This article, using scientific knowledge, looks at the COVID-19 dynamics of contagion to identify ideal measures that should be taken to stop contagion. These ideal measures, then, compared with real policies will allow assessing the potential for a second wave.

Our aim, for this series, is to find ways to improve how we foresee if, where and when a second wave or recurrent ones, could strike, and how lethal they could be. We assume the virus does not mutate and disappear. Here, we seek a way to evaluate the measures and policies countries and non-state actors take against the COVID-19 to estimate if they mitigate or not the risks of contagion and thus of a second wave.

In other words, what we are trying to find out is how adequate the measures implemented are to control the contagion. This control is crucial if we do not want to see again infections and then severe cases rise exponentially and uncontrollably. This would mean a second wave with a return to lockdown.

To achieve our aim, we need to understand how the COVID-19 spreads, hence the various dynamics of contagion at work. Thus, we retrace the way contagion takes place, at individual level, in the case of the COVID-19 pandemic. To do so, we use and synthesise knowledge scientists accumulated since the start of the pandemic to date. As a result, we obtain an ideal benchmark against which measures and policies can be evaluated. From a policy-orientated perspective, we thus also obtain indicators for better monitoring of the situation on the ground and for steering policies.

We thus assess how efficient our net is. Ideally, we would also need to be able to determine how many cases can slip through our net. The more numerous the remaining undetected cases, the higher the likelihood to see a new dire wave, the closer that can take place in time and the more intense and dangerous the wave.

First, we look at the dynamic of infection through transmission and at incubation. This gives us crucial elements notably related to individual protective measures and to quarantines for individuals which appear not to have the COVID-19. Second, we identify possible cases of contagion, focusing mainly on contagion taking place outside the hospital track. In other words we look at the contagion that is more difficult to identify and control because it is not easily observable and collides with everyday life. We thus address pre-symptomatic contagion, asymptomatic contagion, contagion for mild COVID-19 disease and post recovery contagion. Finally, synthesising the knowledge gathered, we summarise the ideal measures that could be taken in a table to ease assessment (direct access to summary table). We give a more detailed example of what should be the ideal duration of quarantine for travels and of the risks entailed.

Infection, transmission and Incubation

To become infected, someone needs to receive a minimal dose of virus. Once this dose reaches “our respiratory tract, one or two cells will be infected and will be re-programmed to produce many new viruses within” a certain amount of time (Dr Michael Skinner, “Expert reaction to questions about COVID-19 and viral load“, ScienceMediaCentre, 26 March 2020). The new viruses infect in turn other cells, which, produce new viruses etc. As far as the COVID-19 is concerned, we do not know yet this minimal infectious dose.

Then, the amount of virus an infected individual produces is the viral load (Prof Jonathan Ball, Ibid.). Note that we do not know if, for the COVID-19, there is a link between high viral load and severity of illness (Marta Gaglia and Seema Lakdawala, “What we do and do not know about COVID-19’s infectious dose and viral load“, The Conversation, 14 April 2020).

Now two things happen, which do not always take place synchronously, but that are often considered together: infecting other people and developing symptoms and becoming ill. Here we focus mainly on the contagion aspect of the COVID-19, paying as much attention as possible to what happens outside hospitals.

Viral shedding, spreading the disease and contagion

Now, the infected person will also expel some of the virus that has replicated within her body in the environment through various means. This is known as viral shedding.

Once another person absorbs parts of this viral shedding and as soon as the minimal infectious dose is reached, the second person becomes infected and the process continues. Contagion has taken place.

Erin Bromage, Associate Professor of Biology, describes how this process can take place in a post that is very easy to read (“The Risks – Know Them – Avoid Them“, 6 May 2020). He points out that contamination may occur at once, or through absorption of many smaller doses of virus. Nonetheless, in that case, we do not know the exact process through which each dose of virus remains in the organism and for how long, if a small dose could become inactive or be expelled for example.

We know that the virus is transmitted through respiratory droplets as well as through contact with infected materials. However, recently American studies have shown that the virus could also be airborne, which other scientists still debate (e.g. Tanya Lewis, “How Coronavirus Spreads through the Air: What We Know So Far“, The Scientific American, 12 May 2020). Lewis explains that the difference between airborne contagion and contagion through respiratory droplets is thin, and depends actually on the size of the droplets (Ibid,). Airborne contagion “refers to transmission of a pathogen via aerosols—tiny respiratory droplets that can remain suspended in the air (known as droplet nuclei)—as opposed to larger droplets that fall to the ground within a few feet” (Ibid.).

As a result ventilation becomes an importent factor that must be considered as favouring contagion or, on the contrary, making infection more difficult (Ibid., Bromage, Ibid.). It may either help clear virus present in the air and on surfaces, or, on the contrary, move infectious viral elements elsewhere, where people may become infected… when they thought they respected social distancing. Bromage, for example, explains that infection may take place within an empty room that has been previously infected. He also highlights the dangers of air conditioning that may propagate virus throughout space.

Thus, Bromage stresses that the fundamental equation is “Successful Infection = Exposure to Virus x Time”, and that this equation is strongly impacted by ventilation, i.e. volume and flow of air (Ibid.).

Incubation

Usually, once infected, at one stage, symptoms may appear. As a result, people who are ill and have symptoms may withdraw from society, which diminish the risk to transmit the disease. This is even more so if the symptoms are strong enough to incapacitate the infected individual. Meanwhile, the patient also needs care.

The time between contamination and appearance of symptoms is called the incubation period. To date, a study reviewing 181 cases, estimates that “fewer than 2.5% of infected persons will show symptoms within 2.2 days (CI, 1.8 to 2.9 days)”, and 50% of people will have developed symptoms between 4.5 and 5.8 days after contamination (Stephen A. Lauer, MS, PhD et al., “The Incubation Period of Coronavirus Disease 2019 (COVID-19) From Publicly Reported Confirmed Cases: Estimation and Application“, Annals of Internal Medicine, 5 May 2020). 97.5% of those who develop symptoms will do so within 11.5 days (CI, 8.2 to 15.6 days) of infection (Ibid.). However, “these estimates imply that, under conservative assumptions, 101 out of every 10 000 cases (99th percentile, 482) will develop symptoms after 14 days of active monitoring or quarantine.”

Previously, Zhong et al., had estimated the longest incubation period to 24 day (Clinical characteristics of 2019 novel coronavirus infection in China, 6 February 2020, medRxiv). Meanwhile Chinese officials had reported a case with a longer incubation period of 27 days (Angela Betsaida B. Laguipo, “Coronavirus incubation period could be 27 days, longer than previously thought“, News Medical, 24 February 2020).

This appears to correspond to a little noticed fact: in April, China increased the length of its quarantine in Heilongjang from 14 days to 28 days (Reuters, “China’s Harbin orders 28-day quarantine after rise in imported cases“, 12 April 2020). The system of quarantine and their duration is however complex and diverse in China, and all arrival cities or regions do not use a 28 days length (see European Chamber, Travel Policies to and from Cities in China, 15 May 2020).

Yet, an illness does not always develop in such an easily observable way. We have other cases, which favour contagion, as happens with the COVID-19.

The COVID-19 and contagion

Pre-symptomatic contagion

If a person is infected and is contagious before to become symptomatic, then the virus may spread more. Indeed, as people have neither felt unwell nor, once the new disease has been identified, detected as infected, then they carry on with their lives. Meanwhile, they contaminate other people and materials.

This is the case with the SARS-CoV-2. He et al. found that 44% of secondary cases, despite strong diverse measures to suppress the pandemic, were infected by pre-symptomatic patients (“Temporal dynamics in viral shedding and transmissibility of COVID-19‘, 15 April 2020). They “inferred that infectiousness started from 2.3 days (95% CI, 0.8–3.0 days) before symptom onset and peaked at 0.7 days (95% CI, −0.2–2.0 days) before symptom onset”. As a result, they recommend that “the definition of contacts covers 2 to 3 days prior to symptom onset of the index case”.

Another more recent study, from India, considering 1251 individuals from the literature, assessed that 68,4% of infections resulted from pre-symptomatic individuals (Meher K Prakash, “Quantitative COVID-19 infectiousness estimate correlating with viral shedding and culturability suggests 68% pre-symptomatic transmissions“, medRxiv 2020.05.07.20094789).

However here, because patients are contagious before symptom onset, then, the problem is that scientists and people fighting against the pandemic need to work backwards. They work from the time of symptom onset, the first easily observable evidence they have of illness. But, once illness has started, then we are already up to three days late on the virus, if we consider He et al. findings, with the longest confidence interval, to be on the safe side.

Thus, during these three days, the virus has had time to propagate among the population. This explains the importance of testing and searching for contact cases, as a key way to fight against a pandemic. Testing and contact tracing is also an attempt to move from working backward to working forward, meanwhile anticipating and not anymore reacting to the virus.

Pre-symptomatic contagion combined with early incubation

Furthermore, let us combine pre-symptomatic contagion with knowledge on infection and incubation. We may estimate that if “fewer than 2.5%” show symptoms within 2.2 days”, knowing that infectiousness starts 2.3 days before symptoms onset, then “fewer than 2.5%” of infected people will be infectious quasi immediately, probably within hours. As a result, they will also have time to infect others extremely rapidly. Research looking for this exact phenomenon will need to confirm or falsify such findings.

Nonetheless, waiting for further research, safety and precaution demand that such cases and corresponding estimates be integrated within a framework for action. The quasi-instantaneity of the phenomenon means that, for up to 2,5% of infected people, contagion is almost certain to happen whatever the tests and contact tracing carried out.

Indeed, to stop these people infecting others, we would need to know they are infected at the very moment they are and to be able to immediately isolate them. This would mean creating a device that can test individuals permanently, without secondary effects nor pain and without errors. Furthermore, this device would have to be able to alert the infected people. Receiving the signal, these infected people could behave in such a way they won’t risk infecting others. However, considering possible or rather probable unwillingness of a fraction of the population to comply with isolation needs, trends towards incivility and more rarely even malevolence, it is likely that the device would also have to warn authorities. Assuming such a device were to exist, ethicals debate are likely.

In any case, once infection is detected, isolation would have to be implemented immediately – the easiest and least constraining isolation being truly efficient masks, of course.

Waiting for such a device, the only way to stop this specific type of contagion, and until these 2.5% can be better characterised, is to lessen or even stop the quantity of virus each and every individual can shed in the environment, on the one hand, and to heighten to the maximum the protection of another person against absorbing the virus. This means efficient face masks and rigorous hygiene to stop contamination through surfaces and materials (for a recent review of studies on face masks’ efficiency see, Chu et al., “Physical distancing, face masks, and eye protection to prevent person-to-person transmission of SARS-CoV-2 and COVID-19: a systematic review and meta-analysis“, The Lancet, 1 June 2020).

Asymptomatic contagion

We saw that symptoms, which mean that people feel unwell, are a natural way to slow and reduce contagion. Indeed, people stop their usual activity because the do not feel well. However, other possibilities exits.

If people are ill and contagious, without ever developing symptoms – they are asymptomatic – then the virus may spread more. Indeed, these people will be completely unaware that they are ill, and how could they know? They will thus carry on with their usual activities, meanwhile infecting others.

Furthermore, many detection systems (at least up until the COVID-19) were implemented to identify symptoms. Thus, even once a new epidemic is detected, asymptomatic people will not be stopped by the various measures taken to stop contamination (Monica Gandhi, M.D., M.P.H.et al. “Asymptomatic Transmission, the Achilles’ Heel of Current Strategies to Control Covid-19“, The New England Journal of Medicine, 24 April 2020). Thus contagion may spread even when one thinks protected by various systems.

COVID-19 patients can be asymptomatic and contagious

This is what happened with the COVID-19.

We now know from different studies carried out in different countries that asymptomatic patients are contagious (Monica Gandhi, M.D., M.P.H.et al., ibid; Zhou R, et al., “Viral dynamics in asymptomatic patients with COVID-19“, International Journal of Infectious Diseases, 7 May 2020).

We had early indications of this with the case of the early German cluster (24 January 2020, warning correspondance 30 January 2020 in NEJM), even though at the time the WHO refused to recognise the possibility of asymptomatic contagion (see Rothe et al. 2020 “Transmission of 2019-nCoV Infection from an Asymptomatic Contact in Germany“, NEJM; Helene Lavoix, The New Coronavirus COVID-19 Mystery – Fact-Checking, The Red (Team) Analysis Society, 5 February 2020).

The WHO, mentioned asymptomatic cases in its situation report-46 on 6 March 2020. In its 27 May 2020 Interim Guidance “Clinical management of COVID-19” it recognises the contagious potential of asymptomatic patients (see pp. 11, 40).

How many patients could be asymptomatic?

We are still unsure of the number of COVID-19 patients who could be asymptomatic. Findings vary widely.

Early estimates, mixing asymptomatic and paucisymptomatic patients, assess that between 30% to 60% of COVID-19 infected patients will be in these cases (Institut Pasteur, updated 27 mai 2020).

In a study on 78 COVID-19 patients “from 26 cluster cases of exposure to the Hunan seafood market or close contact with other patients with COVID-19”, Yang et al. found that 42.3% patients were asymptomatic (Comparison of Clinical Characteristics of Patients with Asymptomatic vs Symptomatic Coronavirus Disease 2019 in Wuhan, China. JAMA Netw Open 27 May 2020).

In another study on a cruise ship departing from Ushuaia, Argentina in mid-March 2020, and infected with the COVID-19, the authors found that 84% of the COVID-19-positive patients were asymptomatic (Ing A.J., et al., “COVID-19: in the footsteps of Ernest Shackleton“, Thorax, 27 May 2020).

The percentages are so high that it is crucial to consider these cases. What may be good news in terms of health and severity of disease – the number of asymptomatic patients – may, on the contrary be bad news in terms of controlling contagion.

Dynamics of asymptomatic contagion

Yang et al. (Ibid.) found that the median duration of viral shedding for asymptomatic patients was 8 days, with a possible range from 3-12 days, compared with 19 days, with a possible range from 16-24 days for symptomatic ones.

Another 7 May 2020 Chinese study on a few cases (31 patients initially asymptomatic, out of which 9 remained asymptomatic), showed that the duration of asymptomatic patients’ viral shedding was between 5 and 14 days, and similar to the duration of the viral shedding of symptomatic patients – between 5 and 16 days (Zhou R, et al., ibid.). The good news was that the viral load of asymptomatic patients in this study was not as high as for symptomatic patients (Ibid.). Zhou et al. thus suggest “the possibility of transmission during their asymptomatic period” while calling for further research.

The study also highlighted that the viral load peaked earlier in asymptomatic patients (as selected in the study – Zhou et al., Ibid.).

However, because we do not know when infection took place for each patient (we only know the date when they tested positive to COVID-19 and hospitalised), it is difficult to infer anything certain in terms either of exact peak time for viral load or even maximum duration of viral shedding (Zhou et al., Ibid.). We also have no idea about the incubation period, as the latter is calculated according to symptoms.

Even though the contagion potential of asymptomatic people may be lower, for our purpose, we need nonetheless to take it into account. As for the duration of viral shedding to consider, because the studies available still concern a small number of patients, out of caution and considering the risks, it seems better to consider the longest possible duration, i.e. 14 days.

As for pre-symptomatic infections, the only way to stop contagion spread by asymptomatic patients is first to identify them through testing and second to isolate them. The duration of the isolation must be, ideally, the whole length of the period during which they could possibly transmit the virus, i.e. the duration of the viral shedding. Here we have, however, a problem, as appeared in Zhou et al. study. Once we identify someone who is infected and does not have any symptoms, we do not have any way to know when this person has been infected, nor if s/he is pre-symptomatic or asymptomatic.

If we imagine s/he was infected the day of detection (in the case of the shortest possible incubation), s/he may start developing symptoms two to three days later. Thus it was a pre-symptomatic case. The isolation period must be the classical isolation period of a symptomatic patient with COVID-19, starting from symptom onset (and NOT from the day of detection), as detailed below.

If we s/he does not develop symptoms, then it is an asymptomatic case, and the patient must be kept in isolation during the longest possible viral shedding duration, i.e. 14 days. Logically, if the duration identified by research is correct, then the patient should stop being infectious before the end of the 14 days. Tests ideally will need to be done again during this period, and, again ideally, the person will not be released from quarantine both before 14 days and before testing negative (including a system to account for false negative).

Mildly symptomatic contagion

Then, we have people who are contagious and only have very mild symptoms. Notably at the start of the epidemic, when it is not yet known, these people will not stay at home because of these mild symptoms, which will also allow the virus to spread.

Later, once the epidemic and the risks in terms of contagion are known, economic duress, job and career competition, as well as absence of support in everyday life are also likely to favour a behaviour where mildly symptomatic cases may be forced or strongly enticed to overcome mild symptoms and proceed as usual. Incivility and malevolence may also possibly become factors of conscious and willed spread of the disease.

How many symptomatic COVID-19 patients develop mild symptoms

According to the WHO, 40% of symptomatic COVID-19 patients develop a mild form of disease. We do not know if they include asymptomatic people in this estimate.

As previously, we need to know the duration of viral shedding as well as, ideally, the kinetics of the viral load.

Dynamics of mildly symptomatic contagion

According to He et al. (Temporal dynamics in viral shedding and transmissibility of COVID-19‘, 15 April 2020), the viral load of patients was highest closest to symptom onset and decreased until 21 days after symptoms’ onset, without difference according to illness severity.

This is longer than the estimated duration of viral shedding found by Zhou R, et al., which was between 5 and 16 days.

Meanwhile, in another small study on 16 Chinese patients with mild symptoms, scientists found that “the mean duration of symptoms was estimated to be 8 days (interquartile range, 6.25–11.5). Most important, half (8 of 16) of the patients remained virus positive (a surrogate marker of shedding) even after the resolution of symptoms (median, 2.5 d; range, 1–8 d) (Chang et al., “Time Kinetics of Viral Clearance and Resolution of Symptoms in Novel Coronavirus Infection“, Am J Resp Crit Care Med , 1 May 2020). Thus, at worst, patients with mild symptoms could remain contagious for up to 11,5 days plus 8 days, i.e. 19,5 days.

Peak infectiousness is reached before day 5 after the onset of symptoms and then decline during the first week for patients with mild disease (Wölfel, R. et al., “Virological assessment of hospitalized patients with COVID-2019“, Nature, 1 April 2020). If there is lung infection then the peak is reached around 10 to 11 days.

Furthermore, Wölfel, R. et al underline a very important point: people can both develop antibodies and remain infectious:

“Seroconversion occurred after 7 days in 50% of patients (and by day 14 in all patients), but was not followed by a rapid decline in viral load.” 

Wölfel, R. et al., “Virological assessment of hospitalized patients with COVID-2019“, Nature, 1 April 2020

Thus the idea to use serological tests haphazardly and to let people believe that having developed antibodies – testing positive with serological tests – could make them safe for others is false, thus extremely dangerous and will lead to further contagion.

For its part the WHO highlights that “limited published and pre-published information provides estimates on viral shedding of up to 9 days for mild patients and up to 20 days in hospitalized patients” (Interim Guidance 27 May 2020, p.11). It thus does not concord with what He et al. and Chang et al. found.

For the sake of safety, and waiting for further research, the longest period of danger, i.e. 21 days, must be considered, with possibly lighter yet safe measures for the last 5 days (21 days minus 16 days).

This means that infected people with mild symptoms can potentially remain contagious for up to 21 days following symptom onset plus the up to 3 days of pre-symptomatic contagion. If we take Chang et al. study, the dangerous period is 19,5 days plus 3 days. If these people carry on with their lives, then in 22,5 to 24 days, they have the time to infect quite a lot of other people, according to their lifestyle.

As for the other cases, it is imperative that these patients be isolated. Here, the major hurdle to overcome may not be not knowing about the disease as in asymptomatic and pre-symptomatic contagion, but other factors external to the illness itself, from economic to cultural ones. Of course, these factors will also be active for other cases, but here they are possibly the most important to consider and overcome.

Moderate, severe and critical cases and contagion post-resolution of symptoms

Contagion through moderate disease

When people develop moderate symptoms, i.e. pneumonia (40% cases) (WHO Interim report 27 May 2020, p. 13), even though they are not hospitalised, their condition forces them to stay at home. The potential of contagion is limited to family and health personal caring for the patient.

As long as the illness is unknown, then contagion may spread easily. Once the disease and its infectivity are known, as after a first wave, then the contagion risks should become minimal.

For our purpose it may nonetheless be necessary to check how these patients are handled, considering notably cultural and economic factors. The maximum length of viral shedding of 21 days after symptom onset will need to be applied (He et al., Ibid.).

The WHO suggests that isolation and measures stop 10 days after symptom onset “plus at least 3 days without symptoms (without fever and respiratory symptoms).” (Ibid, p. 11).

Severe and critical disease

Finally, when people develop a severe form of disease, then they are hospitalised. As a result, they are removed from the normal course of life. At the start of an epidemic if a special way to separate them from other patients is not implemented, which may not be as the disease is not identified, or if ever the health system breaks down, then they can contaminate other patients and the medical staff. This risk should disappear or be extremely reduced once the disease is known.

Then, once severely ill patients are released post-recovery, if they are still contagious they will again contaminate other people around them. As they may be convalescent, the contamination may be less intense though.

With the SARS-CoV-2, it seems that viral shedding lasts 20·0 days (IQR 17·0–24·0) from illness onset for severely ill recovering patients, and lasts until death (Huang C. et al., “Clinical features of patients infected with 2019 novel coronavirus in Wuhan, China“, The Lancet, Vol 395 March 28, 2020: 1058).

However, patients may continue to shed virus long after being discharged from hospital. The WHO underlines that “the longest observed duration of viral RNA detection in survivors was 37 days”, using Huang et al (Ibid.) and Zhou F. et al. (“Clinical course and risk factors for mortality of adult inpatients with COVID-19 in Wuhan, China: a retrospective cohort study”, Lancet, 2020).

Meanwhile, the infectious power of the materials with which contagious patients have been in contact also plays a part, including natural elements, such as plants, water, rock, sand. And here our knowledge is even more uncertain. hence we compensate uncertainty by creating barriers between human beings and surfaces where the virus could be. This allows also to overcome uncertainty… better safe than sorry.

Anti-contagion measures and detecting future waves

Here, looking at the dynamics of contagion and taking one by one the various cases through which infection can take place, we have highlighted what could or should ideally be done to stop contagion, according to research and knowledge identified up to 2 June 2020.

Assessing measures and policy against COVID-19 contagion

The further away the measures set up to stop contagion are from the ideal, the more unnoticed contagion can take place.

We summarise these ideal measures in the table below:

	Knowledge gathered		Ideal measure		Main challenges
Transmission	Transmission through respiratory droplets		Face masks and hygiene, social distancing.		Cultural and normative factors, education, economic factors (cost and availability of efficient masks)
	Transmission via aerosols		Face masks and hygiene, social distancing.	Cleaning and adaptation of all air conditioning and ventilations
	Transmission via surfaces	Not included in article
Incubation			Quarantine/isolation for 0 to 28 days		Refusal to be quarantined for so long – cost (but lower than a country lockdown)
Pre-symptomatic contagion		Contagious up to 3 days before symptom onset	Case tracing and testing		The criteria for identification of contagion must be infection, not symptoms
Pre-symptomatic contagion and early incubation	Infection and infectivity take place quasi simulateously	Contagious quasi-instantaneously (within hours?)	Face masks and hygiene		Quasi-instantaneity of viral shedding (? further specific research needed)	Impossible to detect and isolate on time
Asymptomatic cases	Infected up to 27 days before viral shedding starts		Isolation/quarantine for up to 14 days after tested positive		Identification of infection – socio-economic and cultural factors stopping isolation and favouring hiding contacts	Making sure the period is correct, dearth of studies.
Mildly symptomatic contagion	Infected up to 27 days before symptom onset	Contagious up to 3 days before symptom onset	Isolation/quarantine for up to 21 days after symptom onset (irrespective of resolution of symptoms)	Possible lighter measures for the last 5 days (to consider uncertainty and difference among studies)	Identification of symptoms onset, socio-economic and cultural factors stopping isolation and favouring hiding symptoms	Identification of Infection
Moderate disease contagion	Infected up to 27 days before symptom onset	Contagious up to 3 days before symptom onset	Isolation/quarantine for up to 21 days after symptom onset (irrespective of resolution of symptoms)	Most at risk are family and health personal caring for the patient –	Further study needed
Severe disease contagion	Infected up to 27 days before symptom onset	Contagious up to 3 days before symptom onset	Hospital care – contagion within hospital – considered as well handled once disease known	For post-recovery patients, up to 24 days after symptom onset? Until test negative plus 3 days?	Does not fit with length of hospitalisation – further research needed
Ciritical disease contagion	Infected up to 27 days before symptom onset	Contagious up to 3 days before symptom onset	Hospital care – contagion within hospital – considered as well handled once disease known	For post-recovery patients, up to 24 days after symptom onset? Until test negative plus 3 days?	Does not fit with length of hospitalisation – further research needed
Death			Special measures until burial		Cultural and economic factors
All cases			Must test negative at least once (or more) before being released.	Family members and all people in regular contact with people who are ill should be tested regularly during their possible incubation period and carry out strict hygiene measures plus face mask plus protective equipment?	Cultural and normative factors, education, economic factors, (cost and availability of efficient masks)

Evaluation against the ideal measures must be done at country, region or non-state actor level because of the array of measures decided globally. We also need to consider how well these measures are implemented, which may vary according to cases. We would also need to add contagion through materials which we have not detailed here and not forget the critical importance of ventilation and cleaning of air conditioning.

With time, the more unnoticed contagious cases exist, the more likely the quantity of infected people swells. Indeed, day after day, each missed case will potentially infect other people. As the missed cases pile up and infect others, at one stage, even testing – to say nothing of case tracing – may become difficult. The number of cases will be so numerous that we shall see the second wave emerge.

Considering the proportion of disease severity, the more people are infected, the more likely we will be in the case of an uncontrollable contagion with an increasingly intense second wave.

At this stage, we need to introduce other country specific characteristics. Indeed, we need to consider not only the health system but also the specific demographics of a zone, as the severity of the disease, thus hospitalisation, depends on other pathologies and on age (Robert Verity, et al., “Estimates of the severity of coronavirus disease 2019: a model-based analysis“, The Lancet Infectious Diseases, 23 March 2020). Furthermore severity of disease and hospitalisation may also depend on countries and thus domestic clinical studies may be better adapted.

The case of quarantine for arrivals on a territory

Considering the importance of travels for the spread of the pandemic, as highlighted in “The Hidden Origin of the COVID-19 and the Second Wave” (Helene Lavoix, The Red (Team) Analysis Society, 25 May 2020), we look here in more detail to the quarantine that would need to be set up at arrival in a country.

If a quarantine needs to be implemented to isolate someone who is potentially infectious, then this quarantine must last 28 days as detailed above. Such a quarantine will most probably be too long but it will cover the longest possible time of incubation. It will assume that a person was infected on the day of the start of the quarantine, and allow for the longest possible time of incubation.

If, for example, unknowingly the person had been infected 5 days before the start of the quarantine, then the quarantine could ideally be reduced to 23 days (28-5 days). But we do not have a way to know when infection took place. Because of this inability to know exactly when a person is infected, then people cannot be released before these 28 days. Even in this case, it would seem that we do not cover 100% of infections.

Thus, if we compare quarantine policies against this benchmark, we can evaluate the potential for a second wave. The usual 14 days standard tells us that we are missing 101 out of every 10 000 cases, as Lauer et al. highlighted. However, it is difficult to estimate how many people are concerned quantitatively.

Certainly, when the number of infected cases has been lowered thanks to lockdown as in many places, then quarantines may appear as unfair practice. However, if the virus does not change, unfortunately, there is no other way, as long as we have neither vaccination nor certain treatment.

For example, on 31 May 2020, one asymptomatic case was identified in China, which had arrived on a flight chartered from Germany to China, to try to re-kindle business (Stella Qiu, Ryan Woo, “China says 2 new coronavirus cases, asymptomatic case on German charter“, Reuters, 31 May 2020). This shows that even in a country that is said to have mastered its epidemic such as Germany, the virus circulate. Had China not tested business people at arrival and had a quarantine not existed, then the asymptomatic carrier would have been free to move around and infect people for up to 14 days in China (the duration of viral shedding for asymptomatic case). If one traveler was asymptomatic, it means s/he was infected and expelled virus during the flight. Thus, all other passengers may also be incubating. They thus all need to be quarantined. The risk of not doing so is too severe. Actually all passengers could also have been infected before boarding.

As the German symptomatic case arriving in China and as the too short generalised 14 days quarantine show, we are, globally, letting cases slip and move across countries and continents. Thus, social distancing measures, various hygienic measures and face masks here become even more important to try making sure these missed cases will infect as few people as possible.

As far as these individual measures are concerned, note that the burden is on each and every citizen. Somehow, that maybe considered as a test of the true capacity to democracy of a society. Meanwhile, cultural values will be important. For example, the obvious disregard many European populations, notably in capital cities, as well as many Americans, show for face masks and social distancing measures does not bode well for the ability to mitigate a second wave.

Other factors, however, such as population density, legitimacy, economic duress and inequality will also be critical to assess how much citizens will respect measures.

To conclude, once a detailed evaluation of each anti-COVID-19 measure is done for each country, we shall get a more precise assessment of the possibility for a second wave in that country. Using then each departure from the ideal, and characterisation of this departure, we shall be able to create a system of indicators that will be able to warn about happenstance of a second wave. Interestingly, this warning system may help steer policies and thus stop the very occurence of a second wave.

A similar system maybe created for each non-state actor. It will help assessing the potential of this actor as a future cluster and vector of the disease.

Now a crucial question remain, what if the SARS-CoV-2 and its illness, the COVID-19 change? This is what we shall see next.

Detailed Bibliographical References

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