Efficiency of prompt quarantine measures on a susceptible-infected-removed model in networks

Limited efficacy of forward contact tracing in epidemics

Infectious diseases that spread silently through asymptomatic or pre-symptomatic infections represent a challenge for policy makers. A traditional way of achieving isolation of silent infectors from the community is through forward contact tracing, aimed at identifying individuals that might have been infected by a known infected person. In this work we investigate how efficient this measure is in preventing a disease from becoming endemic. We introduce an SIS-based compartmental model where symptomatic individuals may self-isolate and trigger a contact tracing process aimed at quarantining asymptomatic infected individuals. Imperfect adherence and delays affect both measures. We derive the epidemic threshold analytically and find that contact tracing alone can only lead to a very limited increase of the threshold. We quantify the effect of imperfect adherence and the impact of incentivizing asymptomatic and symptomatic populations to adhere to isolation. Our analytical results are confirmed by simulations on complex networks and by the numerical analysis of a much more complex model incorporating more realistic in-host disease progression.

Epidemic control in networks with cliques

Social units, such as households and schools, can play an important role in controlling epidemic outbreaks. In this work, we study an epidemic model with a prompt quarantine measure on networks with cliques (a clique is a fully connected subgraph representing a social unit). According to this strategy, newly infected individuals are detected and quarantined (along with their close contacts) with probability f. Numerical simulations reveal that epidemic outbreaks in networks with cliques are abruptly suppressed at a transition point f_{c}. However, small outbreaks show features of a second-order phase transition around f_{c}. Therefore, our model can exhibit properties of both discontinuous and continuous phase transitions. Next, we show analytically that the probability of small outbreaks goes continuously to 1 at f_{c} in the thermodynamic limit. Finally, we find that our model exhibits a backward bifurcation phenomenon.

New approximations, and policy implications, from a delayed dynamic model of a fast pandemic

We study an SEIQR (Susceptible-Exposed-Infectious-Quarantined-Recovered) model due to Young et al. (2019) for an infectious disease, with time delays for latency and an asymptomatic phase. For fast pandemics where nobody has prior immunity and everyone has immunity after recovery, the SEIQR model decouples into two nonlinear delay differential equations (DDEs) with five parameters. One parameter is set to unity by scaling time. The simple subcase of perfect quarantining and zero self-recovery before quarantine, with two free parameters, is examined first. The method of multiple scales yields a hyperbolic tangent solution; and a long-wave (short delay) approximation yields a first order ordinary differential equation (ODE). With imperfect quarantining and nonzero self-recovery, the long-wave approximation is a second order ODE. These three approximations each capture the full outbreak, from infinitesimal initiation to final saturation. Low-dimensional dynamics in the DDEs is demonstrated using a six state non-delayed reduced order model obtained by Galerkin projection. Numerical solutions from the reduced order model match the DDE over a range of parameter choices and initial conditions. Finally, stability analysis and numerics show how a well executed temporary phase of social distancing can reduce the total number of people affected. The reduction can be by as much as half for a weak pandemic, and is smaller but still substantial for stronger pandemics. An explicit formula for the greatest possible reduction is given.

A perspective on early detection systems models for COVID-19 spreading

The ongoing COVID-19 epidemic highlights the need for effective tools capable of predicting the onset of infection outbreaks at their early stages. The tracing of confirmed cases and the prediction of the local dynamics of contagion through early indicators are crucial measures to a successful fight against emerging infectious diseases (EID).

The proposed framework is model-free and applies Early Warning Detection Systems (EWDS) techniques to detect changes in the territorial spread of infections in the very early stages of onset. This study uses publicly available raw data on the spread of SARS-CoV-2 mainly sourced from the database of the Italian Civil Protection Department.

Two distinct EWDS approaches, the Hub-Jones (H&J) and Strozzi-Zaldivar (S&Z), are adapted and applied to the current SARS-CoV-2 outbreak. They promptly generate warning signals and detect the onset of an epidemic at early surveillance stages even if working on the limited daily available, open-source data.

Additionally, EWDS S&Z criterion is theoretically validated on the basis of the epidemiological SIR.

Discussed EWDS successfully analyze self-accelerating systems, like the SARS-CoV-2 scenario, to precociously identify an epidemic spread through the calculation of onset parameters. This approach can also facilitate early clustering detection, further supporting common fight strategies against the spread of EIDs. Overall, we are presenting an effective tool based on solid scientific and methodological foundations to be used to complement medical actions to contrast the spread of infections such as COVID-19.

Skepticism and rumor spreading: The role of spatial correlations

Critical thinking and skepticism are fundamental mechanisms that one may use to prevent the spreading of rumors, fake news, and misinformation. We consider a simple model in which agents without previous contact with the rumor, being skeptically oriented, may convince spreaders to stop their activity or, once exposed to the rumor, decide not to propagate it as a consequence, for example, of fact checking. We extend a previous, mean-field analysis of the combined effect of these two mechanisms, active and passive skepticism, to include spatial correlations. This can be done either analytically, through the pair approximation, or simulating an agent-based version on diverse networks. Our results show that while in mean field there is no coexistence between spreaders and susceptibles (although, depending on the parameters, there may be bistability depending on the initial conditions), when spatial correlations are included, because of the protective effect of the isolation provided by removed agents, coexistence is possible.

Compartmental Models of the COVID-19 Pandemic for Physicians and Physician-Scientists

As the novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection spreads globally, physicians and physician-scientists are confronted with an enlarging body of literature about the nature of this pandemic. Understanding the current epidemiological models for disease spread, mortality, and recovery is more important than ever before. One of the most relevant mathematical models relating to the spread of a pandemic is the susceptible-infectious-removed (SIR) model. Other models worth exploring are the susceptible-exposed-infectious-removed (SEIR) and the susceptible-unquarantined-quarantined-confirmed (SUQC) model.

Complete dimensional collapse in the continuum limit of a delayed SEIQR network model with separable distributed infectivity

We take up a recently proposed compartmental SEIQR model with delays, ignore loss of immunity in the context of a fast pandemic, extend the model to a network structured on infectivity and consider the continuum limit of the same with a simple separable interaction model for the infectivities β . Numerical simulations show that the evolving dynamics of the network is effectively captured by a single scalar function of time, regardless of the distribution of β in the population. The continuum limit of the network model allows a simple derivation of the simpler model, which is a single scalar delay differential equation (DDE), wherein the variation in β appears through an integral closely related to the moment generating function of u = β . If the first few moments of u exist, the governing DDE can be expanded in a series that shows a direct correspondence with the original compartmental DDE with a single β . Even otherwise, the new scalar DDE can be solved using either numerical integration over u at each time step, or with the analytical integral if available in some useful form. Our work provides a new academic example of complete dimensional collapse, ties up an underlying continuum model for a pandemic with a simpler-seeming compartmental model and will hopefully lead to new analysis of continuum models for epidemics.

Rapid decay in the relative efficiency of quarantine to halt epidemics in networks

Several recent studies have tackled the issue of optimal network immunization by providing efficient criteria to identify key nodes to be removed in order to break apart a network, thus preventing the occurrence of extensive epidemic outbreaks. Yet, although the efficiency of those criteria has been demonstrated also in empirical networks, preventive immunization is rarely applied to real-world scenarios, where the usual approach is the a posteriori attempt to contain epidemic outbreaks using quarantine measures. Here we compare the efficiency of prevention with that of quarantine in terms of the tradeoff between the number of removed and saved nodes on both synthetic and empirical topologies. We show how, consistent with common sense, but contrary to common practice, in many cases preventing is better than curing: depending on network structure, rescuing an infected network by quarantine could become inefficient soon after the first infection.