Abstract
We study the dynamics of epidemics in a networked metapopulation model. In each subpopulation, representing a locality, disease propagates according to a modified susceptible-exposed-infected-recovered (SEIR) dynamics. We assume that individuals reduce their number of contacts as a function of the weighted sum of cumulative number of cases within the locality and in neighboring localities. We also assume that susceptible and exposed (pre-symptomatic and infectious) individuals can travel between localities. To investigate the combined effects of mobility and contact reduction on disease progression within interconnected localities, we consider a scenario with two localities where disease originates in one and is exported to the neighboring locality via travel of undetected pre-symptomatic individuals. We establish a lower bound on the outbreak size at the origin as a function of the speed of spread. We associate the behavior change at the disease-importing locality due to the outbreak size at the origin with the level of preparedness of the locality. Using the lower bound on the outbreak size at the origin, we establish an upper bound on the outbreak size at the importing locality as a function of the speed of spread and the level of preparedness for low mobility regimes. We show the accuracy of the bounds in determining critical levels of preparedness that stop the disease from becoming endemic at neighboring localities. Finally, we show how the benefit of preparedness diminishes under high mobility rates. Our results highlight the importance of preparedness at localities where cases are beginning to rise, and demonstrate the benefits of increase in contact reduction by considering the outbreaks in neighboring localities with severe, rather than weak, outbreaks.
Competing Interest Statement
The authors have declared no competing interest.
Funding Statement
Joshua S. Weitz was supported, in part, by a grant from the Army Research Office (W911NF1910384).
Author Declarations
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Data Availability
The code is available on Github page of the corresponding author.
https://github.com/ceyhuneksin/reacting_outbreaks_neighboring_localities