needed to separate growth from extinction of infection. In fact we find three regions for a certain parameter where different combinations of parameters determine the behavior of the models. The proofs involve martingale and coupling methods.
Insights
This study explores two stochastic models of parasitic infection, one linear and one non-linear, incorporating host mortality. Findings reveal complex infection dynamics where the basic reproduction ratio alone doesn't predict epidemic growth or extinction.
Area of Science:
- Epidemiology
- Mathematical Biology
- Parasitology
Background:
- Parasitic infections pose significant public health challenges.
- Stochastic models are crucial for understanding disease dynamics and transmission.
- Existing models may not fully capture complex host-parasite interactions.
Purpose of the Study:
- To investigate two related stochastic models of parasitic infection.
- To analyze the influence of density-dependent constraints and host mortality.
- To determine factors governing infection growth and extinction.
Main Methods:
- Development and analysis of a linear and a non-linear stochastic model.
- Inclusion of host mortality and density-dependent transmission.
- Application of martingale and coupling methods for proofs.
Main Results:
- The basic reproduction ratio (R0) is insufficient to predict infection dynamics in all scenarios.
- Three distinct parameter regions dictate model behavior.
- Model outcomes depend on specific parameter combinations, not solely R0.
Conclusions:
- Parasitic infection dynamics are complex and influenced by multiple factors.
- R0 requires careful interpretation in density-dependent, host-mortality scenarios.
- Further research using these models can inform control strategies.