Abstract
Random walkers on a two-dimensional square lattice are used to explore the spatio-temporal growth of an epidemic. We have found that a simple random-walk system generates non-trivial dynamics compared with traditional well-mixed models. Phase diagrams characterizing the long-term behaviors of the epidemics are calculated numerically. The functional dependence of the basic reproductive number R_{0} on the model’s defining parameters reveals the role of spatial fluctuations and leads to a novel expression for R_{0}. Special attention is given to simulations of inter-regional transmission of the contagion. The scaling of the epidemic with respect to space and time scales is studied in detail in the critical region, which is shown to be compatible with the directed-percolation universality class.
Highlights
Random walkers on a two-dimensional square lattice are used to explore the spatio-temporal growth of an epidemic
While these models have been successful in describing an ideal dynamics of epidemic spread, they do not account for inhomogeneity: an infected person has higher probability to transmit the disease to a member of their household[3,4] or to a person in their locale
The current paper focuses on a simple random-walk model that lends itself to analytical analysis, in order to explore epidemic properties that arise in the presence of simple spacial dynamics
Summary
Random walkers on a two-dimensional square lattice are used to explore the spatio-temporal growth of an epidemic. Classic epidemiological m odels[1,2] often assume panmictic populations: every infected person has an equal chance to affect any other person in the population While these models have been successful in describing an ideal dynamics of epidemic spread, they do not account for inhomogeneity: an infected person has higher probability to transmit the disease to a member of their household[3,4] or to a person in their locale. The local neighborhoods of both susceptible and infected persons are dynamic—they vary in space and time depending on the local state of the epidemic These spatio-temporal inhomogeneities are studied in this paper. The second approach, in contrast, requires a small number of well-defined parameters and provides a sound intuition about their effects on the outcome It is especially useful when planning interventions and policy changes, or investigating various “what if ” scenarios.
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