Routes of importation and spatial dynamics of SARS-CoV-2 variants during localised interventions in Chile (preprint)

South America suffered large SARS-CoV-2 epidemics between 2020 and 2022 caused by multiple variants of interest and concern, some causing substantial morbidity and mortality. However, their transmission dynamics are poorly characterised. The epidemic situation in Chile enables us to investigate differences in the distribution and spread of variants Alpha, Gamma, Lambda, Mu and Delta. Chile implemented non-pharmaceutical interventions and an integrated genomic and epidemiological surveillance system that included airport and community surveillance to track SARS-CoV-2 variants. Here we combine viral genomic data and anonymised human mobility data from mobile phones to characterise the routes of importation of different variants into Chile, the relative contributions of airport-based importations to viral diversity versus land border crossings and test the impact of the mobility network on the diffusion of viral lineages within the country. We find that Alpha, Lambda and Mu were identified in Chile via airport surveillance six, four and five weeks ahead of their detection via community surveillance, respectively. Further, some variants that originated in South America were imported into Chile via land rather than international air travel, most notably Gamma. Different variants exhibited similar trends of viral dissemination throughout the country following their importation, and we show that the mobility network predicts the time of arrival of imported lineages to different Chilean comunas. Higher stringency of local NPIs was also associated with fewer domestic viral importations. Our results show how genomic surveillance combined with high resolution mobility data can help predict the multi-scale geographic expansion of emerging infectious diseases. Significance statementGlobal preparedness for pandemic threats requires an understanding of the global variations of spatiotemporal transmission dynamics. Regional differences are important because the local context sets the conditions for the unfolding of local epidemics, which in turn affect transmission dynamics at a broader scale. Knowledge gaps from the SARS-CoV-2 pandemic remain for regions like South America, where distinct sets of viral variants emerged and spread from late 2020 onwards, and where changes in human behaviour resulted in epidemics which differed from those observed in other regions. Our interdisciplinary analysis of the SARS-CoV-2 epidemic in Chile provides insights into the spatiotemporal trends of viral diffusion in the region which shed light on the drivers that can influence future epidemic waves and pandemics.

COVID-19 pandemic re-shaped the global dispersal of seasonal influenza viruses (preprint)

Understanding how the global dispersal patterns of seasonal influenza viruses were perturbed during and after the COVID-19 pandemic is needed to inform influenza intervention and vaccination strategies in the post-pandemic period. Although global human mobility has been identified as a key driver of influenza dispersal1, alongside climatic and evolutionary factors2,3, the impact of international travel restrictions on global influenza transmission and recovery remains unknown. Here we combine molecular, epidemiological, climatic, and international travel data within a phylodynamic framework to show that, despite human mobility remaining the principal driver of global influenza virus dissemination, the pandemics onset led to a shift in the international population structure and migration network of seasonal influenza lineages. We find that South Asia and Africa played important roles as exporters and phylogenetic trunk locations of influenza in 2020 and 2021, and we highlight the association between population movement, antigenic drift and persistence during the intensive non-pharmaceutical interventions (NPIs) phase. The influenza B/Yamagata lineage disappeared in a context of reduced relative genetic diversity, moderate lineage turnover, and lower positive selection pressure. Our results demonstrate that mobility perturbations reshaped the global dispersal dynamics of influenza viruses, with potential implications for vaccine design and genomic surveillance programmes. As the risk of future pandemics persists, our study provides an opportunity to assess the impact of NPIs during the pandemic on respiratory infectious diseases beyond the interplay between SARS-CoV-2 and influenza viruses.

Spatial scales of COVID-19 transmission in Mexico (preprint)

During outbreaks of emerging infectious diseases, internationally connected cities often experience large and early outbreaks, while rural regions follow after some delay. This hierarchical structure of disease spread is influenced primarily by the multiscale structure of human mobility. However, during the COVID-19 epidemic, public health responses typically did not take into consideration the explicit spatial structure of human mobility when designing non-pharmaceutical interventions (NPIs). NPIs were applied primarily at national or regional scales. Here we use weekly anonymized and aggregated human mobility data and spatially highly resolved data on COVID-19 cases, deaths and hospitalizations at the municipality level in Mexico to investigate how behavioural changes in response to the pandemic have altered the spatial scales of transmission and interventions during its first wave (March - June 2020). We find that the epidemic dynamics in Mexico were initially driven by SARS-CoV-2 exports from Mexico State and Mexico City, where early outbreaks occurred. The mobility network shifted after the implementation of interventions in late March 2020, and the mobility network communities became more disjointed while epidemics in these communities became increasingly synchronised. Our results provide actionable and dynamic insights into how to use network science and epidemiological modelling to inform the spatial scale at which interventions are most impactful in mitigating the spread of COVID-19 and infectious diseases in general.

Genomic assessment of invasion dynamics of SARS-CoV-2 Omicron BA.1 (preprint)

SARS-CoV-2 variants of concern (VOCs) arise against the backdrop of increasingly heterogeneous human connectivity and population immunity. Through a large-scale phylodynamic analysis of 115,622 Omicron genomes, we identified >6,000 independent introductions of the antigenically distinct virus into England and reconstructed the dispersal history of resulting local transmission. Travel restrictions on southern Africa did not reduce BA.1 importation intensity as secondary hubs became major exporters. We explored potential drivers of BA.1 spread across England and discovered an early period during which viral lineage movements mainly occurred between larger cities, followed by a multi-focal spatial expansion shaped by shorter distance mobility patterns. We also found evidence that disease incidence impacted human commuting behaviours around major travel hubs. Our results offer a detailed characterisation of processes that drive the invasion of an emerging VOC across multiple spatial scales and provide unique insights on the interplay between disease spread and human mobility.

Global Expansion of SARS-CoV-2 Variants of Concern: Dispersal Patterns and Influence of Air Travel (preprint)

In many regions of the world, the Alpha, Beta and Gamma SARS-CoV-2 Variants of Concern (VOCs) co-circulated during 2020-21 and fueled waves of infections. During 2021, these variants were almost completely displaced by the Delta variant, causing a third wave of infections worldwide. This phenomenon of global viral lineage displacement was observed again in late 2021, when the Omicron variant disseminated globally. In this study, we use phylogenetic and phylogeographic methods to reconstruct the dispersal patterns of SARS-CoV-2 VOCs worldwide. We find that the source-sink dynamics of SARS-CoV-2 varied substantially by VOC, and identify countries that acted as global hubs of variant dissemination, while other countries became regional contributors to the export of specific variants. We demonstrate a declining role of presumed origin countries of VOCs to their global dispersal: we estimate that India contributed <15% of all global exports of Delta to other countries and South Africa <1-2% of all global Omicron exports globally. We further estimate that >80 countries had received introductions of Omicron BA.1 100 days after its inferred date of emergence, compared to just over 25 countries for the Alpha variant. This increased speed of global dissemination was associated with a rebound in air travel volume prior to Omicron emergence in addition to the higher transmissibility of Omicron relative to Alpha. Our study highlights the importance of global and regional hubs in VOC dispersal, and the speed at which highly transmissible variants disseminate through these hubs, even before their detection and characterization through genomic surveillance.

Rapid epidemic expansion of the SARS-CoV-2 Omicron variant in southern Africa (preprint)

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) epidemic in southern Africa has been characterised by three distinct waves. The first was associated with a mix of SARS-CoV-2 lineages, whilst the second and third waves were driven by the Beta and Delta variants respectively. In November 2021, genomic surveillance teams in South Africa and Botswana detected a new SARS-CoV-2 variant associated with a rapid resurgence of infections in Gauteng Province, South Africa. Within three days of the first genome being uploaded, it was designated a variant of concern (Omicron) by the World Health Organization and, within three weeks, had been identified in 87 countries. The Omicron variant is exceptional for carrying over 30 mutations in the spike glycoprotein, predicted to influence antibody neutralization and spike function4. Here, we describe the genomic profile and early transmission dynamics of Omicron, highlighting the rapid spread in regions with high levels of population immunity.

Context-specific emergence and growth of the SARS-CoV-2 Delta variant (preprint)

The Delta variant of concern of SARS-CoV-2 has spread globally causing large outbreaks and resurgences of COVID-19 cases. The emergence of Delta in the UK occurred on the background of a heterogeneous landscape of immunity and relaxation of non-pharmaceutical interventions. Here we analyse 52,992 Delta genomes from England in combination with 93,649 global genomes to reconstruct the emergence of Delta, and quantify its introduction to and regional dissemination across England, in the context of changing travel and social restrictions. Through analysis of human movement, contact tracing, and virus genomic data, we find that the focus of geographic expansion of Delta shifted from India to a more global pattern in early May 2021. In England, Delta lineages were introduced >1,000 times and spread nationally as non-pharmaceutical interventions were relaxed. We find that hotel quarantine for travellers from India reduced onward transmission from importations; however the transmission chains that later dominated the Delta wave in England had been already seeded before restrictions were introduced. In England, increasing inter- regional travel drove Delta's nationwide dissemination, with some cities receiving >2,000 observable lineage introductions from other regions. Subsequently, increased levels of local population mixing, not the number of importations, was associated with faster relative growth of Delta. Among US states, we find that regions that previously experienced large waves also had faster Delta growth rates, and a model including interactions between immunity and human behaviour could accurately predict the rise of Delta there. Delta's invasion dynamics depended on fine scale spatial heterogeneity in immunity and contact patterns and our findings will inform optimal spatial interventions to reduce transmission of current and future VOCs such as Omicron.

Vaccine nationalism and the dynamics and control of SARS-CoV-2 (preprint)

Vaccines provide powerful tools to mitigate the enormous public health and economic costs that the ongoing SARS-CoV-2 pandemic continues to exert globally, yet vaccine distribution remains unequal between countries. To examine the potential epidemiological and evolutionary impacts of 'vaccine nationalism', we extend previous models to include simple scenarios of stockpiling. In general, we find that stockpiling vaccines by countries with high availability leads to large increases in infections in countries with low vaccine availability, the magnitude of which depends on the strength and duration of natural and vaccinal immunity. Additionally, a number of subtleties arise when the populations and transmission rates in each country differ depending on evolutionary assumptions and vaccine availability. Furthermore, the movement of infected individuals between countries combined with the possibility of increases in viral transmissibility may greatly magnify local and combined infection numbers, suggesting that countries with high vaccine availability must invest in surveillance strategies to prevent case importation. Dose-sharing is likely a high-return strategy because equitable allocation brings non-linear benefits and also alleviates costs of surveillance (e.g. border testing, genomic surveillance) in settings where doses are sufficient to maintain cases at low numbers. Across a range of immunological scenarios, we find that vaccine sharing is also a powerful tool to decrease the potential for antigenic evolution, especially if infections after the waning of natural immunity contribute most to evolutionary potential. Overall, our results stress the importance of equitable global vaccine distribution.

Identification of site-specific evolutionary trajectories shared across human betacoronaviruses (preprint)

Comparison of evolution among related viruses can provide insights into shared adaptive processes, for example following host switching to a mutual host species. Whilst phylogenetic methods can help identify mutations that may be important for evolutionary processes such as adaptation to a new host, these can be enhanced by positioning candidate mutations to known functional sites on protein structures. Over the past two decades, three zoonotic betacoronaviruses have significantly impacted human public health: SARS-CoV-1, MERS-CoV and SARS-CoV-2, whilst two other betacoronaviruses, HKU1 and OC43, have circulated endemically in the human population for over 100 years. In this study, we use a comparative approach to prospectively search for potentially evolutionarily-relevant mutations within the Orf1ab and S genes across betacoronavirus species that have demonstrated sustained human-to-human transmission (HKU1, OC43, SARS-CoV-1 and SARS-CoV-2). We used a combination of molecular evolution methods to identify 30 sites that display evidence of homoplasy and/or stepwise evolution, that may be suggestive of adaptation across emerging and endemic betacoronaviruses. Of these, seven sites also display evidence of being selectively relevant. Drawing upon known protein structure data, we find that four of the identified mutations [18121 (exonuclease/27), 21623 (spike/21), 21635 (spike/25) and 23948 (spike/796), in SARS-CoV-2 genome coordinates] are proximal to regions of known functionality. Our results provide a molecular-level context for common evolutionary pathways that betacoronaviruses may undergo during adaptation to the human host.

Genomic epidemiology of SARS-CoV-2 in a UK university identifies dynamics of transmission (preprint)

Understanding the drivers for spread of SARS-CoV-2 in higher education settings is important to limit transmission between students, and onward spread into at-risk populations. In this study, we prospectively sequenced 482 SARS-CoV-2 isolates derived from asymptomatic student screening and symptomatic testing of students and staff at the University of Cambridge from 5 October to 6 December 2020. We performed a detailed phylogenetic comparison with 972 isolates from the surrounding community, complemented with epidemiological and contact tracing data, to determine transmission dynamics. After a limited number of viral introductions into the university, the majority of student cases were linked to a single genetic cluster, likely dispersed across the university following social gatherings at a venue outside the university. We identified considerable onward transmission associated with student accommodation and courses; this was effectively contained using local infection control measures and dramatically reduced following a national lockdown. We observed that transmission clusters were largely segregated within the university or within the community. This study highlights key determinants of SARS-CoV-2 transmission and effective interventions in a higher education setting that will inform public health policy during pandemics.

Genomic epidemiology of SARS-CoV-2 transmission lineages in Ecuador (preprint)

Characterisation of SARS-CoV-2 genetic diversity through space and time can reveal trends in virus importation and domestic circulation, and permit the exploration of questions regarding the early transmission dynamics. Here we present a detailed description of SARS-CoV-2 genomic epidemiology in Ecuador, one of the hardest hit countries during the early stages of the COVID-19 pandemic. We generate and analyse 160 whole genome sequences sampled from all provinces of Ecuador in 2020. Molecular clock and phylgeographic analysis of these sequences in the context of global SARS-CoV-2 diversity enable us to identify and characterise individual transmission lineages within Ecuador, explore their spatiotemporal distributions, and consider their introduction and domestic circulation. Our results reveal a pattern of multiple international importations across the country, with apparent differences between key provinces. Transmission lineages were mostly introduced before the implementation of non-pharmaceutical interventions (NPIs), with differential degrees of persistence and national dissemination.

COVID-19 herd immunity in the Brazilian Amazon (preprint)

The herd immunity threshold is the proportion of a population that must be immune to an infectious disease, either by natural infection or vaccination such that, in the absence of additional preventative measures, new cases decline and the effective reproduction number falls below unity. This fundamental epidemiological parameter is still unknown for the recently-emerged COVID-19, and mathematical models have predicted very divergent results. Population studies using antibody testing to infer total cumulative infections can provide empirical evidence of the level of population immunity in severely affected areas. Here we show that the transmission of SARS-CoV-2 in Manaus, located in the Brazilian Amazon, increased quickly during March and April and declined more slowly from May to September. In June, one month following the epidemic peak, 44% of the population was seropositive for SARS-CoV-2, equating to a cumulative incidence of 52%, after correcting for the false-negative rate of the antibody test. The seroprevalence fell in July and August due to antibody waning. After correcting for this, we estimate a final epidemic size of 66%. Although non-pharmaceutical interventions, plus a change in population behavior, may have helped to limit SARS-CoV-2 transmission in Manaus, the unusually high infection rate suggests that herd immunity played a significant role in determining the size of the epidemic.

Baseline T cell immune phenotypes predict virologic and disease control upon SARS-CoV infection (preprint)

The COVID-19 pandemic has revealed that infection with SARS-CoV-2 can result in a wide range of clinical outcomes in humans, from asymptomatic or mild disease to severe disease that can require mechanical ventilation. An incomplete understanding of immune correlates of protection represents a major barrier to the design of vaccines and therapeutic approaches to prevent infection or limit disease. This deficit is largely due to the lack of prospectively collected, pre-infection samples from indiviuals that go on to become infected with SARS-CoV-2. Here, we utilized data from a screen of genetically diverse mice from the Collaborative Cross (CC) infected with SARS-CoV to determine whether circulating baseline T cell signatures are associated with a lack of viral control and severe disease upon infection. SARS-CoV infection of CC mice results in a variety of viral load trajectories and disease outcomes. Further, early control of virus in the lung correlates with an increased abundance of activated CD4 and CD8 T cells and regulatory T cells prior to infections across strains. A basal propensity of T cells to express IFNg and IL17 over TNFa also correlated with early viral control. Overall, a dysregulated, pro-inflammatory signature of circulating T cells at baseline was associated with severe disease upon infection. While future studies of human samples prior to infection with SARS-CoV-2 are required, our studies in mice with SARS-CoV serve as proof of concept that circulating T cell signatures at baseline can predict clinical and virologic outcomes upon SARS-CoV infection. Identification of basal immune predictors in humans could allow for identification of individuals at highest risk of severe clinical and virologic outcomes upon infection, who may thus most benefit from available clinical interventions to restrict infection and disease.

Comparative analysis reveals the species-specific genetic determinants of ACE2 required for SARS-CoV-2 entry (preprint)

Coronavirus interaction with viral receptor is a primary genetic determinant of host range and tissue tropism. SARS-CoV-2 utilizes ACE2 as the receptor to enter the host cell in a species-specific manner. We and others have previously shown that ACE2 orthologs from New World monkeys, koala and mouse cannot interact with SARS-CoV-2 to mediate viral entry, and this defect can be restored by humanization of the restrictive residues in New World monkey ACE2. To better understand the genetic determinants of susceptibility of ACE2 orthologs to viral entry, we compared koala and mouse ACE2 sequences with human ortholog, and identified the key residues in koala or mouse ACE2 that restrict its viral receptor activity. Humanization of these critical residues could render the capabilities of koala and mouse ACE2 to bind viral spike protein and facilitate the viral entry. Our work identifies the genetic determinant of ACE2 for SARS-CoV-2 susceptibility, and a single mutation could restore the mouse ACE2 receptor activity, providing a potential avenue for the development of mouse model of SARS-CoV-2.

Cryo-EM structure of S-Trimer, a subunit vaccine candidate for COVID-19 (preprint)

Less than a year after its emergence, the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has infected over 22 million people worldwide with a death toll approaching 1 million. Vaccination remains the best hope to ultimately put this pandemic to an end. Here, using Trimer-Tag technology, we produced both wild-type (WT) and furin site mutant (MT) S-Trimers for COVID-19 vaccine studies. Cryo-EM structures of the WT and MT S-Trimers, determined at 3.2 Angstrom and 2.6 Angstrom respectively, revealed that both antigens adopt a tightly closed conformation and their structures are essentially identical to that of the previously solved full-length WT S protein in detergent. These results validate Trimer-Tag as a platform technology in production of metastable WT S-Trimer as a candidate for COVID-19 subunit vaccine.

SARS-CoV-2 Nsp1 suppresses host but not viral translation through a bipartite mechanism (preprint)

The Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) is a highly contagious virus that underlies the current COVID-19 pandemic. SARS-CoV-2 is thought to disable various features of host immunity and cellular defense. The SARS-CoV-2 nonstructural protein 1 (Nsp1) is known to inhibit host protein translation and could be a target for antiviral therapy against COVID-19. However, how SARS-CoV-2 circumvents this translational blockage for the production of its own proteins is an open question. Here, we report a bipartite mechanism of SARS-CoV-2 Nsp1 which operates by: (1) hijacking the host ribosome via direct interaction of its C-terminal domain (CT) with the 40S ribosomal subunit and (2) specifically lifting this inhibition for SARS-CoV-2 via a direct interaction of its N-terminal domain (NT) with the 5 untranslated region (5 UTR) of SARS-CoV-2 mRNA. We show that while Nsp1-CT is sufficient for binding to 40S and inhibition of host protein translation, the 5 UTR of SARS-CoV-2 mRNA removes this inhibition by binding to Nsp1-NT, suggesting that the Nsp1-NT-UTR interaction is incompatible with the Nsp1-CT-40S interaction. Indeed, lengthening the linker between Nsp1-NT and Nsp1-CT of Nsp1 progressively reduced the ability of SARS-CoV-2 5 UTR to escape the translational inhibition, supporting that the incompatibility is likely steric in nature. The short SL1 region of the 5 UTR is required for viral mRNA translation in the presence of Nsp1. Thus, our data provide a comprehensive view on how Nsp1 switches infected cells from host mRNA translation to SARS-CoV-2 mRNA translation, and that Nsp1 and 5 UTR may be targeted for anti-COVID-19 therapeutics.

An immunodominance hierarchy exists in CD8+ T cell responses to HLA-A*02:01-restricted epitopes identified from the non-structural polyprotein 1a of SARS-CoV-2. (preprint)

COVID-19 vaccines are being rapidly developed and human trials are underway. Almost all of these vaccines have been designed to induce antibodies targeting spike protein of SARS-CoV-2 in expectation of neutralizing activities. However, non-neutralizing antibodies are at risk of causing antibody-dependent enhancement. Further, the longevity of SARS-CoV-2-specific antibodies is very short. Therefore, in addition to antibody-induced vaccines, novel vaccines on the basis of SARS-CoV-2-specific cytotoxic T lymphocytes (CTLs) should be considered in the vaccine development. Here, we attempted to identify HLA-A*02:01-restricted CTL epitopes derived from the non-structural polyprotein 1a of SARS-CoV-2. Eighty-two peptides were firstly predicted as epitope candidates on bioinformatics. Fifty-four in 82 peptides showed high or medium binding affinities to HLA-A*02:01. HLA-A*02:01 transgenic mice were then immunized with each of the 54 peptides encapsulated into liposomes. The intracellular cytokine staining assay revealed that 18 out of 54 peptides were CTL epitopes because of the induction of IFN-{gamma}-producing CD8+ T cells. In the 18 peptides, 10 peptides were chosen for the following analyses because of their high responses. To identify dominant CTL epitopes, mice were immunized with liposomes containing the mixture of the 10 peptides. Some peptides were shown to be statistically predominant over the other peptides. Surprisingly, all mice immunized with the liposomal 10 peptide mixture did not show the same reaction pattern to the 10 peptides. There were three pattern types that varied sequentially, suggesting the existence of an immunodominance hierarchy, which may provide us more variations in the epitope selection for designing CTL-based COVID-19 vaccines. ImportanceFor the development of vaccines based on SARS-CoV-2-specific cytotoxic T lymphocytes (CTLs), we attempted to identify HLA-A*02:01-restricted CTL epitopes derived from the non-structural polyprotein 1a of SARS-CoV-2. Out of 82 peptides predicted on bioinformatics, 54 peptides showed good binding affinities to HLA-A*02:01. Using HLA-A*02:01 transgenic mice, 18 in 54 peptides were found to be CTL epitopes in the intracellular cytokine staining assay. Out of 18 peptides, 10 peptides were chosen for the following analyses because of their high responses. To identify dominant epitopes, mice were immunized with liposomes containing the mixture of the 10 peptides. Some peptides were shown to be statistically predominant. Surprisingly, all immunized mice did not show the same reaction pattern to the 10 peptides. There were three pattern types that varied sequentially, suggesting the existence of an immunodominance hierarchy, which may provide us more variations in the epitope selection for designing CTL-based COVID-19 vaccines.

Evolution and epidemic spread of SARS-CoV-2 in Brazil (preprint)

Brazil currently has one of the fastest growing SARS-CoV-2 epidemics in the world. Due to limited available data, assessments of the impact of non-pharmaceutical interventions (NPIs) on virus transmission and epidemic spread remain challenging. We investigate the impact of NPIs in Brazil using epidemiological, mobility and genomic data. Mobility-driven transmission models for Sao Paulo and Rio de Janeiro cities show that the reproduction number (Rt) reached below 1 following NPIs but slowly increased to values between 1 to 1.3 (1.0 - -1.6). Genome sequencing of 427 new genomes and analysis of a geographically representative genomic dataset from 21 of the 27 Brazilian states identified >100 international introductions of SARS-CoV-2 in Brazil. We estimate that three clades introduced from Europe emerged between 22 and 27 February 2020, and were already well-established before the implementation of NPIs and travel bans. During this first phase of the epidemic establishment of SARS-CoV-2 in Brazil, we find that the virus spread mostly locally and within-state borders. Despite sharp decreases in national air travel during this period, we detected a 25% increase in the average distance travelled by air passengers during this time period. This coincided with the spread of SARS-CoV-2 from large urban centers to the rest of the country. In conclusion, our results shed light on the role of large and highly connected populated centres in the rapid ignition and establishment of SARS-CoV-2, and provide evidence that current interventions remain insufficient to keep virus transmission under control in Brazil.

Serial Interval Distribution of SARS-CoV-2 Infection in Brazil (preprint)

Using 65 transmission pairs of SARS-CoV-2 reported to the Brazilian Ministry of Health we estimate the mean and standard deviation for the serial interval to be 2.97 and 3.29 days respectively. We also present a model for the serial interval probability distribution using only two parameters.