Abstract
Different strains of influenza viruses spread in human populations during every epidemic season. As the size of an infected population increases, the virus can mutate itself and grow in strength. The traditional epidemic SIR model does not capture virus mutations and, hence, the model is not sufficient to study epidemics where the virus mutates at the same time as it spreads. In this work, we establish a novel framework to study the epidemic process with mutations of influenza viruses, which couples the SIR model with replicator dynamics used for describing virus mutations. We formulated an optimal control problem to study the optimal strategies for medical treatment and quarantine decisions. We obtained structural results for the optimal strategies and used numerical examples to corroborate our results.
| Original language | English (US) |
|---|---|
| Article number | 103 |
| Journal | Games |
| Volume | 9 |
| Issue number | 4 |
| DOIs | |
| State | Published - Dec 1 2018 |
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Keywords
- Epidemic process
- Evolutionary games
- Optimal control
- SIR model
- Virus mutation
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics
Cite this
Optimal control of heterogeneous mutating viruses. / Gubar, Elena; Taynitskiy, Vladislav; Zhu, Quanyan.
In: Games, Vol. 9, No. 4, 103, 01.12.2018.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Optimal control of heterogeneous mutating viruses
AU - Gubar, Elena
AU - Taynitskiy, Vladislav
AU - Zhu, Quanyan
PY - 2018/12/1
Y1 - 2018/12/1
N2 - Different strains of influenza viruses spread in human populations during every epidemic season. As the size of an infected population increases, the virus can mutate itself and grow in strength. The traditional epidemic SIR model does not capture virus mutations and, hence, the model is not sufficient to study epidemics where the virus mutates at the same time as it spreads. In this work, we establish a novel framework to study the epidemic process with mutations of influenza viruses, which couples the SIR model with replicator dynamics used for describing virus mutations. We formulated an optimal control problem to study the optimal strategies for medical treatment and quarantine decisions. We obtained structural results for the optimal strategies and used numerical examples to corroborate our results.
AB - Different strains of influenza viruses spread in human populations during every epidemic season. As the size of an infected population increases, the virus can mutate itself and grow in strength. The traditional epidemic SIR model does not capture virus mutations and, hence, the model is not sufficient to study epidemics where the virus mutates at the same time as it spreads. In this work, we establish a novel framework to study the epidemic process with mutations of influenza viruses, which couples the SIR model with replicator dynamics used for describing virus mutations. We formulated an optimal control problem to study the optimal strategies for medical treatment and quarantine decisions. We obtained structural results for the optimal strategies and used numerical examples to corroborate our results.
KW - Epidemic process
KW - Evolutionary games
KW - Optimal control
KW - SIR model
KW - Virus mutation
UR - http://www.scopus.com/inward/record.url?scp=85060309903&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85060309903&partnerID=8YFLogxK
U2 - 10.3390/g9040103
DO - 10.3390/g9040103
M3 - Article
AN - SCOPUS:85060309903
VL - 9
JO - Games
JF - Games
SN - 2073-4336
IS - 4
M1 - 103
ER -