key: cord-315756-g6g34uvh
authors: Danchin, A.; TURINICI, G.
title: Immunity after COVID-19: protection or sensitization ?
date: 2020-05-23
journal: nan
DOI: 10.1101/2020.05.21.20108860
sha: 
doc_id: 315756
cord_uid: g6g34uvh

Motivated by historical and present clinical observations, we discuss the possible unfavorable evolution of the immunity (similar to documented antibody-dependent enhancement scenarios) after a first infection with COVID-19. More precisely we ask the question of how the epidemic outcomes are affected if the initial infection does not provide immunity but rather sensitization to future challenges. We first provide background comparison with the 2003 SARS epidemic. Then we use a compartmental epidemic model structured by immunity level (taken here as age classes) that we fit on available data; this allows to derive quantitative insights into the future number of severe cases and deaths.

most relevant lessons from the course taken by the disease will take time. In particular many perplexing questions have not yet found adequate answers, that would be crucial for the design of optimal treatment policies and healthcare strategies, both at the individual and societal level. Among these questions, prominent ones are: Why are the mortality patterns so skewed toward higher ages? What is the common denominator of the observed comorbidities that affect in a non-negligible way the outcome of the disease? What is the size of the asymptomatic cohorts? Are asymptomatic (or paucisymptomatic) cases a barrier or an accelerator of the disease propagation? etc. To these salient questions, which deal with the present situation, we should add questions relative to future outbreaks, their severity and characteristics. This is particularly important as health authorities have, for obvious reasons, focused on the design of vaccines, despite the fact that vaccines are sometimes extremely difficult to obtain [17] . In particular while a response to previous infections is usually protective it can sometimes be deleterious and result in severe outcomes (see e.g. [16] ). Answering many of these questions requires deep understanding of the immune response of the host, whether innate or acquired, at the cellular or humoral level. Recent research pointed out that it is critical to investigate previous history of interaction between host and infective virus strains [1] . In this context, the question of whether previous infection with coronaviruses is beneficial or detrimental to the immunity of the host is a matter of active debate, see for instance [2, 21, 22] .

Here, we focus on the so-called antibody-dependent enhancement (ADE) mechanism (related to the more colorful name of cytokine storm). ADE corresponds to a situation where antibodies that normally alleviate the consequences of a viral infection end up doing the op-posite: they fail to control the virus' pathogenicity by failing to be neutralizing (i.e., the antibodies are not able to kill the virus), or even enhance its virulence either by facilitating its entry into the cell (thus enhancing the viral reproduction potential), or by triggering an extensive and misadapted reaction, thereby causing damage to the host organs through hyper-inflammation (cytokine storm).

Several documented examples are known that give rise to ADE: in SARS (see [3] ), dengue (see [11] ), HIV-1 [25] to cite but a few. This is even already documented in the case of COVID-19 as the similarity with dengue fever has resulted in false-positive identification when using diagnostic tests based on serology (see for example in Singapore [26] ). Let us illustrate the first two situations more in detail: for dengue fever it is established that a previous infection with a virus belonging to a particular serotype family can cause adverse reaction upon re-infection with a virus from another serotype (see [11] ). This unwanted outcome was demonstrated in a study that monitored two dengue fever outbreaks: a first one in Cuba in 1977 [9] , followed by a second one twenty years later (1997) [12] . Being infected during the first epidemic was proven to negatively influence the outcome of patients infected in the 1997 epidemic (with a dengue fever serotype that differed from that of 1997). To put this otherwise, the acquired immune response was fit for a given serotype but detrimental upon challenge with a different serotype. In the present context, the large time lapse between the two dates is worth emphasizing. Irrespective of whether or not the challenge is or is not related to a different serotype, we will call this situation a "Cuban hypothesis" and discuss it below.

A misadapted immune response is not limited to infection by the dengue virus (DENV). Another documented ADE case in animal models concerns the coronavirus family. M. Bolles and his collaborators (see [3] ) tested a coronavirus vaccine on animal models and the results differed, depending on the age of the vaccinated animal: while the vaccine provided partial protection against both homologous and heterologous viruses for young animal models, the same performed poorly in aged animal models and was potentially pathogenic. This shows that a faulty immune response can depend on the general maturation of the immune system, with a significant age-dependent component.

At least four human coronaviruses [229E, NL63, OC43 and HKU1 [5] ] are known to be endemic. They infect mainly the upper respiratory tract. To these we must add the now well-known strains SARS-CoV-1 (responsible for the 2003 epidemic), MERS-CoV and SARS-CoV-2. If a "Cuban hypothesis" is found to account for the persistent development of related diseases, the challenge by any one of these viruses or novel variants may reach human populations in a variety of forms. This dire anticipation prompted us to investigate the impact of such a scenario on the immune system status within the population at large. In this context, we address here the following questions: In the absence of any relevant serological information, we compared age-dependent case fatality ratios of the SARS 2003 and COVID-19. More precisely, using data from [15] (see [4, 13] for additional data) we computed the age-dependent death rate for all 1755 SARS 2003 patients in Hong Kong. The benefit of using this database is that is contains information on all patients and therefore has no representation bias. For COVID-19 such data is not yet available so we use the Institut National d'Études Démographiques (INED) database [7] at the date of May 4th 2020. The two bases do not allocate cases exactly to the same age groups, we grouped together the 5-year 2003 data to fit the 2020 INED 10year database ranges and on the other hand use uniform attribution for ages in the "above 75" 2003 HK class) to fill two corresponding classes "70-79" and "80+".

The epidemic model we explored is the following: any patient starts in a "Susceptible" (notation "S") class, can progress to the "Exposed" (notation "E") class and then either to a "Severely infected" (label "I") or "Mild infected" class (including the asymptomatic and undetected individuals, denoted "M"). The mild infected progress to a "Mild Recovered" "R M " class while the "Infected" can either die (class "Deceased", "D") or recover, class "R". The model is structured by immunity . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 23, 2020. . https://doi.org/10.1101/2020.05.21.20108860 doi: medRxiv preprint level and k is the immunity index; in practice a immunity group corresponds here to a decennial age group in the list "0-9 years" (k = 1), "10-19 years" (k = 2), ..., "80-89 years" (k = 9), "90+ years" (k = 10). Note that, as in the Pasteur Institute study [19] , we excluded from this analysis the dynamics of the COVID-19 epidemic within the retirement homes for aged people in France, as both the demographics of this part of the population and the transmission dynamics are very specific, while the data used to describe the COVID-19 dynamics in this setting is very uncertain.

Mathematically the model is written (see figure 1 for an illustration):

(1)

with the notations

To model the impact of previous infections on the next possible epidemic we have to take several facts into account: while the SARS 2003 had a negligible asymptomatic class (see [14] ) the COVID-19 has nonnegligible number of mild or even asymptomatic individuals. Those patients are usually not detected and their estimation is statistically challenging. Even more difficult is to extrapolate the state of the immune system after a mild or severe infection and how this can be translated to future immune unbalanced response. Our hypothesis is the following: a coronavirus infection will sensitize all infected persons to future infections. To quantify such an additional sensitivity we can only use data from the severely infected classes and take death as the extreme case of severity, statistically, within the group as a whole. Thus, when we consider the severely infected persons this group experienced a deleterious alteration of their immune system, which is quantified by the intensity of the outcome (death). We calculated, using the data from Santé Publique France [20, obtained as r c = 70/(70 + 922) = 7, 05%. We subsequently compared this rate with the natural death rate of the French population which is r n = 0, 9%. Following this approach we concluded that it would take f c = log(1 + r c )/ log(1 + r n ) 7.6 years of natural evolution to match the unfavorable outcomes of the group (i.e., to observe the same death rate) as that experienced for severe COVID-19 patients. As coronavirus infection is the cause of this outcome, we extrapolated the outcome assuming that each COVID-19 patient "lost" 7.6 years of immune function quality in what coronavirus adequate response is concerned (this is not to be related to chronological or biological age). On the other hand, if we compare with the data from the E-CDC [6] concerning the whole set of COVID-19 patients the rate r c becomes 25987/137779 = 18.86% and f c = 19, 28 years. We see that there is a large uncertainty arising from the way we count the cases. This is not specific to the situation we try to model but a very general difficulty in similar situations. To simplify, we considered that patients who had a first infection with SARS-CoV-2 will experience an alteration of their immune function (relative to coronavirus infections or related medical conditions) and that their immunity parameters will be similar to those of a patient in the next immunity class. In the model (1)-(7) this means that a patient that ends up in R k or R M k will start the next epidemic as if being virtually in the group S k+1 (which means having d k+1 and f k+1 parameters), even if his biological age is still be counted with those in the class S k . Note that this assumption does not imply that the patients that had a mild form of COVID will experience the next time a severe form (there are still mild forms starting in S k ) but only that the parameters f k , d k will change.

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 23, 2020. . https://doi.org/10.1101/2020.05.21.20108860 doi: medRxiv preprint 3 Results

The comparison of the 2003 and 2020 data in figure 2 shows a striking difference between a panel of several European countries (France, Spain, Italy) with respect to the Hong Kong results. All curves share a common shape: a constant null range followed by a marked (exponential) increase starting in the "30-39" age group for the 2003 data and "50-59" group for all countries in 2020. This 20 years shift at the onset of the exponential regime can be interpreted as resulting from the existence of a common cause (situated approximately 30-40 years before 2003 and 50-59 years before 2020, that is, between 1960 and 1970) that affected all people living at that date and which could explain why there are, 30 (respectively 50) years later, affected by the coronavirus outbreaks in a more severe way. Since the cause occurred before 1970 people born after this date will have no fragility, which is precisely what is seen in the plot. We interpret this as an evidence that previous infection history can negatively impact the individual outcome of a future infection. Note that historically the 1960-70 decade is rich in epidemic / virus related events: the Hong Kong flu of 1968-1969 (that killed an estimated 1 million people worldwide) but also the start of the identification of the four endemic human coronaviruses (mid-1960s). Note that such a conclusion is consistent with recent investigations, see [10] that showed that individuals are prone to repeated infection with coronaviruses, with the unfortunate consequence that not only the immunity may vanish (sometimes within a year) but that the re-infection can be more severe. Data displayes in the figure 2 substantiates the same conclusion.

Here, we made use of the methodology described in section A and more specifically the formulas (16) and (19) to estimate the constants f k and d k ; note that there is an important uncertainty in the mortality data (especially for low aged groups) which induces uncertainty in the estimations. Same is true for the overall epidemic size used as input in our model and took from [19] . However the figures are generally in line with known results, in particular the strong correlation between the presence of mild (including asymptomatic) cases and age; see Table 1 for details. Table 1 To estimate parameter d k we used formula (16) and the data from [8] To estimate f k we use (19) and data from INED to fit the total deaths for given attack rate α t = 5.7% as in [19] . 

Here we compared the outcome, in terms of deaths by age groups and severe cases by age groups, of the Cuban hypothesis described in section 3.1. Namely, under the assumption that a patient who had a previous infection will move to another immunity group, we derived the distribution of deaths by age and severe cases by age, computed as detailed in appendix A, proposition 2. The results are plotted in figures 3, 4 and 5. The mean death age goes down from 79.13 to 76.15 and the total number of deaths goes from 16705 up to 20481 (+22.6%). Even more spectacular, the evolution of the number of severe cases goes from 134 000 up to 457 000 (+340%). Note that in both cases the results depend on the total epidemic infection rate, which is between α t = 5.7% (present) and the group immunity rate 1 − 1/R 0 (i.e., 70% for R 0 = 3.3). The hypothesis of a 70% infection . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 23, 2020. . https://doi.org/10.1101/2020.05.21.20108860 doi: medRxiv preprint Fig. 3 Distribution of deaths by age (as ratio D k /D with respect to overall death toll) for the initial infection and projection for a similar secondary infection event. Note that since the ratio is time independent the time at which we compute it does not need to be specified. We consider that after a first infection, recovered individuals in R k and R M k will share the immunity parameters with individuals in the k + 1 group. We take R 0 = 3.3 from [19] , use α = 1−1/R 0 as total attack rate of the first infection within the population and the estimation method described in proposition 2. rate is probably too strong (although mass vaccination may contribute to it) so it should not be taken as an operational forecast but rather as an extreme scenario.

Based on a epidemic model structured by immune function (age groups), we evaluate the probability for a per- son to become a severe case. This quantitative parameter has a large incertitude because of the presence of asymptomatic cases and mild infections. We used figures from the literature that imply that children are largely asymptomatic while the older age classes show up to 20% severe forms.

Next we moved to the heart of our scenario, namely the quantification of the immune function alteration induced by an initial SARS-CoV-2 infection, similar to the antibody-dependent enhancement phenomenon. Note first that the relatively controlled nature of the 2003 SARS epidemic did not allow us to draw conclusions on how the 2003 epidemic influenced the infected (too few cases); by contrast, if a sensitizing process in the immune response triggered by SARS-CoV-2 exists, the pandemic nature of the 2019/20 COVID-19 outbreak will likely have noticeable effects on the overall population health state. In particular, this implies that additional care has to be observed when validating vaccines against the COVID-19.

We developed a scenario meant to explore the consequences that a previous infection changed the likeliness to get a severe form when challenged by a new infection, increasing the death risk of severe forms. Irrespective of the precise figures, we expect that this could be used as a promising methodology to quantify the epidemiological impact of ADE, with coronaviruses as key examples.

The deterioration of the immune function can be evident on two occasions: either when a second epidemic occurs or when submitted to a challenge The challenge can be very diverse, not necessarily in the form of a fully-fledged epidemic but also a small infection with an endemic coronavirus. This may manifest in the form of multi-organ inflammation as witnessed in UK, France, . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 23, 2020. . https://doi.org/10.1101/2020.05. 21.20108860 doi: medRxiv preprint Canada and the US with some presentations recalling the Kawasaki syndrome [24, 18, 23] .

We present simulation data that quantify the possible impact of such a immune function evolution. Of course, our model has many limitations and further investigation into the determinants of the immune dynamics is necessary to wholly the conditions of the correct and impaired immune response. Until this is carried over, past COVID-19 patients should not be considered as having a life-time permanent acquired immunity to SARS-CoV-2 or other coronaviruses.

We denote π k the proportion of people in class k within the total population at t = 0 and make the convention that this is strictly positive (otherwise the class is entirely deleted):

Lemma 1 Suppose that the initial state of the system (1)-(7) satisfies the relations:

Then for any time t ≥ 0 and k, l = 1, ..., K:

Before giving the proof we note that, if all quantities are strictly positive, the hypothesis can be written in a more convenient form as:

, ∀k, l = 1, ...K, which is intuitively not surprising, for instance the first identity says that at the beginning of the epidemic the probability for an individual to belong to the E k class is proportional to the number of people in the S k class. Moreover, we can prove a stronger version of the hypothesis stating that the conclusion is true in an approximate sense even if the hypothesis is not verified (with exponentially vanishing error). In all cases this is true when S(0)/(S(0) + ... + D(0))) 1 which is a generally accepted hypothesis.

Another remark is to be made on the different status of the two identities in (16) : the first one allows to set the d k constants bacause the corresponding data (deaths over deaths plus discharged) is available. On the contrary the second one is not of immediate use because the proportions of mild forms are not known to reasonable precision. On the contrary (17) can be used to compute f k if an estimation of the relative instantaneous epidemic size (α t in the equation below) is available.

Relative instantaneous epidemic size:α t = S(0) − S(t) S(0) .

Note that the estimation (17) involves E(t) which can only be computed after f k are known. So in full rigor this is a fixed point procedure but in practice, given the uncertainties in the value of α t we will neglect E(t) for small values of α t and use the formula:

Proof To prove the assertions we note that for instance equation (2) implies that for any t ≥ 0:

with η(t) a positive function that does not depend on k and l. Together with the hypothesis this proves the first part of (14) . We see that even if the hypothesis is not verified the error term [E k (t)S l (t) − S k (t)E l (t)] (with respect to the conclusion) will decay exponentially fast. The second part of (14) follows from the formula S k (t) = S k (0)e − t 0 (M +I)(τ )dτ . The other parts are obtained in a similar way.

Proposition 1 Under the hypothesis of lemma 1 the aggregate quantities S, E, M , I, R M , R and D follow the reduced SEMIR2D model:

wheref = k f k π k ,d = k d k π k f k /f . In addition,

Proof The proof uses the previous results. For instance from first part of (14) we obtain E k (t) E(t) = S k (t) S(t) which together with the second part of (14) gives the first identify in (31). The other relations are obtained in order from (3) and then (7).

Note that the proposition 1 implies in particular that the distribution { D k (t) D(t) = π k f k d k fd , k ≥ 1} of deceased by age is constant in time, as is the distribution { D k (t)+R k (t)

= π k f k f , k ≥ 1} of severe forms by age.

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted May 23, 2020. . https://doi.org/10.1101/2020.05.21.20108860 doi: medRxiv preprint Proposition 2 Suppose (E + M + I)(0) 0 and that the epidemic is over at t = ∞ (that is (E + M + I)(∞) 0), and denote by α = (S(0) − S(∞))/S(0) the epidemic size in percentages of S(0). Then:

Suppose now that we migrate R k (∞) and R M k (∞) to the k + 1-th class (note that their age still corresponds to the class k). Then the newly formed groups have the following constants f k andd k :

In particular if one compares the initial epidemic and the challenge (denoted with˜superscript) at the same point in time, i.e., I(t)+D(t)+ R(t) =Ĩ(t) +D(t) +R(t), then the ratio of severe forms in the class k between the two outbreaks will bef k /f k and for deathsd k /d k .

Proof: Equation (33) is a consequence of the relation (14) if one sums over l, recall that π k = S k (0)/S(0) and take t → ∞. Relation (34) results from (31),(32): in a similar manner as for (33) one notes that 

where for the last equation we used both hypothesis. Thus in the class k there will be, at challenge, two types of individuals, the ones from S k (∞) having parameters f k and d k and the ones from R k (∞) + R M k (∞) with parameters f k+1 and d k+1 . Using (33), (34) we obtain (35) and (36).

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Acknowledgements We thank the CNRS MODCOV19 research platform for their support.

The authors declare that they have no conflict of interest.