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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.

Abstract 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.

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.

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.

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) induces B and T cell responses, contributing to virus neutralization. In a cohort of 2,911 young adults, we identified 65 individuals who had an asymptomatic or mildly symptomatic SARS-CoV-2 infection and characterized their humoral and T cell responses to the Spike (S), Nucleocapsid (N) and Membrane (M) proteins. We found that previous infection induced CD4 T cells that vigorously responded to pools of peptides derived from the S and N proteins. By using statistical and machine learning models, we observed that the T cell response highly correlated with a compound titer of antibodies against the Receptor Binding Domain (RBD), S and N. However, while serum antibodies decayed over time, the cellular phenotype of these individuals remained stable over four months. Our computational analysis demonstrates that in young adults, asymptomatic and paucisymptomatic SARS-CoV-2 infections can induce robust and long-lasting CD4 T cell responses that exhibit slower decays than antibody titers. These observations imply that next-generation COVID-19 vaccines should be designed to induce stronger cellular responses to sustain the generation of potent neutralizing antibodies.

The V3-crown of the HIV-1 envelope protein largely elicits non-neutralizing antibodies. Here, the authors show that the V3-crown can be targeted by broadly neutralizing designed ankyrin repeat proteins recognizing two conformations one of which resembles CCR5- bound V3.

Serosurveys are an important tool to estimate the true extent of the current SARS-CoV-2 pandemic. So far, most serosurvey data have been analyzed with cutoff-based methods, which dichotomize individual measurements into sero-positives or negatives based on a predefined cutoff. However, mixture model methods can gain additional information from the same serosurvey data. Such methods refrain from dichotomizing individual values and instead use the full distribution of the serological measurements from pre-pandemic and COVID-19 controls to estimate the cumulative incidence. This study presents an application of mixture model methods to SARS-CoV-2 serosurvey data from the SEROCoV-POP study from April and May 2020 in Geneva (2766 individuals). Besides estimating the total cumulative incidence in these data (8.1% (95% CI: 6.8%–9.9%)), we applied extended mixture model methods to estimate an indirect indicator of disease severity, which is the fraction of cases with a distribution of antibody levels similar to hospitalized COVID-19 patients. This fraction is 51.2% (95% CI: 15.2%–79.5%) across the full serosurvey, but differs between three age classes: 21.4% (95% CI: 0%–59.6%) for individuals between 5 and 40 years old, 60.2% (95% CI: 21.5%–100%) for individuals between 41 and 65 years old and 100% (95% CI: 20.1%–100%) for individuals between 66 and 90 years old. Additionally, we find a mismatch between the inferred negative distribution of the serosurvey and the validation data of pre-pandemic controls. Overall, this study illustrates that mixture model methods can provide additional insights from serosurvey data.

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. [ABSTRACT FROM AUTHOR]

Abstract The RNA interference (RNAi) drug ARC-520 was shown to be effective in reducing serum hepatitis B virus (HBV) DNA, hepatitis B e antigen (HBeAg) and hepatitis B surface antigen (HBsAg) in HBeAg-positive patients treated with a single dose of ARC-520 and daily nucleosidic analogue (entecavir). To provide insights into HBV dynamics under ARC-520 treatment and its efficacy in blocking HBV DNA, HBsAg, and HBeAg production we developed a multi-compartmental pharmacokinetic–pharamacodynamic model and calibrated it with frequent measured HBV kinetic data. We showed that the time-dependent single dose ARC-520 efficacies in blocking HBsAg and HBeAg are more than 96% effective around day 1, and slowly wane to 50% in 1–4 months. The combined single dose ARC-520 and entecavir effect on HBV DNA was constant over time, with efficacy of more than 99.8%. The observed continuous HBV DNA decline is entecavir mediated, the strong but transient HBsAg and HBeAg decays are ARC-520 mediated. The modeling framework may help assess ongoing RNAi drug development for hepatitis B virus infection.

Serosurveys are a widely used tool to estimate the cumulative incidence—the fraction of a population that has been infected by a given pathogen. These surveys rely on serological assays that measure the level of pathogen-specific antibodies. Because antibody levels are waning, the fraction of previously infected individuals that have seroreverted increases with time past infection. To avoid underestimating the true cumulative incidence, it is therefore essential to correct for waning antibody levels. We present an empirically supported approach for seroreversion correction in cumulative incidence estimation when sequential serosurveys are conducted in the context of a newly emerging infectious disease. The correction is based on the observed dynamics of antibody titers in seropositive cases and validated using several in silico test scenarios. Furthermore, through this approach we revise a previous cumulative incidence estimate relying on the assumption of an exponentially declining probability of seroreversion over time, of severe acute respiratory syndrome coronavirus 2, of 76% in Manaus, Brazil, by October 2020 to 47.6% (95% confidence region: 43.5–53.5). This estimate has implications, for example, for the proximity to herd immunity in Manaus in late 2020. [ABSTRACT FROM AUTHOR]

Spontaneous or drug-induced loss of hepatitis B e antigen is considered a beneficial event in the disease progression of chronic hepatitis B virus infections. Mathematical models of within-host interactions are proposed; which provide insight into hepatitis B e antibody formation, its influence on hepatitis B e antigen seroclearance, and reversion of anergic cytotoxic immune responses. They predict that antibody expansion causes immune activation and hepatitis B e antigen seroclearance. Quantification of the time between antibody expansion and hepatitis B e antigen seroclearance in the presence and absence of treatment shows that potent short-term treatment speeds up the time between antibody expansion and hepatitis B e antigen seroclearance. The monthly hepatocyte turnover during this time can be increased or decreased by treatment depending on the amount of core promoter or precore mutated virus produced. The results can inform human interventions.

The highly controlled migration of neutrophils toward the site of an infection can be altered when they are trained with lipopolysaccharides (LPS), with high dose LPS enhancing neutrophil migratory pattern toward the bacterial derived source signal and super-low dose LPS inducing either migration toward an intermediary signal or dysregulation and oscillatory movement. Empirical studies that use microfluidic chemotaxis-chip devices with two opposing chemoattractants showed differential neutrophil migration after challenge with different LPS doses. The epigenetic alterations responsible for changes in neutrophil migratory behavior are unknown. We developed two mathematical models that evaluate the mechanistic interactions responsible for neutrophil migratory decision-making when exposed to competing chemoattractants and challenged with LPS. The first model, which considers the interactions between the receptor densities of two competing chemoattractants, their kinases, and LPS, displayed bistability between high and low ratios of primary to intermediary chemoattractant receptor densities. In particular, at equilibrium, we observe equal receptor densities for low LPS (< 15ng/mL); and dominance of receptors for the primary chemoattractant for high LPS (> 15ng/mL). The second model, which included additional interactions with an extracellular signal-regulated kinase in both phosphorylated and non-phosphorylated forms, has an additional dynamic outcome, oscillatory dynamics for both receptors, as seen in the data. In particular, it found equal receptor densities in the absence of oscillation for super-low and high LPS challenge (< 0.4 and 1.1 376 ng/mL). Predicting the mechanisms and the type of external LPS challenge responsible for neutrophils migration toward pro-inflammatory chemoattractants, migration toward pro-tolerant chemoattractants, or oscillatory movement is necessary knowledge in designing interventions against immune diseases, such as sepsis.

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.

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.

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.

Abstract Background Parent-offspring (PO) regression is a central tool to determine the heritability of phenotypic traits; i.e., the relative extent to which those traits are controlled by genetic factors. The applicability of PO regression to viral traits is unclear because the direction of viral transmission—who is the donor (parent) and who is the recipient (offspring)—is typically unknown and viral phylogenies are sparsely sampled. Methods We assessed the applicability of PO regression in a realistic setting using Ornstein–Uhlenbeck simulated data on phylogenies built from 11,442 Swiss HIV Cohort Study (SHCS) partial pol sequences and set-point viral load (SPVL) data from 3293 patients. Results We found that the misidentification of donor and recipient plays a minor role in estimating heritability and showed that sparse sampling does not influence the mean heritability estimated by PO regression. A mixed-effect model approach yielded the same heritability as PO regression but could be extended to clusters of size greater than 2 and allowed for the correction of confounding effects. Finally, we used both methods to estimate SPVL heritability in the SHCS. We employed a wide range of transmission pair criteria to measure heritability and found a strong dependence of the heritability estimates to these criteria. For the most conservative genetic distance criteria, for which heritability estimates are conceptually expected to be closest to true heritability, we found estimates ranging from 32 to 46% across different bootstrap criteria. For less conservative distance criteria, we found estimates ranging down to 8%. All estimates did not change substantially after adjusting for host-demographic factors in the mixed-effect model (±2%). Conclusions For conservative transmission pair criteria, both PO regression and mixed-effect models are flexible and robust tools to estimate the contribution of viral genetic effects to viral traits under real-world settings. Overall, we find a strong effect of viral genetics on SPVL that is not confounded by host demographics.