arXiv 14 Apr 2020 · q-bio.PE · 4 citations (OpenAlex)
arXiv:2004.06680 · PDF · DOI · OpenAlex · Extracted main text
We study the problem of optimal control of the stochastic SIR model. Models of this type are used in mathematical epidemiology to capture the time evolution of highly infectious diseases such as COVID-19. Our approach relies on reformulating the Hamilton-Jacobi-Bellman equation as a stochastic minimum principle. This results in a system of forward backward stochastic differential equations, which is amenable to numerical solution via Monte Carlo simulations. We present a number of numerical solutions of the system under a variety of scenarios.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Pham, H.: Continuous-time Stochastic Control and Optimization with F… (2009) | 0.737 | 3 | 2 | 100% |
| 2 | Hansen, E., and Day, T.: Optimal control of epidemics with limited r… (2011) | 0.644 | 2 | 2 | 100% |
| 3 | Lesniewski, A., and Lesniewski, N.: Options on infectious diseases,… (2020) self | 0.644 | 2 | 2 | 100% |
| 4 | El Karoui, N., Peng, S. and Quenez, M. C.: Backward stochastic diffe… (1997) | 0.511 | 2 | 1 | 100% |
| 5 | Flemming, W. H., Soner, H. M.: Controlled Markov processes and visco… (1992) | 0.511 | 2 | 1 | 100% |
| 6 | Khasminskii, R.: Stochastic Stability of Differential Equations, Spr… (2012) | 0.511 | 2 | 1 | 100% |
| 7 | Leimkuhler, B., and Reich, S.: Simulating Hamiltonian Dynamics, Camb… (2004) | 0.511 | 2 | 1 | 100% |
| 8 | Doyle, A. C.: A Scandal in Bohemia (1891) included in | 0.405 | 1 | 1 | 100% |
| 9 | Anderson, R. M., and May, R. M.: Population biology of infectious di… (1971) | 0.405 | 1 | 1 | 100% |
| 10 | Bellman, R.: Dynamic Programming, Princeton University Press (1957) | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 19 scored citations.