TY - JOUR

T1 - Expected Extinction Times of Epidemics With State-Dependent Infectiousness

AU - Bhimaraju, Akhil

AU - Chatterjee, Avhishek

AU - Varshney, Lav R.

N1 - Funding Information:
This work was supported in part by the NSF under Grant ECCS-2033900, in part by the Center for Pathogen Diagnostics through the ZJU-UIUC Dynamic Engineering Science Interdisciplinary Research Enterprise (DESIRE), and in part by the Department of Science and Technology, Government of India under Grants SERB/SRG/2019/001809 and INSPIRE/04/ 2016/001171.
Publisher Copyright:
IEEE

PY - 2022/5

Y1 - 2022/5

N2 - We model an epidemic where the per-person infectiousness in a network of geographic localities changes with the total number of active cases. This would happen as people adopt more stringent non-pharmaceutical precautions when the population has a larger number of active cases. We show that there exists a sharp threshold such that when the curing rate for the infection is above this threshold, the expected time for the epidemic to die out is logarithmic in the initial infection size, whereas when the curing rate is below this threshold, the expected time for epidemic extinction is infinite. We also show that when the per-person infectiousness goes to zero asymptotically as a function of the number of active cases, the expected extinction times all have the same asymptote independent of network structure. We make no mean-field assumption while deriving these results. Simulations on real-world network topologies bear out these results, while also demonstrating that if the per-person infectiousness is large when the epidemic size is small (i.e., the precautions are lax when the epidemic is small and only get stringent after the epidemic has become large), it might take a very long time for the epidemic to die out. We also provide some analytical insight into these observations.

AB - We model an epidemic where the per-person infectiousness in a network of geographic localities changes with the total number of active cases. This would happen as people adopt more stringent non-pharmaceutical precautions when the population has a larger number of active cases. We show that there exists a sharp threshold such that when the curing rate for the infection is above this threshold, the expected time for the epidemic to die out is logarithmic in the initial infection size, whereas when the curing rate is below this threshold, the expected time for epidemic extinction is infinite. We also show that when the per-person infectiousness goes to zero asymptotically as a function of the number of active cases, the expected extinction times all have the same asymptote independent of network structure. We make no mean-field assumption while deriving these results. Simulations on real-world network topologies bear out these results, while also demonstrating that if the per-person infectiousness is large when the epidemic size is small (i.e., the precautions are lax when the epidemic is small and only get stringent after the epidemic has become large), it might take a very long time for the epidemic to die out. We also provide some analytical insight into these observations.

KW - Epidemic modeling

KW - network analysis

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U2 - 10.1109/TNSE.2021.3131954

DO - 10.1109/TNSE.2021.3131954

M3 - Article

AN - SCOPUS:85120889029

SN - 2327-4697

VL - 9

SP - 1104

EP - 1116

JO - IEEE Transactions on Network Science and Engineering

JF - IEEE Transactions on Network Science and Engineering

IS - 3

ER -