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Publications of Eduardo D. Sontag jointly with M. Sadeghi
Articles in journal or book chapters
  1. M.A. Al-Radhawi, M. Sadeghi, and E.D. Sontag. Long-term regulation of prolonged epidemic outbreaks in large populations via adaptive control: a singular perturbation approach. IEEE Control Systems Letters, pp 10.1109/LCSYS.2021.3083983, 2021. [PDF] Keyword(s): epidemiology, COVID-19, COVID, systems biology.
    Abstract:
    Initial hopes of quickly eradicating the COVID-19 pandemic proved futile, and the goal shifted to controlling the peak of the infection, so as to minimize the load on healthcare systems. To that end, public health authorities intervened aggressively to institute social distancing, lock-down policies, and other Non-Pharmaceutical Interventions (NPIs). Given the high social, educational, psychological, and economic costs of NPIs, authorities tune them, alternatively tightening up or relaxing rules, with the result that, in effect, a relatively flat infection rate results. For example, during the summer in parts of the United States, daily infection numbers dropped to a plateau. This paper approaches NPI tuning as a control-theoretic problem, starting from a simple dynamic model for social distancing based on the classical SIR epidemics model. Using a singular-perturbation approach, the plateau becomes a Quasi-Steady-State (QSS) of a reduced two-dimensional SIR model regulated by adaptive dynamic feedback. It is shown that the QSS can be assigned and it is globally asymptotically stable. Interestingly, the dynamic model for social distancing can be interpreted as a nonlinear integral controller. Problems of data fitting and parameter identifiability are also studied for this model. The paper also discusses how this simple model allows for a meaningful study of the effect of population size, differences in the policy between countries, vaccinations, and the emergence of second waves.


  2. M. Sadeghi, J.M. Greene, and E.D. Sontag. Universal features of epidemic models under social distancing guidelines. Annual Reviews in Control, 2021. Note: To appear (preprint in bioRxiv, 2020, https://www.biorxiv.org/content/10.1101/2020.06.21.163931v2). [PDF] Keyword(s): epidemiology, COVID-19, COVID, systems biology.
    Abstract:
    Different epidemiological models, from the classical SIR system to more sophisticated ones involving population compartments for socially distanced, quarantined, infection aware, asymptomatic infected, and other individuals, share some remarkable dynamic characteristics when contact rates are subject to periodic or one-shot changes. In simple pulsed isolation policies, a linear relationship is found among optimal start time and duration for reduction of the infected peak. If a single interval social distancing starts too early or too late it will be ineffective with respect to decreasing the peak of infection. On the other hand, the nonlinearity of epidemic models leads to non-monotone behavior of the peak of infected population under periodic relaxation policies. This observation led us to hypothesize that an additional single interval social distancing at a proper time can significantly decrease the infected peak of periodic policies, and we verified this improvement.


  3. M. Sadeghi, M.A. Al-Radhawi, M. Margaliot, and E.D. Sontag. No switching policy is optimal for a positive linear system with a bottleneck entrance. IEEE Control Systems Letters, 3:889-894, 2019. Note: (Also in Proc. 2019 IEEE Conf. Decision and Control.). [PDF] Keyword(s): entrainment, switched systems, ribosome flow model, traffic systems, nonlinear systems, nonlinear control.
    Abstract:
    We consider a nonlinear SISO system that is a cascade of a scalar "bottleneck entrance" with a stable positive linear system. In response to any periodic inflow, all solutions converge to a unique periodic solution with the same period. We study the problem of maximizing the averaged throughput via controlled switching. We compare two strategies: 1) switching between a high and low value, and 2 ~using a constant inflow equal to the prescribed mean value. We show that no possible switching policy can outperform a constant inflow rate, though it can approach it asymptotically. We describe several potential applications of this problem in traffic systems, ribosome flow models, and scheduling at security checks.


Internal reports
  1. M. Sadeghi, M.A. Al-Radhawi, M. Margaliot, and E.D. Sontag. On the periodic gain of the Ribosome Flow Model. Technical report, bioRxiv 2018/507988, 2018. [PDF] Keyword(s): systems biology, biochemical networks, ribosomes, RFM.
    Abstract:
    We consider a compartmental model for ribosome flow during RNA translation, the Ribosome Flow Model (RFM). This model includes a set of positive transition rates that control the flow from every site to the consecutive site. It has been shown that when these rates are time-varying and jointly T-periodic, the protein production rate converges to a unique T-periodic pattern. Here, we study a problem that can be roughly stated as: can periodic rates yield a higher average production rate than constant rates? We rigorously formulate this question and show via simulations, and rigorous analysis in one simple case, that the answer is no.



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Last modified: Thu Jun 3 23:14:07 2021
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