Self-isolation or borders closing: What prevents the spread of the epidemic better?

Epidemic propagation risk study with effective fractal dimension

In this article, the risk of epidemic transmission on complex networks is studied from the perspective of effective fractal dimension. First, we introduce the method of calculating the effective fractal dimensionD B ${D}_B$ of the network by taking a scale-free network as an example. Second, we propose the construction method of administrative fractal network and calculate theD B ${D}_B$ . using the classical susceptible exposed infectious removed (SEIR) infectious disease model, we simulate the virus propagation process on the administrative fractal network. The results show that the larger theD B ${D}_B$ is, the higher the risk of virus transmission is. Later, we proposed five parameters P, M, B, F, and D, where P denotes population mobility, M denotes geographical distance, B denotes GDP, F denotesD B ${D}_B$ , and D denotes population density. The new epidemic growth index formulaI = ( P + ( 1 - M ) + B ) ( F + D ) $I = {( {P + ( {1 - M} ) + B} )}^{( {F + D} )}$ was obtained by combining these five parameters, and the validity of I in epidemic transmission risk assessment was demonstrated by parameter sensitivity analysis and reliability analysis. Finally, we also confirmed the reliability of the SEIR dynamic transmission model in simulating early COVID-19 transmission trends and the ability of timely quarantine measures to effectively control the spread of the epidemic.

Empirical study and model simulation of global stock market dynamics during COVID-19

At the beginning of 2020, COVID-19 swept the world and changed various aspects of human society, such as economy and finance, life and health, migration and population. We first empirically study how the dynamic behaviors of stock markets are affected by COVID-19, and focus on the large volatility dynamics, variation-fluctuation correlation function and epidemic-fluctuation correlation function. Then we generalize the Heston model to simulate the global stock market dynamics, and an epidemic index computed from empirical data is directly taken as the external force in the modelling.

Machine learning spatio-temporal epidemiological model to evaluate Germany-county-level COVID-19 risk

As the COVID-19 pandemic continues to ravage the world, it is critical to assess the COVID-19 risk timely on multi-scale. To implement it and evaluate the public health policies, we develop a machine learning assisted framework to predict epidemic dynamics from the reported infection data. It contains a county-level spatio-temporal epidemiological model, which combines spatial cellular automata (CA) with time sensitive-undiagnosed-infected-removed (SUIR) model, and is compatible with the existing risk prediction models. The CA-SUIR model shows the multi-scale risk to the public and reveals the transmission modes of coronavirus in different scenarios. Through transfer learning, this new toolbox is used to predict the prevalence of multi-scale COVID-19 in all 412 counties in Germany. A t-day-ahead risk forecast as well as assessment of the non-pharmaceutical intervention policies is presented. We analyzed the situation at Christmas of 2020, and found that the most serious death toll could be 34.5. However, effective policy could control it below 21thousand, which provides a quantitative basis for evaluating the public policies implemented by the government. Such intervening evaluation process would help to improve public health policies and restart the economy appropriately in pandemics.

International travel-related control measures to contain the COVID-19 pandemic: a rapid review

BACKGROUND

In late 2019, the first cases of coronavirus disease 2019 (COVID-19) were reported in Wuhan, China, followed by a worldwide spread. Numerous countries have implemented control measures related to international travel, including border closures, travel restrictions, screening at borders, and quarantine of travellers.

OBJECTIVES

To assess the effectiveness of international travel-related control measures during the COVID-19 pandemic on infectious disease transmission and screening-related outcomes.

SEARCH METHODS

We searched MEDLINE, Embase and COVID-19-specific databases, including the Cochrane COVID-19 Study Register and the WHO Global Database on COVID-19 Research to 13 November 2020.

SELECTION CRITERIA

We considered experimental, quasi-experimental, observational and modelling studies assessing the effects of travel-related control measures affecting human travel across international borders during the COVID-19 pandemic. In the original review, we also considered evidence on severe acute respiratory syndrome (SARS) and Middle East respiratory syndrome (MERS). In this version we decided to focus on COVID-19 evidence only. Primary outcome categories were (i) cases avoided, (ii) cases detected, and (iii) a shift in epidemic development. Secondary outcomes were other infectious disease transmission outcomes, healthcare utilisation, resource requirements and adverse effects if identified in studies assessing at least one primary outcome.

DATA COLLECTION AND ANALYSIS

Two review authors independently screened titles and abstracts and subsequently full texts. For studies included in the analysis, one review author extracted data and appraised the study. At least one additional review author checked for correctness of data. To assess the risk of bias and quality of included studies, we used the Quality Assessment of Diagnostic Accuracy Studies (QUADAS-2) tool for observational studies concerned with screening, and a bespoke tool for modelling studies. We synthesised findings narratively. One review author assessed the certainty of evidence with GRADE, and several review authors discussed these GRADE judgements.

MAIN RESULTS

Overall, we included 62 unique studies in the analysis; 49 were modelling studies and 13 were observational studies. Studies covered a variety of settings and levels of community transmission. Most studies compared travel-related control measures against a counterfactual scenario in which the measure was not implemented. However, some modelling studies described additional comparator scenarios, such as different levels of stringency of the measures (including relaxation of restrictions), or a combination of measures. Concerns with the quality of modelling studies related to potentially inappropriate assumptions about the structure and input parameters, and an inadequate assessment of model uncertainty. Concerns with risk of bias in observational studies related to the selection of travellers and the reference test, and unclear reporting of certain methodological aspects. Below we outline the results for each intervention category by illustrating the findings from selected outcomes. Travel restrictions reducing or stopping cross-border travel (31 modelling studies) The studies assessed cases avoided and shift in epidemic development. We found very low-certainty evidence for a reduction in COVID-19 cases in the community (13 studies) and cases exported or imported (9 studies). Most studies reported positive effects, with effect sizes varying widely; only a few studies showed no effect. There was very low-certainty evidence that cross-border travel controls can slow the spread of COVID-19. Most studies predicted positive effects, however, results from individual studies varied from a delay of less than one day to a delay of 85 days; very few studies predicted no effect of the measure. Screening at borders (13 modelling studies; 13 observational studies) Screening measures covered symptom/exposure-based screening or test-based screening (commonly specifying polymerase chain reaction (PCR) testing), or both, before departure or upon or within a few days of arrival. Studies assessed cases avoided, shift in epidemic development and cases detected. Studies generally predicted or observed some benefit from screening at borders, however these varied widely. For symptom/exposure-based screening, one modelling study reported that global implementation of screening measures would reduce the number of cases exported per day from another country by 82% (95% confidence interval (CI) 72% to 95%) (moderate-certainty evidence). Four modelling studies predicted delays in epidemic development, although there was wide variation in the results between the studies (very low-certainty evidence). Four modelling studies predicted that the proportion of cases detected would range from 1% to 53% (very low-certainty evidence). Nine observational studies observed the detected proportion to range from 0% to 100% (very low-certainty evidence), although all but one study observed this proportion to be less than 54%. For test-based screening, one modelling study provided very low-certainty evidence for the number of cases avoided. It reported that testing travellers reduced imported or exported cases as well as secondary cases. Five observational studies observed that the proportion of cases detected varied from 58% to 90% (very low-certainty evidence). Quarantine (12 modelling studies) The studies assessed cases avoided, shift in epidemic development and cases detected. All studies suggested some benefit of quarantine, however the magnitude of the effect ranged from small to large across the different outcomes (very low- to low-certainty evidence). Three modelling studies predicted that the reduction in the number of cases in the community ranged from 450 to over 64,000 fewer cases (very low-certainty evidence). The variation in effect was possibly related to the duration of quarantine and compliance. Quarantine and screening at borders (7 modelling studies; 4 observational studies) The studies assessed shift in epidemic development and cases detected. Most studies predicted positive effects for the combined measures with varying magnitudes (very low- to low-certainty evidence). Four observational studies observed that the proportion of cases detected for quarantine and screening at borders ranged from 68% to 92% (low-certainty evidence). The variation may depend on how the measures were combined, including the length of the quarantine period and days when the test was conducted in quarantine.

AUTHORS' CONCLUSIONS

With much of the evidence derived from modelling studies, notably for travel restrictions reducing or stopping cross-border travel and quarantine of travellers, there is a lack of 'real-world' evidence. The certainty of the evidence for most travel-related control measures and outcomes is very low and the true effects are likely to be substantially different from those reported here. Broadly, travel restrictions may limit the spread of disease across national borders. Symptom/exposure-based screening measures at borders on their own are likely not effective; PCR testing at borders as a screening measure likely detects more cases than symptom/exposure-based screening at borders, although if performed only upon arrival this will likely also miss a meaningful proportion of cases. Quarantine, based on a sufficiently long quarantine period and high compliance is likely to largely avoid further transmission from travellers. Combining quarantine with PCR testing at borders will likely improve effectiveness. Many studies suggest that effects depend on factors, such as levels of community transmission, travel volumes and duration, other public health measures in place, and the exact specification and timing of the measure. Future research should be better reported, employ a range of designs beyond modelling and assess potential benefits and harms of the travel-related control measures from a societal perspective.

Epidemic plateau in critical susceptible-infected-removed dynamics with nontrivial initial conditions

Containment measures implemented by some countries to suppress the spread of COVID-19 have resulted in a slowdown of the epidemic characterized by time series of daily infections plateauing over extended periods of time. We prove that such a dynamical pattern is compatible with critical susceptible-infected-removed (SIR) dynamics. In traditional analyses of the critical SIR model, the critical dynamical regime is started from a single infected node. The application of containment measures to an ongoing epidemic, however, has the effect to make the system enter in its critical regime with a number of infected individuals potentially large. We describe how such nontrivial starting conditions affect the critical behavior of the SIR model. We perform a theoretical and large-scale numerical investigation of the model. We show that the expected outbreak size is an increasing function of the initial number of infected individuals, while the expected duration of the outbreak is a nonmonotonic function of the initial number of infected individuals. Also, we precisely characterize the magnitude of the fluctuations associated with the size and duration of the outbreak in critical SIR dynamics with nontrivial initial conditions. Far from herd immunity, fluctuations are much larger than average values, thus indicating that predictions of plateauing time series may be particularly challenging.

Modeling the COVID-19 Pandemic Using an SEIHR Model With Human Migration

The 2019 novel coronavirus disease (COVID-19) outbreak has become a worldwide problem. Due to globalization and the proliferation of international travel, many countries are now facing local epidemics. The existence of asymptomatic and pre-symptomatic transmissions makes it more difficult to control disease transmission by isolating infectious individuals. To accurately describe and represent the spread of COVID-19, we suggest a susceptible-exposed-infected-hospitalized-removed (SEIHR) model with human migrations, where the "exposed" (asymptomatic) individuals are contagious. From this model, we derive the basic reproduction number of the disease and its relationship with the model parameters. We find that, for highly contagious diseases like COVID-19, when the adjacent region's epidemic is not severe, a large migration rate can reduce the speed of local epidemic spreading at the price of infecting the neighboring regions. In addition, since "infected" (symptomatic) patients are isolated almost immediately, the transmission rate of the epidemic is more sensitive to that of the "exposed" (asymptomatic) individuals. Furthermore, we investigate the impact of various interventions, e.g. isolation and border control, on the speed of disease propagation and the resultant demand on medical facilities, and find that a strict intervention measure can be more effective than closing the borders. Finally, we use some real historical data of COVID-19 caseloads from different regions, including Hong Kong, to validate the modified SEIHR model, and make an accurate prediction for the third wave of the outbreak in Hong Kong.

Epidemics with containment measures

We propose a tractable epidemic model that includes containment measures. In the absence of containment measures, the epidemics spread exponentially fast whenever the infectivity rate is positive λ>0. The containment measures are modeled by considering a time-dependent modulation of the bare infectivity λ leading to effective infectivity that decays in time for each infected individual, mimicking, for instance, the combined effect of the asymptomatic onset of the disease, testing policies, and quarantine. We consider a wide range of temporal kernels for effective infectivity, and we investigate the effect of the considered containment measures. We find that not all kernels are able to push the epidemic dynamics below the epidemic threshold with some containment measures only able to reduce the rate of the exponential growth of newly infected individuals. We also propose a pandemic model caused by a growing number of separated foci.