key: cord-0270285-n0jg887j authors: Castro e Silva, A.; Bernardes, A. T.; Barbosa, E.; Dattilo, W.; Ribeiro, S. P. title: Successive pandemic waves with more virulent strains, and the effects of vaccination for SARS-CoV-2 date: 2021-09-23 journal: nan DOI: 10.1101/2021.09.21.21263901 sha: 5efa114f3a907de2eb49fe3e1fa2dbfab70ddba6 doc_id: 270285 cord_uid: n0jg887j Hundred years after the flu pandemic of 1918, the world faces an outbreak of a new severe acute respiratory syndrome, caused by a novel coronavirus. With a high transmissibility, the pandemic spreads worldwide, creating a scenario of devastation in many countries. By middle of 2021, about $3%$ of the world population has been infected and more than 4 million people have died. Different from the $H_1N_1$ pandemic, which had a deadly wave and cessed, the new disease is maintained by successive waves, mainly produced by new virus variants, and the small number of vaccinated people. In the present work, we create a version of the SIR model with spatial localization of persons, their movements, and taking into account social isolation probabilities. We discuss the effects of virus variants, and the role of vaccination rate in the pandemic dynamics. We show that, unless a global vaccination is implemented, we will have continuous waves of infections. At the end of 2019 the world witnessed news about a novel disease that started in Wuhan, China. This illness, called COVID-19, is caused by a SARS class virus named SARS-CoV-2. Due to its high transmission capability, the disease rapidly reached all countries in the globe, mainly through airports networks [1, 2, 3] , and, on March 11th 2020, WHO declared it as a pandemic. As Any responsible sanitary policy adopted to slow down the progress of COVID-19 pandemic should get use of the following three strategies: a) social distancing: the obvious way to reduce susceptible-infected interaction and subsequent contagion, b) mask wearing and hygiene: once it is know that the transmission is mainly through respiratory droplets of infected patients and contact with surfaces infected by aerosol and, lately c) vaccines: a correct vaccination program can decrease the intensity of the disease symptoms among those infected but vaccinated, reducing the public health collapse risk, and the mortality rates, as susceptible but vaccinated people became asymptomatic. Still, the virus will circulate and the lack of a proper vaccination will create outbreaks due to contact between an increasing number of "asymptomatic" with vulnerable susceptible 2 . CC-BY-NC 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 23, 2021. ; https://doi.org/10.1101/2021.09.21.21263901 doi: medRxiv preprint people. As [5] demonstrated, the existence of transient collective immunity may prolong an epidemic, and a bad vaccine scheme may exacerbate this pattern. For the specific case of COVID-19 vaccination, one of the subjects of the present work, there are many factors that must be taken into account for a suitable immunization policy. Among all of them, this work will focus mainly on two aspects: how the virus is evolving into new variants and reinfection. Every time SARS-CoV-2 infects a susceptible person, it starts to make copies of itself replicating its RNA [6, 7] . These changes or mutations in RNA can lead to different scenarios: it can be an evolutionary dead end and kill the virus, it can be an irrelevant and not noticeable change or it can bring some advantages, for example, better dealing with the immune system or better reaching the cells. Even more rarely, whole clusters of mutations can be acquired by the virus during a single infection. When a virus with single or cluster mutation gets spread through populations they are named "Variants of Concern" or VOC. According to CDC [8], a variant becomes a VOC when there is evidence of an increase in transmissibility, or in lethality and severity of the disease, Apart from VOC, there are still the "Variants of Interest" or VOI (variants , η, ι, κ and ζ) and "Variants of High Consequence" (there are no SARS-CoV-2 variants that rise to the level of high consequence until now). The CDC defini-3 . CC-BY-NC 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 23, 2021. ; https://doi.org/10.1101/2021.09.21.21263901 doi: medRxiv preprint tion of a VOI is: a variant with specific genetic markers that have been associated with changes to receptor binding, reduced neutralization by antibodies generated against previous infection or vaccination, reduced efficacy of treatments, potential diagnostic impact, or predicted increase in transmissibility or disease severity. On the other hand, a variant has high consequences when it has clear evidence that prevention measures or medical countermeasures (MCMs) have significantly reduced effectiveness relative to previously circulating variants. The second factor that can impact an immunization policy is the reinfection caused by the loss of immunity. Some works have shown that immunity with greater memory is acquired by infected people who developed severe symptoms, recovered and were vaccinated with at least one dose. However, even in these cases, immunity is not permanent, requiring a new vaccine [9, 10] . The reinfection was dimensioned as rare just before the spreading of the new variants of concern in early 2021 [11] . Still, not necessarily the loss of immunity in front of a variant of concern is a severe and frequent problem yet. However, risks may rise if the pandemic is not controlled and the virus is left to evolve freely [12, 13, 14] . Reduced neutralization of the Delta variant in comparison to the ancestral Wuhan-related strain was already observed [15] , and a complex relation between different variants is also possible. For instance, it was also found that people infected with Beta variant are more susceptible to reinfection by Delta variant [15] . Hence, there is room for the evolution of new variants that could escape the vaccination more aggressively, especially if the vaccination scheme continues to follow a heterogeneous pattern, leaving the most vulnerable populations exposed for longer. In this work, we developed an epidemiological model where events such as the appearance of new variants and reinfection are taken into account. Our results point to an optimal vaccine frequency that should be conducted in a given epidemiological setting. . CC-BY-NC 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 In the present paper, we simulate a version of the SIR model [16] in a city with a population N (t) that may vary over time. Many variants of SIR model were used to simulate different scenarios of SARS-CoV-2 pandemy [17, 18, 19, 20] , however, in order to have a better understanding of how cities' structures and citizen dynamics affect the spreading of a transmissible disease like SARS-Cov-2, we choose to develop an SIR-ABM (Agent Based Model) [21, 22, 23, 24] of a "city" where their citizens start to get infected. The city represents a geographically limited region. Only the arrival and departure of visitors and the deaths of its inhabitants can change its population. As in the previous versions of the SIR model, a S i variable defines the health state of each individual: susceptible, infected, recovered, or immunized. In this work, we have included a fourth state: dead. Factors such as age, sex, or race are not taken into account. In the simulated city, the residents live in houses, and they can move to public establishments (as malls, stadiums, stores, restaurants, etc). In some simulations, people can move to the houses of other people. The day starts with all the residents in their homes, to which they will be linked throughout the simulation. That is, if he/she leaves for another home or any establishment, at the end of the day, he/she will return to his/her home. Each person has a probability of movement P mov , and this probability defines social isolation mobility. There is no natural movement, no duration of the action. The agents disappear from a place and reappear in another. We considered that the time of permanence in public or private places is longer than the travel time. On the other hand, for big cities, one can suppose that the time he/she stays in a mode of public transport, if prolonged, may also be considered as staying in a small public place with the same infection conditions. According to the latest demographic census [25], Brazilian households have an average of 2.9 residents. In our simulations, we used an average of ∼ 3.3. . CC-BY-NC 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 In some simulations, the houses have either 3 or 4 residents, randomly chosen. In other simulations we detail below, we used an occupation given by a Poisson distribution with an average of 3.3 inhabitants. Every public area has a carrying capacity of K, so that If the person is going to move, the places to which he/she will go are chosen at random: houses, small shops, or large stores. Its maximum capacity gives the likelihood of going to a location: it is more likely to go to a large store than to someone else's home. If the selected place has its capacity reached, a new site is drawn until the person moves, ensuring that whoever was chosen to move will make a move. where N inf ected is the total number of infected persons at that place (house or shop), and N max is the maximum capacity of that place. Two steps define the infection of a susceptible person: first, we calculate if he/she will contact a contaminated person. If so, one tests if he/she will have contagion. Contact does not imply contagion. The probability of contagion is β. In the case of COVID-19, β is estimated between [0.2, 0.3]. In the cases simulated in this work, we use a value of β = 0.2 for a "normal" variant and we assume more transmissible variants, with β > 0.2 [26] . If he/she acquires the illness, the probability of becoming infected with one of the variants present in that location is proportional to the frequency with which that variant is in the place, weighted by the transmissibility of the strain. The higher n i * β i , the higher the probability of being infected. n i is the total number of individuals contaminated by the strain β i at that location. The infected individual then becomes a potential transmitter of the disease. If the individual who arrives at a place is infected or immunized S i = 1 or 2, nothing happens to the others. The arrival of an infected person will create the conditions for those who arrive later to be infected. At the end of the day, after performing some movements, all individuals return to their homes. Of course, if he/she has not moved, nothing is tested. However, for those who return to his/her home, the same set of procedures to check for infection is adopted: If the person returning home is susceptible, and someone infected is in the house, the same steps described above are carried out for contact and contagion. There is an asymmetry in the model. If an infected person arrives at a place, we do not test if he/she will infect the susceptible ones already there. This kind of procedure corresponds to a sequential order in the contact/contagion process. It is understood that for huge populations and many days of simulation, this fact does not imply results different from those reported below. . CC-BY-NC 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. We have also simulated the case of incubation. In this case, the susceptible become infected after five days of incubation. During these five days, they can not infect other individuals. After 14 days, an infected individual becomes an immunized or recovered one. He/She remains in this immunized state for T days when he/she returns to the condition of being susceptible. During this period, he/she can not be infected with any variant of the new coronavirus [27, 28] . Our model assumes that visitors arrive and leave the city every day. The number of visitors coming and leaving each day is around 1/1,000 of the total residents. These visitors have a probability of movement equal to 1. It means that a visitor will go to three places (houses, small shops, or large stores). The likelihood of a visitor being infected is 0.1%. In principle, if infected, he/she will have the virus variant with β = 0.2, but some can have a more transmissible variant. We have implemented a version in which visitors are 1% of the population. Of the visitors, 3% may have the new type of virus. In this model, there are no births. There is no increase in the number of inhabitants, except visitors, but it represents a zero change in the population since they arrive and leave. The only factor that can change the resident population is the death caused by disease. We study the effects of a new variant of the virus, which enters via visitors, studying the competition dynamics between different strains. Besides, we also want to study the effects of vaccination, not 8 . CC-BY-NC 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 If that visitor is susceptible, he/she may become infected during the day and transmit the infection. But as he/she only spends a day in the city, he/she will not be subject to death, nor will he/she be able to recover. He/She will also not be vaccinated. In our simulations, vaccination starts from the 300 th day. This date roughly corresponds to the beginning of vaccination campaigns in several countries: between December / 2020 and January / 2021, considering the detection of the pandemic as time zero (around February or March 2020). A P vac percentage of the population is vaccinated each day. When vaccinated, an individual acquires immunity. There is no need to use two doses or intervals between doses of the vaccine to gain immunity. In this simplified version of the model, immunity is acquired at the time of vaccination. An immunized individual will not be infected by any other variant of Sars-Cov-2 (referencias). After T days, the immunized individual returns to the condition of being susceptible. We will show the results with two versions of the model: in the first one, we simulate a city with houses, small and big stores, where the visitors may carry just one virus variant with higher transmissibility. Residents can move to other residents' houses; in the second version, the towns have homes and just one type of store, and the visitors carry many virus variants (described below). In the first version, we studied the effects of vaccination, and it was not in the second version. The central aspect of the first version is to look at the spread of a higher transmissibility strain with vaccination; the second version aims to study the competition between different strains. In both cases, we consider that variants with different transmissibility also have different lethality. The first set of results have been obtained in simulations of cities with two populations: N ∼ 875 thousand residents, and another with N ∼ 8.75 million 9 . CC-BY-NC 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. For each time step, individuals are chosen at random, as described above. One verifies if he/she will leave the house. If so, we draw the total number of moves he/she will make: 1 up to 3. Then, we randomly choose the places for visitation: other houses or small or large stores. He/she leaves the house and goes to each establishment. Each person executes his/her movements, and after completing them, stays at the last site until he/she returns home at the end of the day. In all the simulations discussed below, a portion 10% of the population has a probability of movement of P mov = 0.1, representing the people who are most at home. As described above, visitors come and go. We have assumed a proportion of visitors of 0.1 % of the total initial population per day in the results we show below. These people who arrive and leave remain only one day in the city. A ratio of 1/1,000 may be contaminated. The contamination strain has β = 0.2. In the results shown below P contact is given by equation (1), β = 0.2, δ β = 0.05, P death = 0.01, δ death = 0.004, 1/ gamma = 14, and T = 120 days. On the simulation's 300th day, a vaccination campaign may start. We performed simulations with two vaccination rates. Some simulations used a vaccination probability of P vac = 1/200, representing the typical value of vaccination 11 . CC-BY-NC 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. However, the quantity of those who die from the new variant rises more rapidly, becoming ∼ 50% at the end of the simulation. . CC-BY-NC 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. 14 . CC-BY-NC 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. When the immunization rate assumes the value of 1/200, the picture changes radically, as shown in Figure 6 . Vaccination started on day 300 of the simulation. One observes that there is still the second wave of infections because the virus is widespread in the population. But the number of immunized people increases rapidly, which is a blocking factor for the spread of the pandemic. One also observes that the most aggressive variant is contained, as the value of β av is closer to 0.2. It is important to remember that the rate of contaminated visitors is the same in the three cases discussed so far. The number of deaths also stabilizes with the blockade caused by vaccination. . CC-BY-NC 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 23, 2021. ; https://doi.org/10.1101/2021.09.21.21263901 doi: medRxiv preprint The following Figure 7 reproduces the relationship between daily deaths and the presence of the most aggressive variant. This variant is still present in the second wave but on a smaller percentage than in Figure 3 . Later, this variant becomes marginal. It is necessary to remember that this most aggressive variant enters the population from the visitors, and therefore there will always be, in this model, the presence of this variant. . CC-BY-NC 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. where there is no vaccination. One observes that only with an isolation rate of 70% the pandemic is stopped. In the second case (B), when the vaccination rate is 1/1000, it is observed that there is no significant impact on infection dynamics. Only with a higher vaccination rate (C), as mentioned in the cases of Israel or the USA, can the pandemic be stopped, even with lower isolation rates. . CC-BY-NC 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 23, 2021. ; https://doi.org/10.1101/2021.09.21.21263901 doi: medRxiv preprint . CC-BY-NC 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. To better understand the influence of the city size, the number of individuals, as well as the period of immunization after vaccination, we performed simulations with N 8.75 million individuals and T = 180 days, meaning that a recovered or immunized stays in the S = 2 state for six months. All the parameters are the same as those used in the simulations described above: P mov = 0.6, β = 0.2 for residents, number of visitors 1/1,000, the proportion of contaminated visitors 1/1,000 being those with the highest transmissibility rate 1/90. Vaccination, when it occurs, starts on the 300th day. In Figure 9 , the curves represent only infected (red line) and deaths (green line) densities. Part (A) represents the simulation without vaccination; part (B) represents vaccination starting on the 300th day, with a 1/1,000 of vaccination rate; and part (C) represents the evolution with a 1/200 vaccination rate. Qualitatively, the behavior is the same as discussed above for populations ten times smaller. The main aspect is that the change in the immunization period does not change the evolution of successive waves for the cases without vaccination or with a low vaccination rate. . CC-BY-NC 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 23, 2021. ; https://doi.org/10.1101/2021.09.21.21263901 doi: medRxiv preprint . CC-BY-NC 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 23, 2021. ; https://doi.org/10.1101/2021.09.21.21263901 doi: medRxiv preprint [29, 30] . Due to the full shifting of the original strain by new variants, the β-infection rate was permanently higher after the second wave than it was in the beginning of the pandemics, as shown by average transmission on figure 11. After some waves of infections, the world is facing a new challenge. Some countries, like the USA, have a significant part of the population which refuses to be vaccinated. This likely allows the spread of new variants and they now observe a fifth wave of infection, this time much more intense than the previous one, which occurred in the middle April 2021. Vaccination slowed down and this may cause the present situation. In Israel a new wave is observed. But since they have a high vaccination rate, the number of deaths is smaller than in the previous wave. Brazil presents a different situation. The country started vaccination with a low rate, due to the role of the federal government. However, there was a strong engagement of the population and, after public pressure from but also the action of political sectors, the rates of vaccination increased in the 24 . CC-BY-NC 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. In this paper, we simulated the competition between virus strains, the role of the vaccination rate, and social isolation, which is believed as one of the main aspects to detain the virus's circulation. As in many countries, like Brazil, it is very complicated to maintain social isolation for long periods. We observe stress in parts of populations children out of schools, increase in domestic violence and difficulties to obtain the basic income to sustain the families. Poverty increased in many countries. In the particular case of Brazil, social isolation never reached the adequate or recommended levels, which is responsible for the long plateau of infections and deaths. We show, thus, that the only way to stop the virus circulation, or at least to diminish the contamination rates is increasing the vaccination rates. Low vaccination rates allow the circulation of the many variants and we observe a cyclic problem. The situation gains a much more dramatic feature with the existence of new variants with a higher transmissibility. The many different variants will compete and those with higher transmissibility will win the competition, even with a higher lethality. This picture is observed where the δ variant appeared. This variant rapidly infests people, even those already vaccinated and can cause a higher increase in the total of contamination. This led us to the problem in the beginning of the pandemic, which was how to flatten the infection curve. Because the spread of new strains can overload the healthy systems. The main purpose of this paper is to shed some light in the main aspects of the actual dynamics of the pandemic. It is clear that one needs a global governance to deal with this dynamic, because the total curve of the pandemic dynamics exhibits successive peaks with a distance of about 4 months between 25 . CC-BY-NC 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 23, 2021. ; https://doi.org/10.1101/2021.09.21.21263901 doi: medRxiv preprint them. So, without global control, new variants continue to appear and the infection is partially controlled in one country or region, but increases in other parts, in a dramatic cyclic death wheel. . CC-BY-NC 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 23, 2021. ; https://doi.org/10.1101/2021.09.21.21263901 doi: medRxiv preprint . CC-BY-NC 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 23, 2021. ; https://doi.org/10.1101/2021.09.21.21263901 doi: medRxiv preprint Severe airport sanitarian control could slow down the spreading of covid-19 pandemics in brazil Worldwide covid-19 spreading explained: traveling numbers as a primary driver for the pandemic Global expansion of covid-19 pandemic is driven by population size and airport connections Time-dependent heterogeneity leads to transient suppression of the covid-19 epidemic, not herd immunity Mechanisms of viral mutation, Cellular and molecular life sciences Origin and crossspecies transmission of bat coronaviruses in china Naturally enhanced neutralizing breadth against sars-cov-2 one year after infection Sars-cov-2 infection induces long-lived bone marrow plasma cells in humans Assessment of sars-cov-2 reinfection 1 year after primary infection in a population in lombardy, italy From spanish flu to syndemic covid-19: long-standing sanitarian vulnerability of manaus, warnings from the brazilian rainforest gateway Transmission heterogeneities, kinetics, and controllability of sars-cov-2 The effect of travel restrictions on the spread of the 2019 novel coronavirus (covid-19) outbreak Are pangolins the intermediate host of the 2019 novel coronavirus (sars-cov-2)? 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(which was not certified by peer review) preprint The copyright holder for this this version posted Sars-cov-2 transmission from people without covid-19 symptoms Epidemiology and genetics in the coevolution of parasites and hosts Evolution of virulence in emerging epidemics This research did not receive any specific grant from funding agencies in the commercial, or non-profit sectors. SPR acknowledges grant from Conselho Nacional de Desenvolvimento Científico e Tecnológico -CNPq, through proccess 306572/2019-2. The authors declare that there are no conflicts of interest. It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.