Uniformly accurate nonlinear transmission rate models arising from disease spread through pair contacts
| Autor: | Jonathan J. Wylie, Tom Chou |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
education.field_of_study
Transmission rate Population Models Biological 01 natural sciences 010305 fluids & plasmas Perturbation expansion Nonlinear system Nonlinear Dynamics Transmission (telecommunications) Susceptible individual Pairing 0103 physical sciences Humans Disease Susceptibility Statistical physics 010306 general physics education Disease transmission Mathematics |
| Zdroj: | Physical Review E. 103 |
| ISSN: | 2470-0053 2470-0045 |
| DOI: | 10.1103/physreve.103.032306 |
| Popis: | We derive and asymptotically analyze mass-action models for disease spread that include transient pair formation and dissociation. Populations of unpaired susceptible individuals and infected individuals are distinguished from the population of three types of pairs of individuals: both susceptible, one susceptible and one infected, and both infected. Disease transmission can occur only within a pair consisting of one susceptible individual and one infected individual. We use perturbation expansion to formally derive uniformly valid approximations for the dynamics of the total infected and susceptible populations under different conditions including combinations of fast association, fast transmission, and fast dissociation limits. The effective equations are derived from the fundamental mass-action system without implicitly imposing transmission mechanisms, such as those used in frequency-dependent models. Our results represent submodels that show how effective nonlinear transmission can arise from pairing dynamics and are juxtaposed with density-based mass-action and frequency-based models. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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