Learning from the COVID-19 pandemic: A systematic review of mathematical vaccine prioritization models.

As the world becomes ever more connected, the chance of pandemics increases as well. The recent COVID-19 pandemic and the concurrent global mass vaccine roll-out provides an ideal setting to learn from and refine our understanding of infectious disease models for better future preparedness. In this review, we systematically analyze and categorize mathematical models that have been developed to design optimal vaccine prioritization strategies of an initially limited vaccine. As older individuals are disproportionately affected by COVID-19, the focus is on models that take age explicitly into account. The lower mobility and activity level of older individuals gives rise to non-trivial trade-offs. Secondary research questions concern the optimal time interval between vaccine doses and spatial vaccine distribution. This review showcases the effect of various modeling assumptions on model outcomes. A solid understanding of these relationships yields better infectious disease models and thus public health decisions during the next pandemic.

Canalization reduces the nonlinearity of regulation in biological networks.

Biological networks, such as gene regulatory networks, possess desirable properties. They are more robust and controllable than random networks. This motivates the search for structural and dynamical features that evolution has incorporated into biological networks. A recent meta-analysis of published, expert-curated Boolean biological network models has revealed several such features, often referred to as design principles. Among others, the biological networks are enriched for certain recurring network motifs, the dynamic update rules are more redundant, more biased, and more canalizing than expected, and the dynamics of biological networks are better approximable by linear and lower-order approximations than those of comparable random networks. Since most of these features are interrelated, it is paramount to disentangle cause and effect, that is, to understand which features evolution actively selects for, and thus truly constitute evolutionary design principles. Here, we compare published Boolean biological network models with different ensembles of null models and show that the abundance of canalization in biological networks can almost completely explain their recently postulated high approximability. Moreover, an analysis of random N-K Kauffman models reveals a strong dependence of approximability on the dynamical robustness of a network.

Diffusion and Chemical Degradation of Vitamin B6 in Chickpeas (Cicer arietinum L.) during Hydrothermal Treatments: A Kinetic Approach.

Chickpeas are more sustainable than other food systems and have high a nutritional value, especially regarding their vitamin composition. One of the main vitamins in chickpeas is vitamin B6, which is very important for several human metabolic functions. Since chickpeas are consumed after cooking, our goal was to better understand the role of leaching (diffusion) and thermal degradation of vitamin B6 in chickpeas during hydrothermal processing. Kinetics were conducted at four temperatures, ranging from 25 to 85 °C, carried out for 4 h in an excess of water for the diffusion kinetics, or in hermetic bags for the thermal degradation kinetics. Thermal degradation was modeled according to a first-order reaction, and diffusion was modeled according to a modified version of Fick's second law. Diffusivity constants varied from 4.76 × 10-14 m2/s at 25 °C to 2.07 × 10-10 m2/s at 85 °C; the temperature had an impact on both the diffusivity constant and the residual vitamin B6. The kinetic constant ranged from 9.35 × 10-6 at 25 °C to 54.9 × 10-6 s-1 at 85 °C, with a lower impact of the temperature. In conclusion, vitamin B6 is relatively stable to heat degradation; loss is mainly due to diffusion, especially during shorter treatment times.

Learning from the COVID-19 pandemic: a systematic review of mathematical vaccine prioritization models.

As the world becomes ever more connected, the chance of pandemics increases as well. The recent COVID-19 pandemic and the concurrent global mass vaccine roll-out provides an ideal setting to learn from and refine our understanding of infectious disease models for better future preparedness. In this review, we systematically analyze and categorize mathematical models that have been developed to design optimal vaccine prioritization strategies of an initially limited vaccine. As older individuals are disproportionately affected by COVID-19, the focus is on models that take age explicitly into account. The lower mobility and activity level of older individuals gives rise to non-trivial trade-offs. Secondary research questions concern the optimal time interval between vaccine doses and spatial vaccine distribution. This review showcases the effect of various modeling assumptions on model outcomes. A solid understanding of these relationships yields better infectious disease models and thus public health decisions during the next pandemic.

Modular Control of Biological Networks.

The concept of control is central to understanding and applications of biological network models. Some of their key structural features relate to control functions, through gene regulation, signaling, or metabolic mechanisms, and computational models need to encode these. Applications of models often focus on model-based control, such as in biomedicine or metabolic engineering. This paper presents an approach to model-based control that exploits two common features of biological networks, namely their modular structure and canalizing features of their regulatory mechanisms. The paper focuses on intracellular regulatory networks, represented by Boolean network models. A main result of this paper is that control strategies can be identified by focusing on one module at a time. This paper also presents a criterion based on canalizing features of the regulatory rules to identify modules that do not contribute to network control and can be excluded. For even moderately sized networks, finding global control inputs is computationally very challenging. The modular approach presented here leads to a highly efficient approach to solving this problem. This approach is applied to a published Boolean network model of blood cancer large granular lymphocyte (T-LGL) leukemia to identify a minimal control set that achieves a desired control objective.

A meta-analysis of Boolean network models reveals design principles of gene regulatory networks.

Gene regulatory networks (GRNs) play a central role in cellular decision-making. Understanding their structure and how it impacts their dynamics constitutes thus a fundamental biological question. GRNs are frequently modeled as Boolean networks, which are intuitive, simple to describe, and can yield qualitative results even when data are sparse. We assembled the largest repository of expert-curated Boolean GRN models. A meta-analysis of this diverse set of models reveals several design principles. GRNs exhibit more canalization, redundancy, and stable dynamics than expected. Moreover, they are enriched for certain recurring network motifs. This raises the important question why evolution favors these design mechanisms.

Modularity of biological systems: a link between structure and function.

This paper addresses two topics in systems biology, the hypothesis that biological systems are modular and the problem of relating structure and function of biological systems. The focus here is on gene regulatory networks, represented by Boolean network models, a commonly used tool. Most of the research on gene regulatory network modularity has focused on network structure, typically represented through either directed or undirected graphs. But since gene regulation is a highly dynamic process as it determines the function of cells over time, it is natural to consider functional modularity as well. One of the main results is that the structural decomposition of a network into modules induces an analogous decomposition of the dynamic structure, exhibiting a strong relationship between network structure and function. An extensive simulation study provides evidence for the hypothesis that modularity might have evolved to increase phenotypic complexity while maintaining maximal dynamic robustness to external perturbations.

Modularity of biological systems: a link between structure and function.

This paper addresses two topics in systems biology, the hypothesis that biological systems are modular and the problem of relating structure and function of biological systems. The focus here is on gene regulatory networks, represented by Boolean network models, a commonly used tool. Most of the research on gene regulatory network modularity has focused on network structure, typically represented through either directed or undirected graphs. But since gene regulation is a highly dynamic process as it determines the function of cells over time, it is natural to consider functional modularity as well. One of the main results is that the structural decomposition of a network into modules induces an analogous decomposition of the dynamic structure, exhibiting a strong relationship between network structure and function. An extensive simulation study provides evidence for the hypothesis that modularity might have evolved to increase phenotypic complexity while maintaining maximal dynamic robustness to external perturbations.

Projecting social contact matrices to populations stratified by binary attributes with known homophily.

Contact networks are heterogeneous. People with similar characteristics are more likely to interact, a phenomenon called assortative mixing or homophily. Empirical age-stratified social contact matrices have been derived by extensive survey work. We lack however similar empirical studies that provide social contact matrices for a population stratified by attributes beyond age, such as gender, sexual orientation, or ethnicity. Accounting for heterogeneities with respect to these attributes can have a profound effect on model dynamics. Here, we introduce a new method, which uses linear algebra and non-linear optimization, to expand a given contact matrix to populations stratified by binary attributes with a known level of homophily. Using a standard epidemiological model, we highlight the effect homophily can have on model dynamics, and conclude by briefly describing more complicated extensions. The available Python source code enables any modeler to account for the presence of homophily with respect to binary attributes in contact patterns, ultimately yielding more accurate predictive models.

Ethnic homophily affects vaccine prioritization strategies.

People are more likely to interact with other people of their ethnicity-a phenomenon known as ethnic homophily. In the United States, people of color are known to hold proportionately more high-contact jobs and are thus more at risk of virus infection. At the same time, these ethnic groups are on average younger than the rest of the population. This gives rise to interesting disease dynamics and non-trivial trade-offs that should be taken into consideration when developing prioritization strategies for future mass vaccine roll-outs. Here, we study the spread of COVID-19 through the US population, stratified by age, ethnicity, and occupation, using a detailed, previously-developed compartmental disease model. Based on historic data from the US mass COVID-19 vaccine roll-out that began in December 2020, we show, (i) how ethnic homophily affects the choice of optimal vaccine allocation strategy, (ii) that, notwithstanding potential ethical concerns, differentiating by ethnicity in these strategies can improve outcomes (e.g., fewer deaths), and (iii) that the most likely social context in the United States is very different from the standard assumptions made by models which do not account for ethnicity and this difference affects which allocation strategy is optimal. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Effect of homophily and correlation of beliefs on COVID-19 and general infectious disease outbreaks.

Contact between people with similar opinions and characteristics occurs at a higher rate than among other people, a phenomenon known as homophily. The presence of clusters of unvaccinated people has been associated with increased incidence of infectious disease outbreaks despite high population-wide vaccination rates. The epidemiological consequences of homophily regarding other beliefs as well as correlations among beliefs or circumstances are poorly understood, however. Here, we use a simple compartmental disease model as well as a more complex COVID-19 model to study how homophily and correlation of beliefs and circumstances in a social interaction network affect the probability of disease outbreak and COVID-19-related mortality. We find that the current social context, characterized by the presence of homophily and correlations between who vaccinates, who engages in risk reduction, and individual risk status, corresponds to a situation with substantially worse disease burden than in the absence of heterogeneities. In the presence of an effective vaccine, the effects of homophily and correlation of beliefs and circumstances become stronger. Further, the optimal vaccination strategy depends on the degree of homophily regarding vaccination status as well as the relative level of risk mitigation high- and low-risk individuals practice. The developed methods are broadly applicable to any investigation in which node attributes in a graph might reasonably be expected to cluster or exhibit correlations.

Distinct conformations of the HIV-1 V3 loop crown are targetable for broad neutralization.

The V3 loop of the HIV-1 envelope (Env) protein elicits a vigorous, but largely non-neutralizing antibody response directed to the V3-crown, whereas rare broadly neutralizing antibodies (bnAbs) target the V3-base. Challenging this view, we present V3-crown directed broadly neutralizing Designed Ankyrin Repeat Proteins (bnDs) matching the breadth of V3-base bnAbs. While most bnAbs target prefusion Env, V3-crown bnDs bind open Env conformations triggered by CD4 engagement. BnDs achieve breadth by focusing on highly conserved residues that are accessible in two distinct V3 conformations, one of which resembles CCR5-bound V3. We further show that these V3-crown conformations can, in principle, be attacked by antibodies. Supporting this conclusion, analysis of antibody binding activity in the Swiss 4.5 K HIV-1 cohort (n = 4,281) revealed a co-evolution of V3-crown reactivities and neutralization breadth. Our results indicate a role of V3-crown responses and its conformational preferences in bnAb development to be considered in preventive and therapeutic approaches.

Evaluation of the United States COVID-19 vaccine allocation strategy.

BACKGROUND: Anticipating an initial shortage of vaccines for COVID-19, the Centers for Disease Control (CDC) in the United States developed priority vaccine allocations for specific demographic groups in the population. This study evaluates the performance of the CDC vaccine allocation strategy with respect to multiple potentially competing vaccination goals (minimizing mortality, cases, infections, and years of life lost (YLL)), under the same framework as the CDC allocation: four priority vaccination groups and population demographics stratified by age, comorbidities, occupation and living condition (congested or non-congested). METHODS AND FINDINGS: We developed a compartmental disease model that incorporates key elements of the current pandemic including age-varying susceptibility to infection, age-varying clinical fraction, an active case-count dependent social distancing level, and time-varying infectivity (accounting for the emergence of more infectious virus strains). The CDC allocation strategy is compared to all other possibly optimal allocations that stagger vaccine roll-out in up to four phases (17.5 million strategies). The CDC allocation strategy performed well in all vaccination goals but never optimally. Under the developed model, the CDC allocation deviated from the optimal allocations by small amounts, with 0.19% more deaths, 4.0% more cases, 4.07% more infections, and 0.97% higher YLL, than the respective optimal strategies. The CDC decision to not prioritize the vaccination of individuals under the age of 16 was optimal, as was the prioritization of health-care workers and other essential workers over non-essential workers. Finally, a higher prioritization of individuals with comorbidities in all age groups improved outcomes compared to the CDC allocation. CONCLUSION: The developed approach can be used to inform the design of future vaccine allocation strategies in the United States, or adapted for use by other countries seeking to optimize the effectiveness of their vaccine allocation strategies.

Phylogenetic Cluster Analysis Identifies Virological and Behavioral Drivers of Human Immunodeficiency Virus Transmission in Men Who Have Sex With Men.

BACKGROUND: Identifying local outbreaks and their drivers is a key step toward curbing human immunodeficiency virus (HIV) transmission and potentially achieving HIV elimination. Such outbreaks can be identified as transmission clusters extracted from phylogenetic trees constructed of densely sampled viral sequences. In this study, we combined phylogenetic transmission clusters with extensive data on virological suppression and behavioral risk of cluster members to quantify the drivers of ongoing transmission over 10 years. METHODS: Using the comprehensive Swiss HIV Cohort Study and its drug-resistance database, we reconstructed phylogenetic trees for each year between 2007 and 2017. We identified HIV transmission clusters dominated by men who have sex with men (MSM) and determined their annual growth. We used Poisson regression to assess if cluster growth was associated with a per-cluster infectivity and behavioral risk score. RESULTS: Both infectivity and behavioral risk scores were significantly higher in growing MSM transmission clusters compared to nongrowing clusters (P ≤ .01). The fraction of transmission clusters without infectious members acquiring new infections increased significantly over the study period. The infectivity score was significantly associated with per-capita incidence of MSM transmission clusters in 8 years, while the behavioral risk score was significantly associated with per-capita incidence of MSM transmission clusters in 3 years. CONCLUSIONS: We present a phylogenetic method to identify hotspots of ongoing transmission among MSM. Our results demonstrate the effectiveness of treatment as prevention at the population level. However, the significantly increasing number of new infections among transmission clusters without infectious members highlights a relative shift from diagnosed to undiagnosed individuals as drivers of HIV transmission in Swiss MSM.

A model-based evaluation of the efficacy of COVID-19 social distancing, testing and hospital triage policies.

A stochastic compartmental network model of SARS-CoV-2 spread explores the simultaneous effects of policy choices in three domains: social distancing, hospital triaging, and testing. Considering policy domains together provides insight into how different policy decisions interact. The model incorporates important characteristics of COVID-19, the disease caused by SARS-CoV-2, such as heterogeneous risk factors and asymptomatic transmission, and enables a reliable qualitative comparison of policy choices despite the current uncertainty in key virus and disease parameters. Results suggest possible refinements to current policies, including emphasizing the need to reduce random encounters more than personal contacts, and testing low-risk symptomatic individuals before high-risk symptomatic individuals. The strength of social distancing of symptomatic individuals affects the degree to which asymptomatic cases drive the epidemic as well as the level of population-wide contact reduction needed to keep hospitals below capacity. The relative importance of testing and triaging also depends on the overall level of social distancing.

Widespread B cell perturbations in HIV-1 infection afflict naive and marginal zone B cells.

Perturbations in B cells are a hallmark of HIV-1 infection. This is signified by increased numbers of exhausted CD21neg memory B cells, driven by continuous antigen-specific and bystander activation. Using high-dimensional flow cytometry, we demonstrate that this exhausted phenotype is also prevalent among peripheral antigen-inexperienced naive and marginal zone (MZ) B cells in acute and chronic HIV-1 infection. A substantial fraction of naive and MZ B cells exhibit down-regulated CD21 levels and diminished response to B cell receptor (BCR)-dependent stimulation. Compared with CD21pos subsets, the CD21neg naive and MZ B cells differ in the expression of chemokine receptors and activation markers. Effective antiretroviral treatment normalizes peripheral naive and MZ B cell populations. Our results emphasize a more widely spread impairment of B cells in HIV-1 infection than previously appreciated, including antigen-inexperienced cells. This highlights the importance of monitoring functional capacities of naive B cells in HIV-1 infection, as exhausted CD21neg naive B cells may severely impair induction of novel B cell responses.

Correlates of broadly neutralizing antibody development.

PURPOSE OF REVIEW: Broadly neutralizing antibodies (bnAbs) are considered a key component of an effective HIV-1 vaccine, but despite intensive efforts, induction of bnAbs by vaccination has thus far not been possible. Potent bnAb activity is rare in natural infection and a deeper understanding of factors that promote or limit bnAb evolution is critical to guide bnAb vaccine development. This review reflects on recent key discoveries on correlates of bnAb development and discusses what further insights are needed to move forward. RECENT FINDINGS: An increasing number of parameters have been implicated to influence bnAb development in natural infection. Most recent findings highlight a range of immune factors linked with bnAb evolution. Novel approaches have brought exciting progress in defining signatures of the viral envelope associated with bnAb activity. SUMMARY: Focused efforts of recent years have unraveled a multiply layered process of HIV-1 bnAb development. As it is understood today, bnAb evolution can be triggered and influenced by a range of factors and several different pathways may exist how bnAb induction and maturation can occur. To capitalize on the gained knowledge, future research needs to validate factors to identify independent drivers of bnAb induction to advance vaccine design.

Importance of routine viral load monitoring: higher levels of resistance at ART failure in Uganda and Lesotho compared with Switzerland.

Objectives: Emerging resistance to antiretroviral drugs may jeopardize the achievements of improved access to ART. We compared the prevalence of different resistance mutations in HIV-infected adults with virological failure in a cohort with regular routine viral load (VL) monitoring (Switzerland) and cohorts with limited access to VL testing (Uganda and Lesotho). Methods: We considered individuals who had genotypic resistance testing (GRT) upon virological failure (≥1000 copies/mL) and were on ART consisting of at least one NNRTI and two NRTIs. From Lesotho, individuals with two subsequent VLs ≥1000 copies/mL despite enhanced adherence counselling (n = 58) were included in the analysis. From Uganda, individuals with a single VL ≥1000 copies/mL (n = 120) were included in the analysis. From the Swiss HIV Cohort Study (SHCS), a population without history of monotherapy or dual therapy with the first GRT upon virological failure (n = 61) was selected. Results: We found that 50.8% of individuals in the SHCS, 72.5% in Uganda and 81.0% in Lesotho harboured HIV with high-level resistance to at least two drugs from their current regimen. Stanford resistance scores were higher in Uganda compared with Switzerland for all drugs used in first-line treatment except zidovudine and tenofovir (P < 0.01) and higher in Lesotho compared with Uganda for all drugs used in first-line treatment except zidovudine (P < 0.01). Conclusions: Frequent VL monitoring and possibly pretreatment GRT as done in the SHCS pays off by low levels of resistance even when treatment failure occurs. The high-level resistance patterns in Lesotho compared with Uganda could reflect a selection of strains with multiple resistance during enhanced adherence counselling.

Tracing HIV-1 strains that imprint broadly neutralizing antibody responses.

Understanding the determinants of broadly neutralizing antibody (bNAb) evolution is crucial for the development of bNAb-based HIV vaccines1. Despite emerging information on cofactors that promote bNAb evolution in natural HIV-1 infections, in which the induction of bNAbs is genuinely rare2, information on the impact of the infecting virus strain on determining the breadth and specificity of the antibody responses to HIV-1 is lacking. Here we analyse the influence of viral antigens in shaping antibody responses in humans. We call the ability of a virus strain to induce similar antibody responses across different hosts its antibody-imprinting capacity, which from an evolutionary biology perspective corresponds to the viral heritability of the antibody responses. Analysis of 53 measured parameters of HIV-1-binding and neutralizing antibody responses in a cohort of 303 HIV-1 transmission pairs (individuals who harboured highly related HIV-1 strains and were putative direct transmission partners or members of an HIV-1 transmission chain) revealed that the effect of the infecting virus on the outcome of the bNAb response is moderate in magnitude but highly significant. We introduce the concept of bNAb-imprinting viruses and provide evidence for the existence of such viruses in a systematic screening of our cohort. The bNAb-imprinting capacity can be substantial, as indicated by a transmission pair with highly similar HIV-1 antibody responses and strong bNAb activity. Identification of viruses that have bNAb-imprinting capacities and their characterization may thus provide the potential to develop lead immunogens.

Inferring the age difference in HIV transmission pairs by applying phylogenetic methods on the HIV transmission network of the Swiss HIV Cohort Study.

Age-mixing patterns are of key importance for understanding the dynamics of human immunodeficiency virus (HIV)-epidemics and target public health interventions. We use the densely sampled Swiss HIV Cohort Study (SHCS) resistance database to study the age difference at infection in HIV transmission pairs using phylogenetic methods. In addition, we investigate whether the mean age difference of pairs in the phylogenetic tree is influenced by sampling as well as by additional distance thresholds for including pairs. HIV-1 pol-sequences of 11,922 SHCS patients and approximately 240,000 Los Alamos background sequences were used to build a phylogenetic tree. Using this tree, 100 per cent down to 1 per cent of the tips were sampled repeatedly to generate pruned trees (N = 500 for each sample proportion), of which pairs of SHCS patients were extracted. The mean of the absolute age differences of the pairs, measured as the absolute difference of the birth years, was analyzed with respect to this sample proportion and a distance criterion for inclusion of the pairs. In addition, the transmission groups men having sex with men (MSM), intravenous drug users (IDU), and heterosexuals (HET) were analyzed separately. Considering the tree with all 11,922 SHCS patients, 2,991 pairs could be extracted, with 954 (31.9 per cent) MSM-pairs, 635 (21.2 per cent) HET-pairs, 414 (13.8 per cent) IDU-pairs, and 352 (11.8 per cent) HET/IDU-pairs. For all transmission groups, the age difference at infection was significantly (P < 0.001) smaller for pairs in the tree compared with randomly assigned pairs, meaning that patients of similar age are more likely to be pairs. The mean age difference in the phylogenetic analysis, using a fixed distance of 0.05, was 9.2, 9.0, 7.3 and 5.6 years for MSM-, HET-, HET/IDU-, and IDU-pairs, respectively. Decreasing the cophenetic distance threshold from 0.05 to 0.01 significantly decreased the mean age difference. Similarly, repeated sampling of 100 per cent down to 1 per cent of the tips revealed an increased age difference at lower sample proportions. HIV-transmission is age-assortative, but the age difference of transmission pairs detected by phylogenetic analyses depends on both sampling proportion and distance criterion. The mean age difference decreases when using more conservative distance thresholds, implying an underestimation of age-assortativity when using liberal distance criteria. Similarly, overestimation of the mean age difference occurs for pairs from sparsely sampled trees, as it is often the case in sub-Saharan Africa.