Covid-19 disease dynamics with vaccination: The effect of uncertainty

Rate parameters are critical in estimating the covid burden using mathematical models. In the Covid-19 mathematical models, these parameters are assumed to be constant. However, uncertainties in these rate parameters are almost inevitable. In this paper, we study a stochastic epidemic model of the SARS-CoV-2 virus infection in the presence of vaccination in which some parameters fluctuate around its average value. Our analysis shows that if the stochastic basic reproduction number (SBRN) of the system is greater than unity, then there is a stationary distribution, implying the long-time disease persistence. A sufficient condition for disease eradication is also prescribed for which the exposed class goes extinct, followed by the infected class. The disease eradication criterion may not hold if the rate of vaccine-induced immunity loss increases or/and the force of infection increases. Using the Indian Covid-19 data, we estimated the model parameters and showed the future disease progression in the presence of vaccination. The disease extinction time is estimated under various conditions. It is revealed that the mean extinction time is an increasing function of both the force of infection and immunity loss rate and shows the lognormal distribution. We point out that disease eradication might not be possible even at a higher vaccination rate if the vaccine-induced immunity loss rate is high. Our observation thus indicates the endemicity of the disease for the existing vaccine efficacy. The disease eradication is possible only with a higher vaccine efficacy or a reduced infection rate.

Distributions of extinction times from fossil ages and tree topologies: the example of mid-Permian synapsid extinctions

Given a phylogenetic tree that includes only extinct, or a mix of extinct and extant taxa, where at least some fossil data are available, we present a method to compute the distribution of the extinction time of a given set of taxa under the Fossilized-Birth-Death model. Our approach differs from the previous ones in that it takes into account (i) the possibility that the taxa or the clade considered may diversify before going extinct and (ii) the whole phylogenetic tree to estimate extinction times, whilst previous methods do not consider the diversification process and deal with each branch independently. Because of this, our method can estimate extinction times of lineages represented by a single fossil, provided that they belong to a clade that includes other fossil occurrences. We assess and compare our new approach with a standard previous one using simulated data. Results show that our method provides more accurate confidence intervals. This new approach is applied to the study of the extinction time of three Permo-Carboniferous synapsid taxa (Ophiacodontidae, Edaphosauridae, and Sphenacodontidae) that are thought to have disappeared toward the end of the Cisuralian (early Permian), or possibly shortly thereafter. The timing of extinctions of these three taxa and of their component lineages supports the idea that the biological crisis in the late Kungurian/early Roadian consisted of a progressive decline in biodiversity throughout the Kungurian.

Genomic anatomy of male-specific microchromosomes in a gynogenetic fish

Unisexual taxa are commonly considered short-lived as the absence of meiotic recombination is supposed to accumulate deleterious mutations and hinder the creation of genetic diversity. However, the gynogenetic gibel carp (Carassius gibelio) with high genetic diversity and wide ecological distribution has outlived its predicted extinction time of a strict unisexual reproduction population. Unlike other unisexual vertebrates, males associated with supernumerary microchromosomes have been observed in gibel carp, which provides a unique system to explore the rationales underlying male occurrence in unisexual lineage and evolution of unisexual reproduction. Here, we identified a massively expanded satellite DNA cluster on microchromosomes of hexaploid gibel carp via comparing with the ancestral tetraploid crucian carp (Carassius auratus). Based on the satellite cluster, we developed a method for single chromosomal fluorescence microdissection and isolated three male-specific microchromosomes in a male metaphase cell. Genomic anatomy revealed that these male-specific microchromosomes contained homologous sequences of autosomes and abundant repetitive elements. Significantly, several potential male-specific genes with transcriptional activity were identified, among which four and five genes displayed male-specific and male-biased expression in gonads, respectively, during the developmental period of sex determination. Therefore, the male-specific microchromosomes resembling common features of sex chromosomes may be the main driving force for male occurrence in gynogenetic gibel carp, which sheds new light on the evolution of unisexual reproduction.

Extinction time of the logistic process

The logistic birth and death process is perhaps the simplest stochastic population model that has both density-dependent reproduction and a phase transition, and a lot can be learned about the process by studying its extinction time, $\tau_n$ , as a function of system size n. A number of existing results describe the scaling of $\tau_n$ as $n\to\infty$ for various choices of reproductive rate $r_n$ and initial population $X_n(0)$ as a function of n. We collect and complete this picture, obtaining a complete classification of all sequences $(r_n)$ and $(X_n(0))$ for which there exist rescaling parameters $(s_n)$ and $(t_n)$ such that $(\tau_n-t_n)/s_n$ converges in distribution as $n\to\infty$ , and identifying the limits in each case.

Cheater suppression and spite through quorum sensing

The evolutionary consequences of quorum sensing in regulating bacterial cooperation are not fully understood. In this study, we reveal unexpected consequences of regulating public good production through quorum sensing on bacterial population dynamics, showing that quorum sensing can be a "spiteful" alternative to unregulated production. We analyze a birth-death model of bacterial population dynamics accounting for public good production and the presence of non-producing cheaters. Our model demonstrates that when demographic noise is a factor, the consequences of controlling public good production according to quorum sensing depend on the cost of public good production and the presence of alternative sources of the fitness benefits provided by public goods. When public good production is inexpensive, quorum sensing is a spiteful alternative to unconditional production, in terms of the mean population extinction time. When costs are higher, quorum sensing becomes a selfish strategy for the producing strain, both stabilizing cooperation and decreasing the risk of population extinction.

Distributions of extinction times from fossil ages and tree topologies: the example of some mid-Permian synapsid extinctions

Given a phylogenetic tree of extinct and extant taxa with fossils where the only temporal information stands in the fossil ages, we devise a method to compute the distribution of the extinction time of a given set of taxa under the Fossilized-Birth-Death model. Our approach differs from the previous ones in that it takes into account the possibility that the taxa or the clade considered may diversify before going extinct, whilst previous methods just rely on the fossil recovery rate to estimate confidence intervals. We assess and compare our new approach with a standard previous one using simulated data. Results show that our method provides more accurate confidence intervals. This new approach is applied to the study of the extinction time of three Permo-Carboniferous synapsid taxa (Ophiacodontidae, Edaphosauridae, and Sphenacodontidae) that are thought to have disappeared toward the end of the Cisuralian, or possibly shortly thereafter. The timing of extinctions of these three taxa and of their component lineages supports the idea that a biological crisis occurred in the late Kungurian/early Roadian.

The Influence of Latent and Chronic Infection on Pathogen Persistence

We extend the classical compartmental frameworks for susceptible-infected-susceptible (SIS) and susceptible-infected-recovered (SIR) systems to include an exposed/latent class or a chronic class of infection. Using a suite of stochastic continuous-time Markov chain models we examine the impact of latent and chronic infection on the mean time to extinction of the infection. Our findings indicate that the mean time to pathogen extinction is increased for infectious diseases which cause exposed/latent infection prior to full infection and that the extinction time is increased further if these exposed individuals are also capable of transmitting the infection. A chronic infection stage can decrease or increase the mean time to pathogen extinction and in particular this depends on whether chronically infected individuals incur disease-induced mortality and whether they are able to transmit the infection. We relate our findings to specific infectious diseases that exhibit latent and chronic infectious stages and argue that infectious diseases with these characteristics may be more difficult to manage and control.

Finite extinction for a doubly nonlinear parabolic equation of fast diffusion type

PurposeThe purpose of this paper is to find a doubly nonlinear parabolic equation of fast diffusion in a bounded domain.Design/methodology/approachFor positive and bounded initial data, the authors study the initial zero-boundary value problem.FindingsThe findings of this study showed the complete extinction of a continuous weak solution at a finite time.Originality/valueThe extinction time is studied earlier but for the Laplacian case. The authors presented the finite extinction time for the case of p-Laplacian.

Adaptive Single-Pole Auto-Reclosing Scheme Based on Secondary Arc Voltage Harmonic Signatures

This paper presents an advanced adaptive single-pole auto-reclosing (ASPAR) scheme based on harmonic characteristics of the secondary arc voltage. For analysis of the harmonics, short-time Fourier transform (STFT), which is a universal signal processing tool for transforming a signal from the time domain to the frequency domain, is utilized. STFT is applied to extract the abnormal harmonic signature from the voltage waveform of a faulted phase when a transient or permanent fault occurs on a power transmission line. The proposed scheme uses the total harmonic distortion (THD) factor to determine the fault type based on the variation and distortion characteristics of the harmonics. Harmonic components in the order of odd/even are also utilized to detect the secondary arc extinction time and guide the reclosing operation. Based on these factors, two coordinated algorithms are proposed to reduce the unnecessary dead time in conventional auto-reclosing methods and enable an optimal reclosing operation in the event of a single-pole to ground fault. The proposed ASPAR scheme is implemented using the electromagnetic transient program (EMTP), and various simulations are conducted for actual 345 and 765 kV Korean study systems.