Schedule

We will review some recent progress on two fronts. First, we discuss a recently developed model of SIS epidemic propagation over hypergraphs. For simplicial and higher-order interactions, we show how a new dynamical behavior domain appears: both a disease-free equilibrium and an endemic equilibrium co-exist and are locally asymptotically stable. Second, we discuss modeling and analysis aspects for the multi-group SIR model. We present analysis results on transient behavior, threshold conditions, stability properties, and asymptotic convergence. In both cases, we pay special attention to monotonicity and contractivity properties of the resulting dynamical models.

In the context of an infectious disease outbreak like the global SARS-CoV-2 pandemic, predicting the course of the epidemic is of paramount importance to plan an effective control strategy and to determine its impact. Multiple population-wide non-pharmaceutical interventions are possible, including social distancing, testing and contact tracing. We propose a SIDARTHE epidemic model for the COVID-19 outbreak, which considers eight stages of infection: susceptible (S), infected (I), diagnosed (D), ailing (A), recognized (R), threatened (T), healed (H) and extinct (E). The model distinguishes between infected individuals depending on whether they have been diagnosed and on the severity of their symptoms. The distinction between diagnosed and non-diagnosed infected is important, because diagnosed individuals are isolated, hence less likely to spread the disease, and can explain misperceptions of the case fatality rate and of the epidemic spread. Being able to predict the amount of patients that will develop life-threatening symptoms is important, since the disease frequently requires hospitalisation (and even Intensive Care Unit admission) and challenges the healthcare system capacity. We show how the basic reproduction number can be redefined in the new framework, thus capturing the potential for epidemic containment. Simulation results are compared with real data on the COVID-19 epidemic in Italy; the analysis of different possible scenarios suggests the effectiveness of combined social-distancing measures and widespread testing and contact tracing to control the pandemic.

The ongoing COVID-19 pandemic is caused by a novel coronavirus that was only identified in December 2019. Due to the novelty of the virus and the speed at which it is currently sweeping the world, the questions we have are constantly changing. Is social distancing working? How effectively did we 'flatten the curve' back in March? Is airline travel safe? When will this all be over? As we gather data and learn more about the virus, our questions will also continue to evolve. This talk will look at how various tools from Systems and Control Theory and Network Science can be used to model and analyze the spread of the virus across different regions with the questions above in mind. Unlike most existing compartmental models that assume well mixed populations or populations with known degree distributions, we will discuss network models at both the individual (person-to-person contacts) level and the region level (mobility between different cities/states by car/train/plane). In particular we will discuss which models are most suitable for addressing which types of socially relevant questions, and how the models can be used to make projections and policy recommendations.

In traditional compartmental epidemic models, after recovery from an infection, agents return to the susceptible state or they acquire full immunity to reinfection. We present a model for spreading over a network of heterogeneous agents that generalizes existing models to accommodate realistic conditions in which agents may acquire only partial or possibly compromised immunity after exposure to an infection. Reproduction numbers that account for network structure and heterogeneity provide the means to distinguish different behavioral regimes and can be used to design control strategies to mitigate spreading, even when resources are scarce. For example, in the bistable regime, not accounted for in traditional models, if measures are not taken, there can be a rapid resurgent epidemic after what looks like convergence to an infection-free state. To investigate the implications of reactive strategies, such as quarantining and social distancing, we present an active control model in which contact rate is controlled in continuous time as a feedback function of low-pass filtered observations of level of infection in the population. In homogeneous populations, this feedback diminishes spreading. However, in populations with heterogeneity in feedback strategy based on risk profile, we prove conditions that result in sustained oscillations in the infected population level.

A major concern in battling the COVID-19 pandemic has been the lack of reliable case reporting due to insufficient and inadequate testing. It is, for example, near impossible to assess attack rates and infection-fatality ratios based on case counts while large parts of the population remain untested. But the data is not useless. In this talk, we will discuss what characteristics of an outbreak can and cannot be inferred from case counts, and how this depends on the testing protocol. In particular, we demonstrate that infection spreading rates can be estimated reasonably well from case counts even if testing is limited to individuals with severe symptoms. Using examples from U.S. states, we also discuss how various testing protocols are reflected in signatures in the data. Finally, we assume a control perspective and discuss how testing protocols should be designed on both smaller (e.g. campus) and larger (e.g. city) scales so that testing combined with isolation becomes a control strategy that can stabilize the infection spread. The talk is based on a collaborative research effort by the COVID-19 working group Isolat at MIT’s Institute of Data, Systems, and Society (IDSS).

Testing, tracking and tracing abilities have been identified as pivotal in helping countries in safely reopening activities after the first wave of the COVID-19 virus, as well as in effectively dealing with second waves should they emerge in the future. Canonical tracing techniques, mostly based on smartphone apps, reconstruct past history of contacts, with the aim of isolating or notifying people that may have been in contact with known positive individuals. These methods, however, are not preemptive, as traced contacts are revealed only after the infection took place and, as such, they may lose effectiveness due to the combination of the large incubation time and the relatively fast exponential spread of the COVID-19 infection. In this work, we study alternative testing techniques for infection mitigation which, instead of relying on past contacts history, exploit graph theory and probability/correlation estimation methods to proactively identify the best pool of individuals to test each day. Our results show that, from well-known graph centrality algorithms, such as PageRank, to less-conventional approaches, based on the Kemeny constant and on infection probability estimation methods, proactive testing techniques yield promising results in identifying possible super-spreaders and in mitigating new virus outbreaks.

Information products provide agents with additional information that is used to update their actions. In many situations access to such products can be quite limited. For instance, in epidemics there tends to be a limited supply of medical testing kits. These testing kits are an information product because their output of a positive or a negative answer informs individuals and authorities on the underlying state and the appropriate course of action. In this talk, using an analytical model, we show how the accuracy of the test in detecting the underlying state serves as a rationing device to ensure that the limited supply of information products is appropriately allocated to the high demand by heterogeneous agents. We find that under many settings, providing perfect information (or a perfect test) is sub-optimal, and dominated by a moderately good test. We use a numerical study of an evolving epidemic to confirm our theoretically arrived insight that it is better to quickly release a moderately good test with high sensitivity and moderately high specificity (even if a better test is available).

Widespread and universal testing of all people for SARS-CoV-2, including those who have no symptoms, could help prevent the spread of COVID-19 by identifying people who are in need of care possibly before they become seriously ill, as well as those with mild or no symptoms who are nonetheless capable of spreading the disease. A positive test early in the course of the illness enables individuals to isolate themselves – reducing the chances that they will infect others and allowing them to seek treatment earlier, likely reducing disease severity and the risk of long-term disability, or death.

Frequent testing of people who have been in contact with others who have a documented infection could also be key to containing the spread. A negative test doesn’t mean an individual is in the clear; false negative test rates are not insignificant and the individual could still be or become infectious shortly thereafter. It has been noted that nearly half of all SARS-CoV-2 infections are transmitted by people who are not showing any symptoms. Thus, identifying infected individuals while they are presymptomatic, as well as those who are asymptomatic, may play a major role in stopping the pandemic.

However, widespread and frequent testing are difficult to implement for many reasons, ranging from a lack of availability of resources for the tests and access to lab facilities, to shortages of personnel to carry out the testing of patients and perform lab-based evaluation of samples. As a result, frequent, widespread testing has not been available in all areas of the world to all citizens. This raises many issues and questions:

• How should resources for testing be allocated in a population if not everyone can be frequently tested?

• Are there alternatives to individual sampling that can lead to faster and cheaper identification of exposed subpopulations?

• How can test data be used to form a better understanding of the disease spread and inform effective policies?

• How good is the test data we have?

• How good does the data need to be in order to be useful?

• How quickly do we need results?

We will analyse and discuss how the choice of model complexity impacts the predictive power of some epidemics models. We describe theoretical analysis of parameter identifiability and discuss the discrepancy between different simulation studies and the actual outcome during the COVID-19 pandemic. We also discuss the different information sources available to aid analysis in an ongoing pandemic, and discuss their usefulness, based on our experience from the Swedish health care system. The contribution is a cooperation between modeling experts from the major Swedish universities and Swedish health care experts with long experience, responsible for analysis during the COVID-19 pandemic and tracking the seasonal influenza for many years. We describe how this was used to aid the the planning within the Swedish health care system.

The sudden increase in COVID-19 cases is putting high pressure on healthcare services worldwide. At this stage, fast, accurate and early clinical assessment of the disease severity is vital. To support decision making and logistical planning in healthcare systems, this study leverages a database of blood samples from 485 infected patients in the region of Wuhan, China, to identify crucial predictive biomarkers of disease mortality. For this purpose, machine learning tools selected three biomarkers that predict the mortality of individual patients more than 10 days in advance with more than 90% accuracy: lactic dehydrogenase (LDH), lymphocyte and high-sensitivity C-reactive protein (hs-CRP).Overall, this Article suggests a simple and operable decision rule to quickly predict patients at the highest risk, allowing them to be prioritized and potentially reducing the mortality rate. This talk is based on this paper published in Nature Machine Intelligence.

To better capture the dynamics of the COVID-19 epidemics in Italy, as in other countries with a regional (or federal) administrative structure, it is of utmost importance to capture regional differences in mitigating the spread of the diseases, considering the heterogeneity at the regional level of the effects of national measures and local intervention strategies. Also, it is crucial to model flows of potential infected among the regions at a finer level than aggregate SIR family models allow.In this study we take Italy as a study case and propose a network model where each of the 20 administrative regions in which Italy is split into is considered as a node, edges representing flows of people to and from each region. Both short distance edges and long distance edges are considered in the model. The aim of the study is to capture at a finer level the dynamics of the epidemics both at the regional and the national level highlighting differences between regional dynamics and the aggregate effect of these at the national level. We use the proposed model to analyse the COVID-19 spread across the country, and to explore different feedback control based mitigation strategies to avoid the return of an epidemic in future waves. In so doing, we derive sufficient conditions based on applying appropriate matrix measures to the so-called next generation matrix and explore different optimal control approaches to devise intermittent regional strategies to contain and mitigate future epidemic phenomena.

The ongoing COVID-19 pandemic has motivated an innumerable number of researchers, companies, and governments to attempt to forecast the spread of the disease. Scouring this vast spectrum of predictions, it is clear that there is no consensus and that capturing the behavior of the outbreak remains elusive. The majority of the data available appears to support the hypothesis that the disease follows some variant of an SIR (susceptible-infected-removed) model. It is well known that the reproduction number of the SIR model (both networked and group models) depends on the number of susceptible individuals in the population. Therefore, forecasts of the spread, and consequently the number of susceptible, are essential for understanding in what stage of the outbreak we are currently operating. Several natural questions arise:

• What can be done to improve forecasts of the outbreak/avoid overfitting in order to help design and implement mitigation efforts?

• When sickness and deaths are in the balance, as they are now, how should researchers approach the exploitation vs exploration tradeoff?

• How can we learn from this outbreak and adapt the findings in preparation for future possible outbreaks?

Motivated by the ongoing pandemic COVID-19, we propose a closed-loop framework that combines inference from testing data, learning the parameters of the dynamics and optimal resource allocation for controlling the spread of the susceptible-infected-recovered (SIR) epidemic on networks. Our framework incorporates several key factors present in testing data, such as high risk individuals are more likely to undergo testing and infected individuals potentially act as asymptomatic carriers of the disease. We then present two tractable optimization problems to evaluate the trade-off between controlling the growth-rate of the epidemic and the cost of non-pharmaceutical interventions (NPIs). Our results provide compelling insights for policy-makers, including the significance of early testing and the emergence of a second wave of infections if NPIs are prematurely withdrawn.

Among the many mathematical models in epidemiology, the deterministic SIS Network model is a fundamental one which has been studied extensively by various scientific communities. On strongly connected networks, it is well known that there exists an endemic equilibrium (the disease persists in all nodes of the network) if and only if the reproduction number of the network system is greater than 1. In fact, the endemic equilibrium is unique and is asymptotically stable for all feasible nonzero initial conditions. This talk investigates the use of control in order to drive the network system to the healthy equilibrium (where every node is disease free). We consider a broad class of distributed feedback controllers, with the recovery rate of each node being the control input. We illustrate the significant challenges involved in feedback control when the uncontrolled network system has a reproduction number greater than 1, but also highlight some benefits. We then discuss the results and their implications, laying groundwork for the further development of feedback control approaches to tackling epidemic spread over networks.

Mitigation of the novel coronavirus has required control programs at the societal scale (e.g. shelter-in-place orders, closure of businesses and facilities, quarantine policies, travel restrictions). The economic and social impacts of these controls are enormous, hence government authorities and the general public are naturally anxious to quickly ease the controls. Yet, easing the controls seems to carry considerable risk, as doing so would again allow for exponential growth in case counts -- in system-theoretic terms, cause the null equilibrium of the system to revert to instability. The intrinsic challenge associated with easing controls is further compounded by the significant inertia inherent to enacting and modifying these societal-scale policies. The purpose of this talk is to explore how network-theoretic modeling and controls-engineering concepts can be brought to bear to design the removal or easing of infectious-disease controls. With this goal in mind, I will: 1) brainstorm the factors which impact infectious disease evolution after controls are eased, 2) describe network models that may be useful for studying the easing of controls, and 3) scope control-design problems that may arise in this space.

The ongoing COVID-19 pandemic is caused by a novel coronavirus identified in December 2019 and currently sweeping the world. Since the first case reported, the virus has spread rapidly all over the world. The pandemic clearly shows that in metapopulations, the most serious source of infection and disease spreading is due to infected individuals traveling between populations. During this period, each country or state adopted different travel restriction and lockdown policies at different points in time. It is important to fully understand and quantify the effects of those polices so that we can know what strategies are best to face the expected next wave or future outbreaks. There are few mathematical models which attempt to capture the dynamics of epidemic spreading over metapopulations with social distancing, travel restriction, and lockdown policies, let alone their applications have been limited to theoretical and numerical analyses. Past experience shows that coordinating mitigation efforts among countries and states is a difficult task, and sometimes even impossible, due to different governmental and social norms and practices. Meanwhile, there are significant differences in COVID-19 detecting capacities, which causes varying delays in reporting the confirmed cases. Detection and control of the virus spreading thus require robust and distributed strategies. Almost all the existing control and decision approaches do not explicitly capture these uncertainties and require centralized implementations.

The goal of this panel is to initiate discussions on how we can establish a resilient framework which can detect, respond and control the next wave or future pandemic outbreaks in a real-time and distributed manner.

Several natural questions, important also for policy making, arise:

• How do we model and quantify the effects of social distancing, travel restriction, and lockdown policies?

• How much more effective would mandated shelter-in-place be in containing the spread, compared with other practices?

• Is it worth the social cost?

• What is the effect of 10% of the population ignoring these protocols?

• How do we effectively track the confirmed and suspected cases?

• How do we coordinate mitigation efforts among different regions?

• What is the optimal length of quarantine?

• How do we efficiently use the collected data?

In this talk, we consider decentralized (game-theoretic) vaccination decisions by humans during susceptible-infected-susceptible epidemics on networks. We consider a population game framework where nodes choose whether or not to vaccinate themselves, and the epidemic risk is defined as the infection probability at the endemic state of the epidemic. We examine the impacts of behavioral biases and nonlinear probability weighting by human decision-makers on the Nash equilibrium protection strategies. In particular, we characterize the effects of over- and under-estimation of infection probabilities on the vaccination decisions by the individuals in the network. We first establish the existence and uniqueness of a threshold equilibrium where nodes with degrees larger than a certain threshold vaccinate. When the perceived vaccination cost is sufficiently high, we show that behavioral biases cause fewer players to vaccinate, and vice versa. We quantify this effect for a class of networks with power-law degree distributions by proving tight bounds on the ratio of equilibrium thresholds under behavioral and true perceptions of probabilities. We further characterize the socially optimal vaccination policy and investigate the inefficiency of the Nash equilibrium. In particular, we show that reducing the perceived cost of vaccination (e.g., via subsidies, etc.) can compensate for behavioral biases and lead the individuals to make socially optimal decisions.

Scalability problems often arise when studying disease propagation on interaction networks within a community. This problem is further compounded as the scope of the modelling increases to city-wide and multi-city interactions. One approach is to treat each node in the network as a collection of individuals, where the assumption of well-mixing is assumed to be reasonable. This talk will address a distinctive set of reduction techniques that leverages the inherent geographic and functional network-of-networks structures that appears within the network. Geographical layering, such as in multi-city epidemics models, promotes the use of natural time-scale differences in the system. The dynamics can then be individually studied under a separation principle, simplifying analysis. Functional layering, into population types, can be modelled using graph products that factor the network dynamics while preserving the distinctive features of the network structure. Theory relating to network-of-networks with multiple time-scales and Cartesian graph products will be explored with quantitative bounds on the reduced-order models, computationally efficient disease trajectory calculations and analysis of convergence to disease-free state, and the design of distributed controllers. These scalable techniques on large-scale network can provide efficient modelling, performant vaccination strategies, and distributed infection management systems.

More than 150 COVID-19 vaccine candidates were under development in June 2020, of which a much smaller subset will be safe and provide lasting immunity. Multiple vaccine candidates were found to be safe and then entered phase III human trials in Summer 2020 to test their effectiveness in providing some protection against the disease.

A vaccine will not be available to the public by then, however. The discovery of a COVID-19 vaccine that is effective in humans is not the same thing as making that vaccine available to the world. Many time-consuming engineering tasks are involved in going from the biology of creating a COVID-19 vaccine to the vaccination of billions of individuals needed to protect the world population. A major bottleneck to world-scale vaccination is the time required to develop a process to manufacture billions of doses within the existing supply chains and equipment while maintaining the highest levels of safety in the product.

After a brief summary of the most promising COVID-19 vaccines and the bottlenecks in vaccine manufacturing in general, ways are described for using feedback control to shorten the timeline. The first set of technologies are applicable to all vaccine types and involve the use of fully automated modular manufacturing systems. Control theory and algorithms are described for addressing the characteristics of these highly uncertain, nonlinear, hybrid, distributed parameter systems. The second set of technologies is specific to the main class of vaccines, live-attenuated viral vaccines, which use a weakened form of the virus. The close similarity of the vaccines to the natural infection creates a strong and long-lasting immune response. Such vaccines include influenza (flu), measles, mumps, rubella, rotavirus, smallpox, chickenpox, and yellow fever. In a case study, feedback control enables more than a factor of five increase in vaccine production.

The ongoing pandemic has stimulated an impressive race all around the world to develop a vaccine against Covid-19. As of September 4, more than 170 candidate vaccines are currently tracked by the World Health Organization (WHO).

The standard procedures for testing vaccines typically take years, a significantly long period of time necessary to ensure the highest safety standards, in fact higher than for other drugs, because they are given to millions of healthy people.

Indeed, typical testing involves several steps:

- Pre-clinical stage: researchers give administer the vaccine to animals to see if it triggers an immune response.

- Phase 1: the vaccine is given to a small group of people to determine whether it is safe and to learn more about the immune response it provokes.

- Phase 2: the vaccine is given to hundreds of people so scientists can learn more about its safety and correct dosage.

- Phase 3: the vaccine is given to thousands of people to confirm its safety – including rare side effects – and effectiveness. These trials involve a control group which is given a placebo.

The emergency has pushed for a rapid response and scientists are hoping to develop a vaccine for Covid-19 within 12 to 18 months.

After these phases, a massive vaccine production will be necessary. This will represent a focal challenge for the pharmaceutical industry.

Several natural questions arise:

• How should we behave while waiting for the vaccine to be available?

• How long will it take before the vaccine is available?

• What are the potential risks of the vaccine, in light of such a short testing period?

• What about liability?

• Should vaccination be compulsory to ensure herd immunity?

• How should we cope with possible resistance to mass vaccination (e.g. anti-vax movements)?

• Will the vaccine be accessible to everybody or there will be a "vaccine sovereignity"?

• How can we help?

• Can our models forecast the effects of vaccination in a reliable way and influence political decisions?

• How control can be instrumental in speeding the vaccine manufacturing process?