key: cord-0962733-i863q03q authors: Rom-Kedar, V.; Yaniv, O.; Malka, R.; Shapiro, E. title: The Immune-Buffer COVID-19 Exit Strategy that Protects the Elderly date: 2020-09-14 journal: nan DOI: 10.1101/2020.09.12.20193094 sha: 2a5866d07f4684d504ceaf38912a8410f67372d5 doc_id: 962733 cord_uid: i863q03q COVID-19 is a viral respiratory illness, caused by the SARS-CoV-2 virus with frequent symptoms of fever and shortness of breath. COVID-19 has a high mortality rate among elders. The virus has spread world-wide, leading to shut-down of many countries around the globe with the aim of stopping the spread of the disease. To date, there are uncertainties regarding the main factors in the disease spread, so sever social distancing measures and broad testing are required in order to protect the population at risk. With the increasing spread of the virus, there is growing fraction of the general population that may be immune to COVID-19, following infection. This immunised cohort can be uncovered via large-scale screening for the SARS-CoV-2 (Corona) virus and/or its antibodies. We propose that this immune cohort be deployed as a buffer between the general population and the population most at risk from the disease. Here we show that under a broad range of realistic scenarios deploying such an immunized buffer between the general population and the population at risk may lead to a dramatic reduction in the number of deaths from the disease. This provides an impetus for: screening for the SARS-CoV-2 virus and/or its antibodies on the largest scale possible, and organizing at the family, community, national and international levels to protect vulnerable populations by deploying immunized buffers between them and the general population wherever possible. An urgent need of humanity in the face of the COVID-19 pandemic is to buy time, until treatments and vaccines to the disease become broadly available. The question arises how to best organize the conduct of families, communities and nations in order to minimize morbidity and mortality until treatments and vaccines are available. A salient characteristic of COVID-19 is that specic sub-populations suer much higher rates of severe illness requiring hospitalization and intensive care, as well mortality, relative to others. These include especially older age-groups [2, 3] , as well as individuals suering from background illness: hypertension, obesity, diabetes and coronary heart disease [4, 5] . Data from China shows that 81% of fatalities are in the 60+ age group, and in Italy 96.5% of fatalities are in the 60+ age group [2] . Protecting these groups will thus be a central goal of any strategy for alleviating the burden of the current pandemic. Despite eorts to suppress transmission, it is likely that a signicant fraction of the population will eventually be infected, and a minute fraction of these may suer from re-infection (as of August 2020, out of above 17 million recovered patients there are only 3 veried re-infection cases). While a majority of young and healthy individuals will recover following mild illness, or even undergo asymptomatic infection, the high likelihood of widespread transmission underscores the need to protect the vulnerable from infection. At present this can be achieved only by isolating vulnerable individuals from potential sources of transmission. However, it is precisely these vulnerable individuals who are often dependent on continual care and support from family members, medical sta, nursing home sta, and others. Nursing homes for the elderly have tragically become hot-spots of infection [6, 7] . By their very nature, vulnerable individuals cannot be isolated from the segment of the population which we will call`caretakers', on which their well-being depends. Here we propose an approach, termed Immune Buer Strategy (IBS), aimed at protecting vulnerable populations while easing restrictions on the general population and on the interactions of the vulnerable individuals with some of their care takers. The key idea is to make use of able people who have been infected and recovered, as an active buer between the population at risk and the population at large. Depending on the governance mechanism in the country, or the social norms in the community, such people can be hired, drafted, or they may volunteer, into what may be called immune teams. Immune teams will serve as support sta in nursing homes and in hospitals, possibly after undergoing rapid emergency training which will allow them to also serve as nursing aides. Then, such immune teams could replace support sta and possibly, partially, some tasks of the medical sta who have been infected or are in isolation, thus helping prevent the collapse of these systems. As their numbers grow, they will also replace susceptible personnel who have not yet contracted the disease, to further protect the population at risk from being infected. As members of the sta recover, they will return to their positions, gradually replacing the less-trained immune teams. When herd immunity is achieved, including in the support and medical sta, normal functioning can resume. If the vulnerable population could meet only members of the immune teams and no one else, the vulnerable population would be absolutely protected by the IBS. This would lift the main burden from the health system, and will thus allow most of the world to return to normal activity. However, this is unrealistic. To assess the possible benets of a realistic IBS, by which some of the caretakers of the vulnerable population are irreplaceable, we constructed a mathematical model 2 . 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) preprint The copyright holder for this this version posted September 14, 2020. . https://doi.org/10.1101/2020.09.12.20193094 doi: medRxiv preprint which examines this strategy and performed simulations under a range of assumptions (see [8] for a review of various mathematical models of COVID-19). The mathematical model we propose is a variant of SEIR type models with several compartments and infection stages as detailed below (in particular it includes symptomatic and asymptomatic infections and allows to also examine the inuence of re-infections). Importantly, despite the usual notorious sensitivity of our model to parameters such as social distancing [9] , the model shows that the immune buer strategy is robust. We rst describe the model construction (with additional details in the Appendix), then its results, and then its implications. There are 5 compartments, divided to two rings of interactions. Each compartment has 7 stages, with two of them causing infections to members of the same ring. The vulnerable population interactions with each compartment is additive whereas the general population interactions with the sta is mixed. The mathematical model we derive is a variant of the SEIR models [10] , see Figure 1 . A traditional SEIR model describes the dynamics of a single population across 4 stages (Susceptible, Exposed, Infected and Recovered). Here, we describe the more elaborated dynamics, with both recovery or death as possible end stages, and with dividing the infected stage into three stages: those infected without symptoms, with symptoms and those in isolation. When tracking the dynamics of dierent sub-populations, we add compartment for each sub population, and model the interaction between those sub-populations by cross compartments interaction terms. Specically, we divide the population into ve compartments: the vulnerable individuals (denoted by N ), the essential caretakers (M ess, who, due to their specialized professional skills, cannot be replaced), the non-essential caretakers (M , who can be replaced by immune teams), the caretakers who are on leave (denoted by M res), and, nally, the general population (G). Each of the 5 sub-populations is further divided to 7 stages: 1-Susceptible, 2-Exposed, 3-Infected and Asymptomatic, 4-Infected and symptomatic, 5-Isolated, 6-Recovered, 7-Dead (the division to these stages is similar to the single population model of [11] ). Susceptible individuals become Exposed 3 . 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) preprint The copyright holder for this this version posted September 14, 2020. . https://doi.org/10.1101/2020.09.12.20193094 doi: medRxiv preprint (the latent stage of the disease) due to contacts with infected symptomatic or asymptomatic individuals. Exposed individuals who become symptomatic move to the Isolated state from which they either recover or die. Exposed individuals who become asymptomatic infect the susceptible population at a weaker rate, until they recover and join the Recovered state. The cross-compartment interaction terms ensue from the following assumptions: the on-duty caretakers come into contact with both the general population and the vulnerable population, but, individuals from the general and from the vulnerable populations do not have direct contacts. Thus, the caretakers are the buer between the general and the vulnerable populations. In the absence of intervention, this buer is leaky: some of the caretakers become infected and infect vulnerable individuals who in turn infect additional vulnerable individuals and caretakers. The intervention is aiming to reduce this leakage. Currently, these chains of infections can cause devastating outbreaks leading to deaths in vulnerable communities (see e.g. [12] ). The governments and the public monitor such outbreaks and employ social distancing strategies that lower/raise R 0 as well as the extra precautions taken when dealing with the vulnerable population. The dashed line in Figure 2 shows such outbreaks in our model with no intervention (R 0 and the vulnerable-caretakers protection factor are changed at policy changing dates, see below). Employing the IBS intervention, the fraction of recovered individuals in the caretaker compartment is increased through recruitment of recovered individuals from the general population (immune teams), at a maximal set rate, pending on availability. In Figs 2,3, this maximal rate is set to be near the optimal rate of 1%/day of the initial caretakers, M (0). Simultaneously, the number of potentially infectious caretakers is decreased by the same rate, when possible, by moving susceptible non-essential caretakers to the susceptible on-leave caretakers compartment, M res. In addition, when susceptible caretakers (either those still working or those on leave) become infected and recover, they return to work, replacing the immune teams which had been recruited from the general population. The parameters (rates of transfer among the dierent stages and the parameters for a-symptomatic infections) are taken, as far as possible, to be as in the Imperial-UK modelling study [12] (see Table 1 ). The additional parameters in our model (e.g. the duration of the isolation stage and the lower infection rates of the vulnerable compartment within itself and with the caretakers as well as the death rates) are set to reasonable values which keep the results without intervention consistent with the available data and allow tting. Briey (see details in the Appendix), calibration was done rst to the Israel data set of active cases and deaths [13] (active cases assumed to reect symptomatic cases due to the test strategy of Israel). Seven tting parameters were optimized by a least square t to the data: R 0 at each date of the 6 policy changes in Israel till August 2, and the non-essential help reduction factor µ M that was changed at the lock-down date from its initial value to the tted value (without this change the number of deaths did not match the data). To examine the IBS eectiveness, this parameter, µ M , is changed to µ M = 0.5 when the IBS is employed; its initial value is µ M = 0.6 and after lock down it is reduced to µ M = 0.2, reecting the strong regulations in elder's homes. For Germany, the help reduction factor after lock-down was taken to be the one tted for Israel, and the 6 R 0 values at the policy changing dates were tted only to the number of deaths from the data set, as it is suspected that the number of symptomatic patients in Germany was larger than reported due to the selection protocol of individuals to be tested. Tables 1 and 2 provide the parameters and initialization of the model, Table 3 provides the sensitivity analysis to each of the parameters with and without the IBS, and Figures 9 and 10 4 . 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) preprint The copyright holder for this this version posted September 14, 2020. . https://doi.org/10.1101/2020.09.12.20193094 doi: medRxiv preprint show the resulting tting to the historical data sets. Typical results of the tted model are shown in Figure 2 . We see that the immune buer approach allows to relax the social distancing restrictions as it contributes to a signicant reduction in the death toll and towards attening of the curve; hereafter, a signicant reduction of the peak of symptomatic sick people from the vulnerable population. At the beginning of August 2020, the value of R 0 = 1.2 gave the best t for the death data set, and lead to the beginning of a second infection wave. In The reduction is similar to the reduction achieved by imposing further restrictions on the general population so that R 0 is decreased to R 0 = 1.1 (with µ M = 0.5). In fact, a longer integration of additional 100 days shows that the number of deaths for this latter case of R 0 = 1.1 is larger than the one achieved by the IBS with R 0 = 1.2 (see Figure 11 in the Appendix). The novel feature of the model is demonstrated in Figure 3 . By actively increasing the number of recovered individuals in the caretaker sta through recruitment of recovered individuals from the general population while, simultaneously, actively lowering the number of potentially infectious individuals (by moving, when possible, susceptible caretakers to alternative temporary employment), the caretaker sta buer becomes gradually more immune and the idealized immune buer limit is approached long before the general population gains herd immunity. Indeed, notice that the replacement of susceptible caretakers (large drop in the solid green line) is completed about a month before the large drop in the control population of the susceptible caretakers (dashed green line). This latter drop corresponds to the dangerous stage by which many caretakers get infected as the infection becomes widely spread in the general population. The daily recruitment rate of 1% of the replaceable caretakers corresponds, roughly, to the optimal recruiting rates. Smaller rates (0.5%) lead to reduced eectiveness, while higher rates hardly improve the eectiveness of the strategy (see Table 3 ). The strategy is eective for other countries. The possibility of re-infection of recovered patients is highly debated and is raised repeatedly as a concern in general, and even more so for strategies that rely on the immunity of the recovered population. Allowing the recovered to be re-infected with a 10% rate relative to the susceptible infection rates (which is by several orders of magnitude larger than the currently known re-infection rate) shows hardly any dierence in the results, see More generally, the strategy is robust to changes in parameters as summarised in Table 3 and in Figures 6 and 7 . In Table 3 we x all parameters and i.c. as in Tables 1 and 2 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) preprint The copyright holder for this this version posted September 14, 2020. . either ±50% or, if such a change leads to number of deaths which is either 50% below or 150% above current values, the parameter is dened as a sensitive parameter 1 . In such a case the range is set so that the number of deaths will be in this range. The resulting variation in the control and in the Immune-Buer Strategy deaths and maximal loads per 10K of the vulnerable population along these intervals are recorded (to gain intuition, the ordering at the intervals end points is kept). Table 3 shows that for a xed parameter set, with a single parameter being varied, for most parameters, a three fold change in this single parameter leaves the IBS eective in cutting by approximately half the deaths and maximal loads when these are higher than current values. Notably, for many of these (e.g. the symptomatic fraction), such a three fold change can change the number of deaths and/or the maximal loads considerably (for the symptomatic fraction -a three fold change). Yet, even though the evolution of the epidemic depends signicantly on these parameters the IBS eectiveness does not: the cases where the IBS eectiveness is decreased are only those with signicantly low death numbers. In particular, when the IBS help reduction factor µ M is too low (e.g. kept at the tted value of 0.2) the number of deaths remains low and the IBS is not needed and is ineective. 1 We made one exception -we kept the vulnerable recovery period parameter as a regular and not as a sensitive parameter since the slightly higher death rates at the low bound (160% above the current value) reected transient sensitivity. 6 . 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) preprint The copyright holder for this this version posted September 14, 2020. . Interestingly, the dynamics without intervention is sensitive only to the following parameters: the symptomatic and asymptomatic infection periods, latency period and the fraction of the vulnerable population (and, clearly, to R 0 and µ M -the dependence on the R 0 parameters is shown after the IBS policy change as, prior to the IBS employment, these parameters are used as tting parameters for the prior data). In Figure 6 (respectively Fig 7) , histograms of 500 runs with roughly ±10% variations in all regular parameters and ±2% variations in the sensitive parameters for the Germany parameters (respectively the Israel parameters) are shown. More precisely, to retain the positive character of the parameters and initialization, we draw each parameter p with meanp and standard deviation ap from a the Gamma distribution Γ(K, θ) = Γ(1/a 2 , a 2p ) where a = 0.05 for regular parameters and a = 0.01 for the sensitive parameters (the meanp is taken from Tables 1 and 2 and the sensitivity is determined from Table 3 , similar results are found for uniform distribution of the parameters on the intervals [p(1 − 2a),p(1 + 2a)]). Comparing the rst two rows of Figure 6 we see that the mean of the distributions for the number of deaths and for the maximal loads are reduced by more than 45% and 60% respectively for Germany (and by more than 65% and 70% for Israel, see Figure 7 ). These gures (and Table 3 ) suggest that the strategy moves the right part of the deaths/maximal load distribution to the left, namely that it is most eective for the critical situations where the number of casualties is large. In Figure 8 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) preprint The copyright holder for this this version posted September 14, 2020. . Figure 4 : The immune-buer exit strategy applied to a small young country. A hypothetical strategy for Israel using parameters that t the Israeli historical data till August 2. If on August 2 the restriction are lifted to R 0 = 1.2, µ M = 0.5, the immune-buer strategy reduces deaths and attens the curve by 70% when compared with lifting the regulation without any additional measures. For a 6 months outlook, this exit strategy is comparable to retaining restriction at the much lower R 0 = 1.05. 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 this version posted September 14, 2020. . Table 3 ), the number of resulting deaths quickly becomes unreasonable (even though the IBS cuts it by approximately half ). So the IBS can be utilized together with a somewhat relaxed social distancing program but cannot replace it altogether. The immune-buer strategy may be needed for quite a long period: even when COVID-19 vaccines will be available, vaccination of the elderly may be less eective [14] or unsafe [15] . When vaccination will be available, the IBS can be implemented together with prioritization of the susceptible caretakers to vaccination. The degree of eectiveness of the strategy depends on many parameters listed in Tables 1 and 2 , which we divide to three categories: epidemiological, global interaction and local interaction parameters: • Epidemiological parameters of COVID-19 are uncontrolled parameters that are determined by the virus strain and environmental factors. These parameters govern the duration of latency, infectiousness, recovery, the basic transmission rates, the percentage of asymptomatic infections and the death rates (assuming a reasonable health system). Rough estimates for the mean rates appear in several previous works (e.g., see [12] ). As data is gathered, these estimates and their distributions is improved. In our model the epidemiological parameters are taken as much as possible in accordance with available estimates on COVID-19 [12] . We show that these, together with tuning of R 0 , provide a reasonable t to current data, see Tables 1, 2 and Figures 9 and 10 in the Appendix. Notably, even though the infection dynamics depends sensitively on some of these parameters (see Table 3 ), we showed that the IBS is signicant in all cases in which signicant epidemics develops. . 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 this version posted September 14, 2020. . Early implementation of the immune buer strategy makes it more eective (see e.g. the dependence on dates in Table 3 ). To implement it, extensive serological, PCR and other tests aimed at identifying recovered, disease free recruits from the recovered general population is needed. . 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) preprint The copyright holder for this this version posted September 14, 2020. . Additionally, an ecient recruitment and training procedure for the recovered recruited teams and a program for alternative temporary employment for the susceptible caretakers that are relocated are needed. Such programs must also address the despotic social and ethical dangers of poor unemployed persons seeking to get infected so they can belong to the immune team. The immune-buer strategy aims to allow the population at risk a way to successfully cross the dire straits of the pandemic, until the safe haven of herd immunity has been reached without living in total isolation. The immune buer strategy is not an alternative to other measures being undertaken, including social distancing and contact tracing, but it is a method which can be incorporated with other measures to better protect the population at risk, in spite of, or while tolerating, a certain level of progression of the disease among the general population. . 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) preprint The copyright holder for this this version posted September 14, 2020. . https://doi.org/10.1101/2020.09.12.20193094 doi: medRxiv preprint see Figure 1 : d Where T ot α = S α + E α + I α + Is α + As α + R α correspond to all alive 2 people in compartment α ∈ {N, M, M ess, M res, G} and S, E, I, .., T ot correspond to the vector of all compartments at the corresponding stages (here we concentrate on care-homes that transfer COVID-19 patients to a hospital. For studying hospitals' dynamics one could possibly take into account the possible infections of the sta by the isolated hospitalized patients, yet, with protection, this seems to be 2 we assume that the isolated people do not infect, yet they do reduce the number of encounters in the population. 14 . 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) preprint The copyright holder for this this version posted September 14, 2020. . https://doi.org/10.1101/2020.09.12.20193094 doi: medRxiv preprint We dene so, at each policy change we change β according to the new values of R 0 . Denoting by Y j ∈ R 7 + the vector of the population of all stages of compartment α(j) (so Y i j = n(i) α(j) , i = 1, .., 7, j = 1, ..5, e.g., Y 1 2 = S M ), the above equations are of a block diagonal form of a linear transfer between the states and a single term B j (y) which corresponds to the infectious component which mixes between the dierent compartments. More conveniently, we re-write the equations in vector form as 15 . 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) preprint The copyright holder for this this version posted September 14, 2020. . https://doi.org/10.1101/2020.09.12.20193094 doi: medRxiv preprint For generality sake we also include in A α the natural death term of a population at all stages, −δ α (in the simulations it is set to zero) and in B α the plausible re-infection term ρF α (Y ) which is added to the exposed stage and subtracted from the recovered stage (ρ is non-zero only in Figure 5 ). Similarly, we can add a migration term to the general population from other communities. The care-takers and the general population have the same internal dynamics so A j = A 2 , j = 3, 4, 5 whereas the vulnerable population has shorter recovery period and larger death rate as listed in Table 1 . With no intervention, the non-isolated persons of the rst three (N, M, M ess) and the last four (M, M ess, M res, G) compartments are in contact, where M res is empty. We assume the interactions of the vulnerable population with each compartment is separate, where µ j denotes the factor of the extra precautions taken when compartment j deals with the vulnerable population. The infection function, F (Y j ), is the relative fraction of the two infectious stages of the Y j population (the infected and asymptomatic states), divided by the live population of the Y j population: If re-infections are possible at some reduced rate, ρ, the recovered population can be re-infected in the same fashion as the susceptible one, as reected by the corresponding term in the matrix B α . We assume complete mixing between the last four compartments. Thus, the infection of the general population is F 5 (Y ) = βF ( 5 j=2 Y j ) where the function F is dened by 6 (so Y j is replaced in the formula by the sum 5 j=2 Y j ). For the caretakers, the interaction occurs both with the general population and the caretakers (as for the general population) and, also, separately, with the vulnerable population, hence, B j (Y ) = B 5 (Y ) + βµ j F (Y 1 ), where µ j corresponds to the extra protection of the j th caretaker compartments. The model (3) depends on the following parameters; The interaction term F α (Y ) depends on 5 parameters (β, R AS , µ N , µ M , µ M ess ), the matrices A α , j(α) = 1, .., 5 depend in principle on 31 parameters (σ, γ EI α , γ IIs α , γ IsR α , γ IsD α , γ AsR α , δ α ), yet, with the exception of γ IsD N , γ IsR N , we take all the parameters to be independent of α. We also x for all the simulations δ α = 0 and usually (with the exception of Fig 5) ρ = 0, so, nally, we have 8 free parameters for A α and all in all 13 non-trivial epidemiological parameters that are set as in Table 1 . Due to policy changes by the governments, 16 . 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) preprint The copyright holder for this this version posted September 14, 2020. . https://doi.org/10.1101/2020.09.12.20193094 doi: medRxiv preprint R 0 and µ M change at prescribed dates at which policy changes are announced as explained next. All other parameters and initial settings are xed as listed in Tables 1 and 2 (there, parameters were chosen as in [12] when available and by crude estimates otherwise. The sensitivity to all these parameters and initialization is listed in Table 3 ). In particular, all parameters that are crudely estimated are not sensitive. In order to validate the model, we used the daily counts of COVID-19 related deaths, and counts of positive COVID-19 tests (also referred as active cases), as reported in [13] . This data needs to be complemented by data regarding changes in government policy and in public media announcements, as these change the population behaviour -both R 0 and µ M . We thus found, from Wikipedia [16] , the description of the pandemic development in each country till the beginning of August. From this description we chose 6 main dates in which we believe a major change in the public behavior occurred. Calibration was done rst to the Israel data set of active cases and deaths till August 2nd, 2020, as shown in Figure 9 (active cases assumed to reect symptomatic cases due to the test strategy of Israel). At the lock-down date (the third policy change date), we checked for each µ M = 0.1, .., 0.6, what is the best least square t to the data of a vector of 6 R 0 values at the 6 policy change dates. With the tted µ M change at lock down, we t to the German deaths data the 6 R 0 values at the dates of policy changes of the German government till August 7th 2020 using the same method Here, the number of reported active cases is much smaller than the simulated number of cases. We chose not to t these curves as we believe that due to the historic low-testing policy in Germany the simulations are closer to the real numbers. We see that with the increased level of testing in Germany the simulated and reported numbers become closer. The intervention changes the model (3) as follows. We introduce in the general population compartment a recruited stage, Y RR G , which includes, as long as needed, the recovered individuals from the general population who replace the care-takers who can be replaced. Then, the active sta becomes: Active(Y ) = T ot M ess + T ot M + Y RR G . 17 . 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) preprint The copyright holder for this this version posted September 14, 2020. . https://doi.org/10.1101/2020.09.12.20193094 doi: medRxiv preprint Figure 9 : Calibration of the model for Israel: data set and a 7 parameters tted model for both the number of deaths and the active cases (6 R 0 at policy change dates and µ M after lock down). where maxcap = P errec 100 S M (0) = P errec 100 · helpratio · V rat · CoP op (10) these dene the recruiting and release scheme between the general population recovered and recruited stages: d Additionally, if there are sucient sta members in the susceptible stage (we set, for deniteness, Y S M > 2maxcap) and recruitment occurs, we ask them not to attend the vulnerable population Early transmission dynamics in wuhan, china, of novel coronavirusinfected pneumonia Case-fatality rate and characteristics of patients dying in relation to covid-19 in italy Report of the WHO-china joint mission on coronavirus disease Presenting characteristics, comorbidities, and outcomes among 5700 patients hospitalized with covid-19 in the new york city area Clinical course and risk factors for mortality of adult inpatients with covid-19 in wuhan, china: a retrospective cohort study Nursing homes are ground zero for covid-19 pandemic Epidemiology of covid-19 in a long-term care facility in king county, washington Insights from early mathematical models of 2019-ncov acute respiratory disease (covid-19) dynamics Why is it dicult to accurately predict the covid-19 epidemic? Mathematical epidemiology: Past, present, and future. Infectious Disease Modelling Modelling the covid-19 epidemic and implementation of population-wide interventions in italy Impact of non-pharmaceutical interventions (npis) to reduce covid19 mortality and healthcare demand covid-19 data repository by the center for systems science and engineering (csse) at johns hopkins university Sars coronavirus vaccine development The early landscape of coronavirus disease 2019 vaccine development in the uk and rest of the world covid-19 pandemic in germany/israel We thank Prof. Guy Katriel for his help in formulating the initial set up of the mathematical model and in numerous discussions along the work. VRK and OY research is supported by the ISF grant 1208/16. Mathematical model for Covid-19 with no intervention