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Epidemic spread and bifurcation effects in two-dimensional network models with viral dynamics
H C Tuckwell1, L Toubiana, J F Vibert
1Epidémiologie et Sciences de l'Information, University of Paris VI, INSERM U444, 27 rue Chaligny, 75571 Paris Cedex 12, France. tuckwell@b3e.jussieu.fr
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 3, 2001
Summary
This study models viral spread in a 2D space, revealing that large epidemics can emerge unexpectedly even with few initial infections. Immunization shows diminishing returns beyond 20% of the population.
Area of Science:
- Epidemiology
- Mathematical Biology
- Network Modeling
Background:
- Previous network models of viral dynamics are extended to incorporate spatial distribution.
- Understanding viral transmission dynamics within host populations is crucial for public health.
- Host-pathogen interactions involve complex factors like viral load, immune response, and transmission rates.
Purpose of the Study:
- To develop and analyze a two-dimensional network model of viral dynamics.
- To investigate the impact of spatial distribution, demographic parameters, and initial infection density on epidemic spread.
- To evaluate the effectiveness of different immunization strategies on the final epidemic size.
Main Methods:
- A network model was developed with individuals placed on a 2D grid.
- Transmission dynamics incorporated saturating emission, a transmission array, and nonlinear absorption functions.
- Numerical simulations were used to study epidemic spread, threshold effects, and the impact of immunization.
Main Results:
- Threshold effects were identified in population viral load and epidemic spread, linked to bifurcations in viral-effector dynamics.
- Epidemic final size distribution is bimodal, heavily dependent on the initial number of infected individuals (N0).
- Immunization shows a nearly linear decline in the final percentage infected up to a 20% immunization rate, with diminishing returns thereafter.
Conclusions:
- Spatial distribution and demographic factors significantly influence viral spread, with critical thresholds for epidemic emergence.
- Large outbreaks are possible even with a low initial number of infected individuals, highlighting the unpredictable nature of epidemics.
- Targeted immunization strategies are effective, but benefits plateau beyond a certain rate, suggesting a need for optimized approaches.