Minimizing the epidemic final size while containing the infected peak prevalence in SIR systems

Sereno, Juan E.; Anderson, Alejandro; Ferramosca, Antonio; Hernandez‐Vargas, Esteban A.; González, Alejandro H.

doi:10.1016/j.automatica.2022.110496

Cited by 12 publications

(4 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Alternative control approaches for COVID-19 models include optimal control, using predetermined cost functions. For instance, the work [3] uses model predictive control to minimize the costs of mitigation strategies while ensuring that the capacity of a regional healthcare system network is not exceeded, [4] establishes the existence of optimal controls under transmission and treatment uncertainty, [20] derives optimal controls using social distancing as a control policy, the data-driven optimal control approach in [21] uses learning methods to estimate model parameters to forecast the evolution of an outbreak over short time periods and to provide scheduled controls, [22] uses an agestructured population compartmental finite-dimensional optimal control model to optimize vaccination policy to minimize deaths, the work [24] finds optimal strategies as combinations of implementing multiple non-pharmaceutical interventions, [25] derives optimal social distancing strategies using on-off social isolation strategies, [27] uses optimal control to optimize timings for two-dose vaccine roll outs, [30] uses optimal control methods to study trade-offs between lives saved versus reduced time under control, and [33] uses optimal control to minimize the epidemic final size while keeping the infected peak prevalence controlled at each time. The preceding works are notable, because policy makers generally have certain control objectives in mind that are not necessarily expressed in a mathematically rigorous way.…”

Section: 4mentioning

confidence: 99%

See 1 more Smart Citation

Feedback control of isolation and contact for SIQR epidemic model via strict Lyapunov function

Ito

Malisoff

Mazenc

2023

MCRF

View full text Add to dashboard Cite

<p style='text-indent:20px;'>We derive feedback control laws for isolation, contact regulation, and vaccination for infectious diseases, using a strict Lyapunov function. We use an SIQR epidemic model describing transmission, isolation via quarantine, and vaccination for diseases to which immunity is long-lasting. Assuming that mass vaccination is not available to completely eliminate the disease in a time horizon of interest, we provide feedback control laws that drive the disease to an endemic equilibrium. We prove the input-to-state stability (or ISS) robustness property on the entire state space, when the immigration perturbation is viewed as the uncertainty. We use an ISS Lyapunov function to derive the feedback control laws. A key ingredient in our analysis is that all compartment variables are present not only in the Lyapunov function, but also in a negative definite upper bound on its time derivative. We illustrate the efficacy of our method through simulations, and we discuss the usefulness of parameters in the controls. Since the control laws are feedback, their values are updated based on data acquired in real time. We also discuss the degradation caused by the delayed data acquisition occurring in practical implementations, and we derive bounds on the delays under which the ISS property is ensured when delays are present.</p>

show abstract

Section: 4mentioning

confidence: 99%

“…By separately considering the cases where ϵ satisfies |ϵ| ∞ ∈ [0, min{B, ψ ⋆ /4}) and where the preceding inclusion is violated, we can combine (33) with (34) to obtain…”

mentioning

confidence: 99%

Feedback control of isolation and contact for SIQR epidemic model via strict Lyapunov function

Ito

Malisoff

Mazenc

2023

MCRF

View full text Add to dashboard Cite

show abstract

“…Albi et al [31] put forward an optimal control problem of a socially structured Mathematics 2024, 12, 1484. https://doi.org/10.3390/math12101484 https://www.mdpi.com/journal/mathematics epidemic model in the presence of uncertain data to reduce the spread of epidemics by applying non-pharmaceutical intervention measures. Sereno et al [32] investigate how to minimize an epidemic's final scale while keeping the infected peak prevalence controlled at any time. Kuddus et al [33] perform a mathematical analysis of COVID-19 and find out the most effective control measure with the cost-benefit of the health economy.…”

Section: Introductionmentioning

confidence: 99%

Optimal Control for an Epidemic Model of COVID-19 with Time-Varying Parameters

2024

Mathematics

View full text Add to dashboard Cite

The coronavirus disease 2019 (COVID-19) pandemic disrupted public health and economies worldwide. In this paper, we investigate an optimal control problem to simultaneously minimize the epidemic size and control costs associated with intervention strategies based on official data. Considering people with undetected infections, we establish a control system of COVID-19 with time-varying parameters. To estimate these parameters, a parameter identification scheme is adopted and a mixed algorithm is constructed. Moreover, we present an optimal control problem with two objectives that involve the newly increased number of infected individuals and the control costs. A numerical scheme is conducted, simulating the epidemic data pertaining to Shanghai during the period of 2022, caused by the Omicron variant. Coefficient combinations of the objectives are obtained, and the optimal control measures for different infection peaks are indicated. The numerical results suggest that the identification variables obtained by using the constructed mixed algorithm to solve the parameter identification problem are feasible. Optimal control measures for different epidemic peaks can serve as references for decision-makers.

show abstract

“…During the COVID-19 outbreak, some public health measures were studied and various strategies were proposed to help mitigate the spread of SARS-CoV-2 that were considered realistic achievable scenarios. Utilizing SIR-type models, Sereno et al 15 explored strategies to minimize the total number of infections while simultaneously managing the peak prevalence of infected individuals and mitigating the impact of non-pharmaceutical interventions. Afshar-Nadjafi et al 16 simulated different stochastic networks to study seesaw lockdown scenarios with different levels of constraint, and they showed that the outbreak can be flattened by up to 120%, i.e., the duration of the peak can be shifted from 42 days to 92 days under softer alternatives instead of a complete restriction.…”

Section: Introductionmentioning

confidence: 99%

Assessing the impacts of vaccination and viral evolution in contact networks

Blanco-Rodríguez,

Tetteh,

Hernández-Vargas

2024

Sci Rep

View full text Add to dashboard Cite

A key lesson learned with COVID-19 is that public health measures were very different from country to country. In this study, we provide an analysis of epidemic dynamics using three well-known stochastic network models—small-world networks (Watts–Strogatz), random networks (Erdös–Rényi), and scale-free networks (Barabási–Albert)—to assess the impact of different viral strains, lockdown strategies, and vaccination campaigns. We highlight the significant role of highly connected nodes in the spread of infections, particularly within Barabási–Albert networks. These networks experienced earlier and higher peaks in infection rates, but ultimately had the lowest total number of infections, indicating their rapid transmission dynamics. We also found that intermittent lockdown strategies, particularly those with 7-day intervals, effectively reduce the total number of infections, serving as viable alternatives to prolonged continuous lockdowns. When simulating vaccination campaigns, we observed a bimodal distribution leading to two distinct outcomes: pandemic contraction and pandemic expansion. For WS and ER networks, rapid mass vaccination campaigns significantly reduced infection rates compared to slower campaigns; however, for BA networks, differences between vaccination strategies were minimal. To account for the evolution of a virus into a more transmissible strain, we modeled vaccination scenarios that varied vaccine efficacy against the wild-type virus and noted a decline in this efficacy over time against a second variant. Our results showed that vaccination coverage above 40% significantly flattened infection peaks for the wild-type virus, while at least 80% coverage was required to similarly reduce peaks for variant 2. Furthermore, the effect of vaccine efficacy on reducing the peak of variant 2 infection was minimal. Although vaccination strategies targeting hub nodes in scale-free networks did not substantially reduce the total number of infections, they were effective in increasing the probability of preventing pandemic outbreaks. These findings underscore the need to consider the network structure for effective pandemic control.

show abstract

Minimizing the epidemic final size while containing the infected peak prevalence in SIR systems

Cited by 12 publications

References 19 publications

Feedback control of isolation and contact for SIQR epidemic model via strict Lyapunov function

Feedback control of isolation and contact for SIQR epidemic model via strict Lyapunov function

Optimal Control for an Epidemic Model of COVID-19 with Time-Varying Parameters

Assessing the impacts of vaccination and viral evolution in contact networks

Contact Info

Product

Resources

About