The convergence in distribution of some simple epidemics

A group of n susceptible individuals exposed to a contagious disease isconsidered. It is assumed that at each point in time one or more susceptible individuals can contract the disease. The progress of this simple batch epidemic is modeled by a stochastic process X_n(t), t[0, ∞), representing the number of infectiveindividuals at time t. In this paper our analysis is restricted to simple batch epidemics with transition rates given by [α²X_n(t){n −X_n(t) +X_n(0)}]^1/2, t[0, ∞), α(0, ∞). This class of simple batch epidemics generalizes a model used and motivated by McNeil (1972) to describe simple epidemic situations. It is shown for this class of simple batch epidemics, that X_n(t), with suitable standardization, converges in distribution as n→∞ to a normal random variable for all t(0, t₀), and t₀ is evaluated.     

Transmission and containment of the SARS-CoV-2 Delta variant of concern in Guangzhou,China: A population-based study

BackgroundThe first community transmission of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) Delta variant of concern (VOC) in Guangzhou, China occurred between May and June 2021. Herein, we describe the epidemiological characteristics of this outbreak and evaluate the implemented containment measures against this outbreak.Methodology/Principal findingsGuangzhou Center for Disease Control and Prevention provided the data on SARS-CoV-2 infections reported between 21 May and 24 June 2021. We estimated the incubation period distribution by fitting a gamma distribution to the data, while the serial interval distribution was estimated by fitting a normal distribution. The instantaneous effective reproductive number (R_t) was estimated to reflect the transmissibility of SARS-CoV-2. Clinical severity was compared for cases with different vaccination statuses using an ordinal regression model after controlling for age. Of the reported local cases, 7/153 (4.6%) were asymptomatic. The median incubation period was 6.02 (95% confidence interval [CI]: 5.42–6.71) days and the means of serial intervals decreased from 5.19 (95% CI: 4.29–6.11) to 3.78 (95% CI: 2.74–4.81) days. The incubation period increased with age (P<0.001). A hierarchical prevention and control strategy against COVID-19 was implemented in Guangzhou, with R_t decreasing from 6.83 (95% credible interval [CrI]: 3.98–10.44) for the 7-day time window ending on 27 May 2021 to below 1 for the time window ending on 8 June and thereafter. Individuals with partial or full vaccination schedules with BBIBP-CorV or CoronaVac accounted for 15.3% of the COVID-19 cases. Clinical symptoms were milder in partially or fully vaccinated cases than in unvaccinated cases (odds ratio [OR] = 0.26 [95% CI: 0.07–0.94]).Conclusions/SignificanceThe hierarchical prevention and control strategy against COVID-19 in Guangzhou was timely and effective. Authorised inactivated vaccines are likely to contribute to reducing the probability of developing severe disease. Our findings have important implications for the containment of COVID-19.     

Simple Uniaxial and Uniform Biaxial Deformation of Nearly Isotropic Incompressible Tissues

A method is developed for analyzing in a unified manner both uniaxial and uniform biaxial strain data obtained from nearly isotropic tissues. The formulation is a direct application of nonlinear elasticity theory pertaining to large deformations. The general relation between Eulerian stress (σ) and extension ratio (λ) in soft isotropic elastic bodies undergoing uniform deformation takes the simple form: σ = ((λ³ - 1)/λ) f(λ), where f(λ) must be determined for each material. The extension ratio may be either greater than 1.0 (uniaxial elongation), or lie between zero and 1.0 (uniform biaxial extension). Simple analytical functions for f(λ) are most readily found for each tissue by plotting all data as (λ³ - 1)/λσ vs. λ. Of those tissues investigated in this way (dog pericardium and pleura, and cat mesentery and dura), all but pleura could be adequately described by a parabola: 1/f(λ) = 1/k{[(λ_M - λ)(λ - λ_m)]/[λ_M - λ_m}. In these instances, three material constants per tissue (K, λ_M, λ_m) served to predict approximately the stresses attained during both small and large deformations, in strips and sheets alike. It was further found that the uniaxial strain asymptote (λ_M) was linearly related to the biaxial strain asymptote (Λ_M), thus effectively reducing the number of constants by one.     

The asymptotic normality of a simple batch epidemic process

A group of n susceptible individuals exposed to a contagious disease isconsidered. It is assumed that at each point in time one or more susceptible individuals can contract the disease. The progress of this simple batch epidemic is modeled by a stochastic process X_n(t), t∈[0, ∞), representing the number of infectiveindividuals at time t. In this paper our analysis is restricted to simple batch epidemics with transition rates given by $\text{[α}{}^2\text{X}{}_{\mathrm{n}}\text{(t){n ?X}{}_{\mathrm{n}}\text{(t) +X}{}_{\mathrm{n}}\text{(0)}]}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{, t∈[0, ∞), α∈(0, ∞)}$. This class of simple batch epidemics generalizes a model used and motivated by McNeil (1972) to describe simple epidemic situations. It is shown for this class of simple batch epidemics, that X_n(t), with suitable standardization, converges in distribution as n→∞ to a normal random variable for all t∈(0, t₀), and t₀ is evaluated.     

Energetics of Contraction in Phasic and Tonic Skeletal Muscles of the Chicken

Comparative energetics of chicken latissimus dorsi muscles, tonic anterior (ALD) and phasic posterior (PLD), were investigated by measuring initial heat production. Heat components were analyzed in terms of the equation: E = A + W + α_F(L) + f(P, t) As the muscles were stretched by increments, heat produced in isometric twitches and tetani decreased in a linear fashion. Two processes are involved: one tension independent, the activation heat, or A; and the other tension dependent, W_i + α_F(L) + f(P, t). In twitches, A, per unit tension, is equivalent in the PLD and ALD. Tension-dependent heat, per unit tension, is greater in the PLD due to W_i; but tension-time-related heat, f(P, t), per unit tension, is similar in both muscles. In tetanic contractions, differences in A and f(P, t), per unit tension, are attributed to the greater V_max in the PLD. The differences in the energetics of isometric contractions in the PLD and ALD, therefore, can be explained by inherent differences in tension development, compliance, and myosin and reticular ATPase activities. Data from isotonic twitches were quantified by means of the equivalent tension technique. Both muscles exhibited an extra heat associated with shortening, α_F(L). In the PLD, the ratio α_F/P_ot is greater; it is load independent and ½ the value of a/P_o in both muscles. Enthalpy efficiency, W_e + W_i/E, is comparable in both muscles. A Fenn effect is observed only when isotonic energy liberation is compared to a decreasing isometric energy expenditure base line.     

Cross-Correlation Functions for a Neuronal Model

Cross-correlation functions, R_XY(t,τ), are obtained for a neuron model which is characterized by constant threshold θ, by resetting to resting level after an output, and by membrane potential U(t) which results from linear summation of excitatory postsynaptic potentials h(t). The results show that: (1) Near time lag τ = 0, R_XY(t,τ) = f_U [θ-h(τ), t + τ] {h′(τ) + E_U [u′(t + τ)]} for positive values of this quantity, where f_U(u,t) is the probability density function of U(t) and E_U [u′(t + τ)] is the mean value function of U′(t + τ). (2) Minima may appear in R_XY(t,τ) for a neuron subjected only to excitation. (3) For large τ, R_XY(t,τ) is given approximately by the convolution of the input autocorrelation function with the functional of point (1). (4) R_XY(t,τ) is a biased estimator of the shape of h(t), generally over-estimating both its time to peak and its rise time.     

Mitochondrial Oscillations and Waves in Cardiac Myocytes: Insights from Computational Models

Periodic cellwide depolarizations of mitochondrial membrane potential (Ψ_M) which are triggered by reactive oxygen species (ROS) and propagated by ROS-induced ROS release (RIRR) have been postulated to contribute to cardiac arrhythmogenesis and injury during ischemia/reperfusion. Two different modes of RIRR have been described: Ψ_M oscillations involving ROS-sensitive mitochondrial inner membrane anion channels (IMAC), and slow depolarization waves related to mitochondrial permeability transition pore (MPTP) opening. In this study, we developed a computational model of mitochondria exhibiting both IMAC-mediated RIRR and MPTP-mediated RIRR, diffusively coupled in a spatially extended network, to study the spatiotemporal dynamics of RIRR on Ψ_M. Our major findings are: 1), as the rate of ROS production increases, mitochondria can exhibit either oscillatory dynamics facilitated by IMAC opening, or bistable dynamics facilitated by MPTP opening; 2), in a diffusively-coupled mitochondrial network, the oscillatory dynamics of IMAC-mediated RIRR results in rapidly propagating (∼25 μm/s) cellwide Ψ_M oscillations, whereas the bistable dynamics of MPTP-mediated RIRR results in slow (0.1-2 μm/s) Ψ_M depolarization waves; and 3), the slow velocity of the MPTP-mediated depolarization wave is related to competition between ROS scavenging systems and ROS diffusion. Our observations provide mechanistic insights into the spatiotemporal dynamics underlying RIRR-induced Ψ_M oscillations and waves observed experimentally in cardiac myocytes.     

Effect of collisions on Van Kampen waves

The time evolution of Van Kampen waves is analyzed by solving the kinetic equation for the plasma particle distribution function. The damping law for Van Kampen waves, ∝Bexp(?C(Ωt)³), obtained earlier from qualitative considerations, is confirmed. The values of the constants B and C are found, and comparison with the previous analysis is made.     

Use of Mycobacterium smegmatis Deficient in ADP-Ribosyltransferase as Surrogate for Mycobacterium tuberculosis in Drug Testing and Mutation Analysis

Rifampicin (Rif) is a first line drug used for tuberculosis treatment. However, the emergence of drug resistant strains has necessitated synthesis and testing of newer analogs of Rif. Mycobacterium smegmatis is often used as a surrogate for M. tuberculosis. However, the presence of an ADP ribosyltransferase (Arr) in M. smegmatis inactivates Rif, rendering it impractical for screening of Rif analogs or other compounds when used in conjunction with them (Rif/Rif analogs). Rifampicin is also used in studying the role of various DNA repair enzymes by analyzing mutations in RpoB (a subunit of RNA polymerase) causing Rif resistance. These analyses use high concentrations of Rif when M. smegmatis is used as model. Here, we have generated M. smegmatis strains by deleting arr (Δarr). The M. smegmatis Δarr strains show minimum inhibitory concentration (MIC) for Rif which is similar to that for M. tuberculosis. The MICs for isoniazid, pyrazinamide, ethambutol, ciprofloxacin and streptomycin were essentially unaltered for M. smegmatis Δarr. The growth profiles and mutation spectrum of Δarr and, Δarr combined with ΔudgB (udgB encodes a DNA repair enzyme that excises uracil) strains were similar to their counterparts wild-type for arr. However, the mutation spectrum of ΔfpgΔarr strain differed somewhat from that of the Δfpg strain (fpg encodes a DNA repair enzyme that excises 8-oxo-G). Our studies suggest M. smegmatis Δarr strain as an ideal model system in drug testing and mutation spectrum determination in DNA repair studies.     

B.1.617.2 (Delta) Variant of SARS-CoV-2: features,transmission and potential strategies

Coronavirus disease 2019 (COVID-19) caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has become a pandemic. With the continuous evolution of the viral genome, SARS-CoV-2 has evolved many variants. B.1.617.2, also called Delta, is one of the most concerned variants. The Delta variant was first reported in India at the end of 2020 but has spread globally, by now, to 135 countries and is not stand still. Delta shared some mutations with other variants, and owned its special mutations on spike proteins, which may be responsible for its strong transmission and increasing virulence. Under these circumstances, a systematic summary of Delta is necessary. This review will focus on the Delta variant. We will describe all the characteristics of Delta (including biological features and clinical characteristics), analyze potential reasons for its strong transmission, and provide potential protective ways for combating Delta.     

Probabilistic Model of Microbial Cell Growth,Division, and Mortality

After a short time interval of length δt during microbial growth, an individual cell can be found to be divided with probability P_d(t)δt, dead with probability P_m(t)δt, or alive but undivided with the probability 1 − [P_d(t) + P_m(t)]δt, where t is time, P_d(t) expresses the probability of division for an individual cell per unit of time, and P_m(t) expresses the probability of mortality per unit of time. These probabilities may change with the state of the population and the habitat''s properties and are therefore functions of time. This scenario translates into a model that is presented in stochastic and deterministic versions. The first, a stochastic process model, monitors the fates of individual cells and determines cell numbers. It is particularly suitable for small populations such as those that may exist in the case of casual contamination of a food by a pathogen. The second, which can be regarded as a large-population limit of the stochastic model, is a continuous mathematical expression that describes the population''s size as a function of time. It is suitable for large microbial populations such as those present in unprocessed foods. Exponential or logistic growth with or without lag, inactivation with or without a “shoulder,” and transitions between growth and inactivation are all manifestations of the underlying probability structure of the model. With temperature-dependent parameters, the model can be used to simulate nonisothermal growth and inactivation patterns. The same concept applies to other factors that promote or inhibit microorganisms, such as pH and the presence of antimicrobials, etc. With P_d(t) and P_m(t) in the form of logistic functions, the model can simulate all commonly observed growth/mortality patterns. Estimates of the changing probability parameters can be obtained with both the stochastic and deterministic versions of the model, as demonstrated with simulated data.     

On enzymic clotting processes V: Rate equations for the case of arbitrary rate of production of the clotting species

The rate theory for enzyme-triggered coagulation reactions, such as the clotting of fibrin or casein, is extended to the case of an arbitrary rate of production of the clotting species. It is shown that the general expression for the growth of the weight-average molecular weight of the clotting product, -M_w, is given by -M_w = M₁{1 + k_s {∫₀^tP(t)² dt}/P(t)}, where M₁ is the “monomer” molecular weight, k_s the smoluchowskian flocculation rate constant and P(t) the total number of monomers produced by the enzyme in t. In the purely smoluchowskian case P(t) stands for the total number of monomers at the beginning of the clotting process. Numerical examples in which the rate of enzymic production is governed by complete Michaelis-Menten kinetics, are compared to cases in which this rate equals V_max- It is shown that after exhaustion of the substrate the system continues to coagulate in a purely smoluchowskian way. Turbidimetric experiments on the clotting of micelles of whole and κ-casein are presented which suggest inactivation of the enzyme by non-productive binding in the flocs formed.     

Mutations in dnaA and a cryptic interaction site increase drug resistance in Mycobacterium tuberculosis

Genomic dissection of antibiotic resistance in bacterial pathogens has largely focused on genetic changes conferring growth above a single critical concentration of drug. However, reduced susceptibility to antibiotics—even below this breakpoint—is associated with poor treatment outcomes in the clinic, including in tuberculosis. Clinical strains of Mycobacterium tuberculosis exhibit extensive quantitative variation in antibiotic susceptibility but the genetic basis behind this spectrum of drug susceptibility remains ill-defined. Through a genome wide association study, we show that non-synonymous mutations in dnaA, which encodes an essential and highly conserved regulator of DNA replication, are associated with drug resistance in clinical M. tuberculosis strains. We demonstrate that these dnaA mutations specifically enhance M. tuberculosis survival during isoniazid treatment via reduced expression of katG, the activator of isoniazid. To identify DnaA interactors relevant to this phenotype, we perform the first genome-wide biochemical mapping of DnaA binding sites in mycobacteria which reveals a DnaA interaction site that is the target of recurrent mutation in clinical strains. Reconstructing clinically prevalent mutations in this DnaA interaction site reproduces the phenotypes of dnaA mutants, suggesting that clinical strains of M. tuberculosis have evolved mutations in a previously uncharacterized DnaA pathway that quantitatively increases resistance to the key first-line antibiotic isoniazid. Discovering genetic mechanisms that reduce drug susceptibility and support the evolution of high-level drug resistance will guide development of biomarkers capable of prospectively identifying patients at risk of treatment failure in the clinic.     

Collective Fluctuations in the Dynamics of Adaptation and Other Traveling Waves

The dynamics of adaptation are difficult to predict because it is highly stochastic even in large populations. The uncertainty emerges from random genetic drift arising in a vanguard of particularly fit individuals of the population. Several approaches have been developed to analyze the crucial role of genetic drift on the expected dynamics of adaptation, including the mean fitness of the entire population, or the fate of newly arising beneficial deleterious mutations. However, little is known about how genetic drift causes fluctuations to emerge on the population level, where it becomes palpable as variations in the adaptation speed and the fitness distribution. Yet these phenomena control the decay of genetic diversity and variability in evolution experiments and are key to a truly predictive understanding of evolutionary processes. Here, we show that correlations induced by these emergent fluctuations can be computed at any arbitrary order by a suitable choice of a dynamical constraint. The resulting linear equations exhibit fluctuation-induced terms that amplify short-distance correlations and suppress long-distance ones. These terms, which are in general not small, control the decay of genetic diversity and, for wave-tip dominated (“pulled”) waves, lead to anticorrelations between the tip of the wave and the lagging bulk of the population. While it is natural to consider the process of adaptation as a branching random walk in fitness space subject to a constraint (due to finite resources), we show that other traveling wave phenomena in ecology and evolution likewise fall into this class of constrained branching random walks. Our methods, therefore, provide a systematic approach toward analyzing fluctuations in a wide range of population biological processes, such as adaptation, genetic meltdown, species invasions, or epidemics.     

Potent universal beta-coronavirus therapeutic activity mediated by direct respiratory administration of a Spike S2 domain-specific human neutralizing monoclonal antibody

Severe Acute Respiratory Syndrome Coronavirus-2 (SARS-CoV-2) marks the third novel β-coronavirus to cause significant human mortality in the last two decades. Although vaccines are available, too few have been administered worldwide to keep the virus in check and to prevent mutations leading to immune escape. To determine if antibodies could be identified with universal coronavirus activity, plasma from convalescent subjects was screened for IgG against a stabilized pre-fusion SARS-CoV-2 spike S2 domain, which is highly conserved between human β-coronavirus. From these subjects, several S2-specific human monoclonal antibodies (hmAbs) were developed that neutralized SARS-CoV-2 with recognition of all variants of concern (VoC) tested (Beta, Gamma, Delta, Epsilon, and Omicron). The hmAb 1249A8 emerged as the most potent and broad hmAb, able to recognize all human β-coronavirus and neutralize SARS-CoV and MERS-CoV. 1249A8 demonstrated significant prophylactic activity in K18 hACE2 mice infected with SARS-CoV-2 lineage A and lineage B Beta, and Omicron VoC. 1249A8 delivered as a single 4 mg/kg intranasal (i.n.) dose to hamsters 12 hours following infection with SARS-CoV-2 Delta protected them from weight loss, with therapeutic activity further enhanced when combined with 1213H7, an S1-specific neutralizing hmAb. As little as 2 mg/kg of 1249A8 i.n. dose 12 hours following infection with SARS-CoV Urbani strain, protected hamsters from weight loss and significantly reduced upper and lower respiratory viral burden. These results indicate in vivo cooperativity between S1 and S2 specific neutralizing hmAbs and that potent universal coronavirus neutralizing mAbs with therapeutic potential can be induced in humans and can guide universal coronavirus vaccine development.     

COVID-19 crisis management in Luxembourg: Insights from an epidemionomic approach

We develop an epidemionomic model that jointly analyzes the health and economic responses to the COVID-19 crisis and to the related containment and public health policy measures implemented in Luxembourg. The model has been used to produce nowcasts and forecasts at various stages of the crisis. We focus here on two key moments in time, namely the deconfinement period following the first lockdown, and the onset of the second wave. In May 2020, we predicted a high risk of a second wave that was mainly explained by the resumption of social life, low participation in large-scale testing, and reduction in teleworking practices. Simulations conducted 5 months later reveal that managing the second wave with moderately coercive measures has been epidemiologically and economically effective. Assuming a massive third (or fourth) wave will not materialize in 2021, the real GDP loss due to the second wave will be smaller than 0.4 percentage points in 2020 and 2021.     

Structural basis for the in vitro efficacy of nirmatrelvir against SARS-CoV-2 variants

The COVID-19 pandemic continues to be a public health threat with emerging variants of SARS-CoV-2. Nirmatrelvir (PF-07321332) is a reversible, covalent inhibitor targeting the main protease (M^pro) of SARS-CoV-2 and the active protease inhibitor in PAXLOVID (nirmatrelvir tablets and ritonavir tablets). However, the efficacy of nirmatrelvir is underdetermined against evolving SARS-CoV-2 variants. Here, we evaluated the in vitro catalytic activity and potency of nirmatrelvir against the M^pro of prevalent variants of concern (VOCs) or variants of interest (VOIs): Alpha (α, B.1.1.7), Beta (β, B.1.351), Delta (δ, B1.617.2), Gamma (γ, P.1), Lambda (λ, B.1.1.1.37/C37), Omicron (ο, B.1.1.529), as well as the original Washington or wildtype strain. These VOCs/VOIs carry prevalent mutations at varying frequencies in the M^pro specifically for α, β, γ (K90R), λ (G15S), and ο (P132H). In vitro biochemical enzymatic assay characterization of the enzyme kinetics of the mutant M^pros demonstrates that they are catalytically comparable to wildtype. We found that nirmatrelvir has similar potency against each mutant M^pro including P132H that is observed in the Omicron variant with a Ki of 0.635 nM as compared to a Ki of 0.933 nM for wildtype. The molecular basis for these observations were provided by solution-phase structural dynamics and structural determination of nirmatrelvir bound to the ο, λ, and β M^pro at 1.63 to 2.09 Å resolution. These in vitro data suggest that PAXLOVID has the potential to maintain plasma concentrations of nirmatrelvir many-fold times higher than the amount required to stop the SARS-CoV-2 VOC/VOI, including Omicron, from replicating in cells.     

Thermoadaptation-Directed Enzyme Evolution in an Error-Prone Thermophile Derived from Geobacillus kaustophilus HTA426

Thermostability is an important property of enzymes utilized for practical applications because it allows long-term storage and use as catalysts. In this study, we constructed an error-prone strain of the thermophile Geobacillus kaustophilus HTA426 and investigated thermoadaptation-directed enzyme evolution using the strain. A mutation frequency assay using the antibiotics rifampin and streptomycin revealed that G. kaustophilus had substantially higher mutability than Escherichia coli and Bacillus subtilis. The predominant mutations in G. kaustophilus were A · T→G · C and C · G→T · A transitions, implying that the high mutability of G. kaustophilus was attributable in part to high-temperature-associated DNA damage during growth. Among the genes that may be involved in DNA repair in G. kaustophilus, deletions of the mutSL, mutY, ung, and mfd genes markedly enhanced mutability. These genes were subsequently deleted to construct an error-prone thermophile that showed much higher (700- to 9,000-fold) mutability than the parent strain. The error-prone strain was auxotrophic for uracil owing to the fact that the strain was deficient in the intrinsic pyrF gene. Although the strain harboring Bacillus subtilis pyrF was also essentially auxotrophic, cells became prototrophic after 2 days of culture under uracil starvation, generating B. subtilis PyrF variants with an enhanced half-denaturation temperature of >10°C. These data suggest that this error-prone strain is a promising host for thermoadaptation-directed evolution to generate thermostable variants from thermolabile enzymes.