key: cord-0539469-y0eage3p
authors: Huang, Yubo; Zhang, Weidong
title: Comprehensive Investigation and Isolation have Effectively Suppressed the Spread of COVID-19
date: 2020-04-24
journal: nan
DOI: nan
sha: d52263cf7a0081be4c3b9a45b55777c395ede6fe
doc_id: 539469
cord_uid: y0eage3p

The outbreak of COVID-19 since Dec. 2019 has caused severe life and economic damage worldwide, many countries are trapped by medical resource constraints or absence of targeted therapeutics, and therefore the implement of systemic policies to block this pandemic should be prioritized. Based on the transmission mechanisms and physicochemical properties of betacoronaviruses, we construct a fine-grained transmission dynamics model (ICRD) to forecast the crucial information of public concern, therein using dynamical coefficients to quantify the impact of the implement time and intensity of containment policies on the spread of epidemic. We find that the comprehensive investigation policy for susceptible population and the quarantine for suspected cases eminently contribute to reduce casualties during the phase of the dramatic increase of diagnosed cases. Statistic evidences strongly suggest that society should take such forceful public health interventions to cut the infection channels in the initial stage until the pandemic is interrupted.

Pneumonia caused by COVID-19 has evolved a worldwide pandemic for which humans have paid more than 2.5 million infections and 180 thousand deaths as of Apr. 21th, 2020 (1) but there are still billions of lives threatened (2) (3) (4) . The transmission of the COVID-19 virus is confirmed through respiratory droplet (5) and has super infectivity beyond SARS and MERS (6) which can even overwhelm countries with advanced medical facilities and therapeutics. Laboratory experiments proved that SARS-CoV-2 can survive temperatures of 56 • C for more than 30 minutes (7) and the experiences from tropical regions (8) illustrated COVID-19 still has transmission capacity under the hydrothermal circumstance (9) . Moreover, the incubation period of COVID-19 is relatively short (5.5 days average) implying that it quickly onset after infection and presents the corresponding clinical symptoms such as fever, cough, and fatigue (10) . Recently, the revised data released by Chinese health authorities definitely delivered that the case fatality rate (CFI) of COVID-19 is seriously underestimated because the phenomenon of missed reports and false positive in the early stage of the epidemic. Given the current statue of the limited pharmaceutical treatments and the unavailable targeted vaccines (11) , the public health interventions are demonstrated as the most functional precautions in many countries (12) (13) (14) , especially contributing to block the pandemic in Wuhan (15) (16) (17) (18) .

On Jan. 23th 2020, Chinese authorities imposed a lockdown in Wuhan since the suspected and diagnosed cases exceed 2,000 which triggers public health emergency response in Hubei Province. The containment efforts including school closures, transports bans and workplace shutdowns were announced to limit the spread of virus. Nevertheless, the epidemic entered the exponential period unstoppably from Feb. onwards (19, 20) and caused global concern and panic. From Feb. 2nd, the successive delivery of the shelter hospitals implied Wuhan had the sufficient wards to isolate and treat symptomatic patients. Meanwhile, people strictly followed the ordinances concerning social distancing, quarantine and careful hand and respiratory hygiene, subsequently wearing personal protective equipments (PPE) (21) , isolating themselves at home, and recording their temperature each day. The communities adopted a comprehensive investigation strategy to detect the suspected cases and reported their trace while hiding their private information (22) resulting in a sub-exponential growth of the infected curve until a peak of 38,020 on Feb. 18th (23) . Despite there is a ethical controversy about whether suspicious persons should be mandatorily isolated from social networks, the experience from Wuhan supported that this policy had effectively cut the transmission channels of COVID-19 and compel the pandemic to a mitigation stage. In post-pandemic phase (24) , Wuhan continued to distribute disinfectors throughout the region including ventilation duct, water pipe, and urban sewers where COVID-19 was sampled in Paris (25) and the central China government stated the pandemic was basically blocked on Mar. 23th. Ultimately, after paying 4,632 deaths nationwide and incalculable economic cost, China has ended its 76-day lockdown of Wuhan, but the relative restrictions still remain in place.

The transmission dynamics observed in different continents and zones are markedly heterogeneous consulting time series data released by public health authorities (26) (27) (28) (29) . The fundamental reasons are that the fluctuation of the objective physical environments and the implementation intensity and duration of the containments policies restricted by public opinion, both presenting challenges to build the dynamic model to forecast the tendency of the pandemic. Furthermore, the CFI and recovery rate change as well with respect to different phases since the gradual enrichment of care experiences and capacities. Therefore, we design dynamical coefficients to quantify the variation of infectivity, investigation and isolation policies, vital dynamics to adjust the social response to the pandemic. Functionally, tuning the boundaries or the derived functions of the dynamical coefficients can subtly regulate the containment efforts and further observe their impact on the infected curves. We then simulate the results about advanc-ing or postponing relative policies and conclude that the output curves are sensitive to these policies. The results of our model introduce statistic evidences that the containment policies can effectively suppress or even block the outbreak of COVID-19 through mapping them into measurable interval coefficients to observe their influence on the epidemic.

From the cases and traces information of patients released by the Wuhan government and CDC, most individuals were infected from a symptomatic or pre-symptomatic infection, especially during the period of exponential and sub-exponential growth, whereas the persons who were infected through asymptomatic or environmental transmission merely accounted for a negligible fraction of infected population. In practical, the boundaries of these four transmissions are ambiguous and the number of asymptomatic infections and secondary infections caused by them is difficult to count. Therefore, we generally assume that the non-isolated infected individuals are the main propagating sources on social networks. We divide the statues of the population into 5 categories: (H)ealthy, (I)nfected, (C)onfirmed, (R)ecovered and (D)ead ( Fig.   1 ). More granular, the infected group I consists of the confirmed C and unconfirmed I − C and therein the confirmed individuals C are either isolated βC (β is the isolation rate) or nonisolated (1 − β)C. The transmission dynamics of virus can be fully described by the ordinary differential equations (namely ICRD model) with respect to time t:

The infected but non-isolated group I − βC has the vital infectiousness since they not only are σ, κ, δ, µ are daily cure rate, incurable mortality rate, natural recovery rate, and non-treatment mortality rate, respectively. Hence ∂ t I quantifies the aggregate incremental cases of infection (Eq. (1)) after removing the recovered and dead population. Limiting to the objective medical testing ability of laboratories, only a fraction of η suspected cases could receive diagnosis within the unit statistical time (η is the algebraic mapping of investigation policy), so the increment of confirmed cases ∂ t C equals to the difference between the newly positive diagnosed cases η(I − C) and dead or recovered cases (σ + κ)C. Evently, we could deduce the daily increase of recovered or dead cases integrating the recovery ratio σ, δ and mortality κ, µ with the infected population (please see Materials and Methods for detailed derivation of Eqs. (1-4) ).

Before we have discussed that β and η reflect the impact of the isolation and investigation poli- Statistic evidences for the power of comprehensive investigation and compulsive isolation policies Compared with the SEIR and S-ICRD, the dynamic coefficients based-ICRD model (D-ICRD) has infinitesimal mean square errors (MSE) with the data released by NHC (Fig. 4) . D-ICRD estimates that the existing infected and confirmed cases would dramatically raised to their peaks (41986, 38758) at Feb. 14th and 17th respectively (Fig 4A) , approximately consisting with the practical inflexion Feb. 18th (38020). In Phase 1, the incomplete investigation policies and limited testing techniques contribute the large interval between the infected and confirmed curves, whereas they gradually coincide with the strengthening of surveillance in phase 2. The truth-values of the recovered cases are always located in the 95% confidence interval (CI) of the curve predicted by D-ICRD but the estimated values are slight higher since the patients who are spontaneously recovered were excluded in the statistics (Fig. 4B) . The death cases calculated by D-ICRD eccentrically deviate from the statistical data before Mar. 8th in Fig. 4C . Until Apr.

17th the government announced that there were 1290 missing victims in the initial collecting stage and then increased death cases to 3869 that located in the 95% CI [3576, 3952] of the predicted value. 

Figs. S1 to S3

Tables S1 to S4

References (4-10) Figure 1 : Transmission mechanism of COVID-19 on social networks. The group of infected but non-isolated (blue and yellow nodes) is the main propagating source of virus through physical contacts (droplet), especially over the incubation period (30, 31) . The infected patients would die or produce antibodies without treatment but undoubtedly the herd immunity would take a long time to achieve and uncountable individuals would lose their lives in this process. Therefore, the diagnosed patients should be isolated from social networks to cut the transmission links (yellow edges). Furthermore, the red edges are more dangerous for the exposed persons and the comprehensive investigation policy for all people and the nucleic acid testing strategy for symptomatic patients should be taken to remove their connections with others. Meanwhile, some carrier would migrate to other place through the global transportation networks. The experiences from China demonstrated that the external input is the largest threat in the post-transmission period (32). The gap between the infected curve and the confirmed curve indicates the number of the infected but unconfirmed group (33) . Most dots are located in the shadow areas except for Phase 1 because the health authorities clarified that there were many infected cases of underreporting. (B) The curve of recovered cases. The calculated data is slightly larger than the amounts counted in hospitals since the spontaneously curative patients are not included and a few medical institutions failed to connect with the information systems in time. (C) The curve of death cases. Blue dots denote the originally released data and the red dots denote the revised data by NHC. According to the revised data, mortality is seriously underestimated at Phase 1 and Phase 2, and the yellow curve is more representative of the death trend of COVID-19 pandemic. 

The Lancet Infectious Diseases

Combating covid-19-the role of robotics in managing public health and infectious diseases

The Lancet Global Health

The lancet infectious diseases

Acknowledgments Thanks all health care workers worldwide for their commitment, dedication, and professionalism in COVID-19 pandemic. This paper is partly supported by the National Science Foundation of China (61473183, U1509211, 61627810), National Key R&D Program of China (SQ2017YFGH001005). No conflicts of interest