Modeling neutral viral mutations in the spread of SARS-CoV-2 epidemics

Eco-evolutionary dynamics in finite network-structured populations with migration

We consider the effect of network structure on the evolution of a population. Models of this kind typically consider a population of fixed size and distribution. Here we consider eco-evolutionary dynamics where population size and distribution can change through birth, death and migration, all of which are separate processes. This allows complex interaction and migration behaviours that are dependent on competition. For migration, we assume that the response of individuals to competition is governed by tolerance to their group members, such that less tolerant individuals are more likely to move away due to competition. We look at the success of a mutant in the rare mutation limit for the complete, cycle and star networks. Unlike models with fixed population size and distribution, the distribution of the individuals per site is explicitly modelled by considering the dynamics of the population. This in turn determines the mutant appearance distribution for each network. Where a mutant appears impacts its success as it determines the competition it faces. For low and high migration rates the complete and cycle networks have similar mutant appearance distributions resulting in similar success levels for an invading mutant. A higher migration rate in the star network is detrimental for mutant success because migration results in a crowded central site where a mutant is more likely to appear.

A mathematical model for COVID-19 considering waning immunity, vaccination and control measures

In this work we define a modified SEIR model that accounts for the spread of infection during the latent period, infections from asymptomatic or pauci-symptomatic infected individuals, potential loss of acquired immunity, people's increasing awareness of social distancing and the use of vaccination as well as non-pharmaceutical interventions like social confinement. We estimate model parameters in three different scenarios-in Italy, where there is a growing number of cases and re-emergence of the epidemic, in India, where there are significant number of cases post confinement period and in Victoria, Australia where a re-emergence has been controlled with severe social confinement program. Our result shows the benefit of long term confinement of 50% or above population and extensive testing. With respect to loss of acquired immunity, our model suggests higher impact for Italy. We also show that a reasonably effective vaccine with mass vaccination program are successful measures in significantly controlling the size of infected population. We show that for a country like India, a reduction in contact rate by 50% compared to a reduction of 10% reduces death from 0.0268 to 0.0141% of population. Similarly, for a country like Italy we show that reducing contact rate by half can reduce a potential peak infection of 15% population to less than 1.5% of population, and potential deaths from 0.48 to 0.04%. With respect to vaccination, we show that even a 75% efficient vaccine administered to 50% population can reduce the peak number of infected population by nearly 50% in Italy. Similarly, for India, a 0.056% of population would die without vaccination, while 93.75% efficient vaccine given to 30% population would bring this down to 0.036% of population, and 93.75% efficient vaccine given to 70% population would bring this down to 0.034%.

Small-Sample Estimation of the Mutational Support and Distribution of SARS-CoV-2

We consider the problem of determining the mutational support and distribution of the SARS-CoV-2 viral genome in the small-sample regime. The mutational support refers to the unknown number of sites that may eventually mutate in the SARS-CoV-2 genome while mutational distribution refers to the distribution of point mutations in the viral genome across a population. The mutational support may be used to assess the virulence of the virus and guide primer selection for real-time RT-PCR testing. Estimating the distribution of mutations in the genome of different subpopulations while accounting for the unseen may also aid in discovering new variants. To estimate the mutational support in the small-sample regime, we use GISAID sequencing data and our state-of-the-art polynomial estimation techniques based on new weighted and regularized Chebyshev approximation methods. For distribution estimation, we adapt the well-known Good-Turing estimator. Our analysis reveals several findings: First, the mutational supports exhibit significant differences in the ORF6 and ORF7a regions (older versus younger patients), ORF1b and ORF10 regions (females versus males) and in almost all ORFs (Asia/Europe/North America). Second, even though the N region of SARS-CoV-2 has a predicted 10% mutational support, mutations fall outside of the primer regions recommended by the CDC.

The Trade-Off between Airborne Pandemic Control and Energy Consumption Using Air Ventilation Solutions

Airborne diseases cause high mortality and adverse socioeconomic consequences. Due to urbanization, more people spend more time indoors. According to recent research, air ventilation reduces long-range airborne transmission in indoor settings. However, air ventilation solutions often incur significant energy costs and ecological footprints. The trade-offs between energy consumption and pandemic control indoors have not yet been thoroughly analyzed. In this work, we use advanced sensors to monitor the energy consumption and pandemic control capabilities of an air-conditioning system, a pedestal fan, and an open window in hospital rooms, classrooms, and conference rooms. A simulation of an indoor airborne pandemic spread of Coronavirus (COVID-19) is used to analyze the Pareto front. For the three examined room types, the Pareto front consists of all three air ventilation solutions, with some ventilation configurations demonstrating significant inefficiencies. Specifically, air-conditioning is found to be efficient only at a very high energy cost and fans seem to pose a reasonable alternative. To conclude, a more informed ventilation policy can bring about a more desirable compromise between energy consumption and pandemic spread control.

Population genetic models for the spatial spread of adaptive variants: A review in light of SARS-CoV-2 evolution

Theoretical population genetics has long studied the arrival and geographic spread of adaptive variants through the analysis of mathematical models of dispersal and natural selection. These models take on a renewed interest in the context of the COVID-19 pandemic, especially given the consequences that novel adaptive variants have had on the course of the pandemic as they have spread through global populations. Here, we review theoretical models for the spatial spread of adaptive variants and identify areas to be improved in future work, toward a better understanding of variants of concern in Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) evolution and other contemporary applications. As we describe, characteristics of pandemics such as COVID-19-such as the impact of long-distance travel patterns and the overdispersion of lineages due to superspreading events-suggest new directions for improving upon existing population genetic models.

Generic approach for mathematical model of multi-strain pandemics

Multi-strain pandemics have emerged as a major concern. We introduce a new model for assessing the connection between multi-strain pandemics and mortality rate, basic reproduction number, and maximum infected individuals. The proposed model provides a general mathematical approach for representing multi-strain pandemics, generalizing for an arbitrary number of strains. We show that the proposed model fits well with epidemiological historical world health data over a long time period. From a theoretical point of view, we show that the increasing number of strains increases logarithmically the maximum number of infected individuals and the mean mortality rate. Moreover, the mean basic reproduction number is statistically identical to the single, most aggressive pandemic strain for multi-strain pandemics.

Modeling the Transmission of the SARS-CoV-2 Delta Variant in a Partially Vaccinated Population

In a population with ongoing vaccination, the trajectory of a pandemic is determined by how the virus spreads in unvaccinated and vaccinated individuals that exhibit distinct transmission dynamics based on different levels of natural and vaccine-induced immunity. We developed a mathematical model that considers both subpopulations and immunity parameters, including vaccination rates, vaccine effectiveness, and a gradual loss of protection. The model forecasted the spread of the SARS-CoV-2 delta variant in the US under varied transmission and vaccination rates. We further obtained the control reproduction number and conducted sensitivity analyses to determine how each parameter may affect virus transmission. Although our model has several limitations, the number of infected individuals was shown to be a magnitude greater (~10×) in the unvaccinated subpopulation compared to the vaccinated subpopulation. Our results show that a combination of strengthening vaccine-induced immunity and preventative behavioral measures like face mask-wearing and contact tracing will likely be required to deaccelerate the spread of infectious SARS-CoV-2 variants.

Mutational landscape and in silico structure models of SARS-CoV-2 spike receptor binding domain reveal key molecular determinants for virus-host interaction

Background

SARS-CoV-2, the causative agent of COVID-19 pandemic is a RNA virus prone to mutations. Formation of a stable binding interface between the Receptor Binding Domain (RBD) of SARS-CoV-2 Spike (S) protein and Angiotensin-Converting Enzyme 2 (ACE2) of host is pivotal for viral entry. RBD has been shown to mutate frequently during pandemic. Although, a few mutations in RBD exhibit enhanced transmission rates leading to rise of new variants of concern, most RBD mutations show sustained ACE2 binding and virus infectivity. Yet, how all these mutations make the binding interface constantly favourable for virus remain enigmatic. This study aims to delineate molecular rearrangements in the binding interface of SARS-CoV-2 RBD mutants.

Results

Here, we have generated a mutational and structural landscape of SARS-CoV-2 RBD in first six months of the pandemic. We analyzed 31,403 SARS-CoV-2 genomes randomly across the globe, and identified 444 non-synonymous mutations in RBD that cause 49 distinct amino acid substitutions in contact and non-contact amino acid residues. Molecular phylogenetic analysis suggested independent emergence of RBD mutants. Structural mapping of these mutations on the SARS-CoV-2 Wuhan reference strain RBD and structural comparison with RBDs from bat-CoV, SARS-CoV, and pangolin-CoV, all bound to human or mouse ACE2, revealed several changes in the interfacial interactions in all three binding clusters. Interestingly, interactions mediated via N487 residue in cluster-I and Y449, G496, T500, G502 residues in cluster-III remained largely unchanged in all RBD mutants. Further analysis showed that these interactions are evolutionarily conserved in sarbecoviruses which use ACE2 for entry. Importantly, despite extensive changes in the interface, RBD-ACE2 stability and binding affinities were maintained in all the analyzed mutants. Taken together, these findings reveal how SARS-CoV-2 uses its RBD residues to constantly remodel the binding interface.

Conclusion

Our study broadly signifies understanding virus-host binding interfaces and their alterations during pandemic. Our findings propose a possible interface remodelling mechanism used by SARS-CoV-2 to escape deleterious mutations. Future investigations will focus on functional validation of in-silico findings and on investigating interface remodelling mechanisms across sarbecoviruses. Thus, in long run, this study may provide novel clues to therapeutically target RBD-ACE2 interface for pan-sarbecovirus infections.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12860-021-00403-4.

Endogenous viral mutations, evolutionary selection, and containment policy design

How will the novel coronavirus evolve? I study a simple epidemiological model, in which mutations may change the properties of the virus and its associated disease stochastically and antigenic drifts allow new variants to partially evade immunity. I show analytically that variants with higher infectiousness, longer disease duration, and shorter latent period prove to be fitter. "Smart" containment policies targeting symptomatic individuals may redirect the evolution of the virus, as they give an edge to variants with a longer incubation period and a higher share of asymptomatic infections. Reduced mortality, on the other hand, does not per se prove to be an evolutionary advantage. I then implement this model as an agent-based simulation model in order to explore its aggregate dynamics. Monte Carlo simulations show that a) containment policy design has an impact on both speed and direction of viral evolution, b) the virus may circulate in the population indefinitely, provided that containment efforts are too relaxed and the propensity of the virus to escape immunity is high enough, and crucially c) that it may not be possible to distinguish between a slowly and a rapidly evolving virus by looking only at short-term epidemiological outcomes. Thus, what looks like a successful mitigation strategy in the short run, may prove to have devastating long-run effects. These results suggest that optimal containment policy must take the propensity of the virus to mutate and escape immunity into account, strengthening the case for genetic and antigenic surveillance even in the early stages of an epidemic.