Disentangling the effect of measures, variants, and vaccines on SARS-CoV-2 infections in England: A dynamic intensity model

In this paper, we estimate the path of daily SARS-CoV-2 infections in England from the beginning of the pandemic until the end of 2021. We employ a dynamic intensity model, where the mean intensity conditional on the past depends both on past intensity of infections and past realized infections. The model parameters are time-varying, and we employ a multiplicative specification along with logistic transition functions to disentangle the time-varying effects of nonpharmaceutical policy interventions, of different variants, and of protection (waning) of vaccines/boosters. Our model results indicate that earlier interventions and vaccinations are key to containing an infection wave. We consider several scenarios that account for more infectious variants and different protection levels of vaccines/boosters. These scenarios suggest that, as vaccine protection wanes, containing a new wave in infections and an associated increase in hospitalizations in the near future may require further booster campaigns and/or nonpharmaceutical interventions.

Optimal strategies for controlling the outbreak of COVID-19: Reducing its cost and duration

Social distancing plays an essential role in controlling the spread of an epidemic, but changing the behavior of individuals regarding social distancing is costly. In order to make a rational decision, individuals must compare the cost of social distancing and the cost of infection. People are typically more likely to change their behavior if they are aware that the government is willing to incur additional cost to shorten the duration of an epidemic. I extend an optimal control problem of social distancing by integrating with the SIR model which describes the disease process. I present an optimal control problem to consider the behavior of susceptible individuals and the government in investment as control strategies and compute the equilibrium strategies under the potency of investment, using relative risk functions according to the investment that is made by susceptible individuals and the government. The equilibrium of this problem represents the optimal control strategies for minimizing the cost and duration of controlling an epidemic. Additionally, the model is evaluated using COVID-19 data from Egypt, Japan, Italy, Belgium, Nigeria, and Germany. The findings extracted from this model could be valuable in developing public health policy in the event of an epidemic. © 2022 Mohammadali Dashtbali, published by De Gruyter.

Inverted oscillator: pseudo hermiticity and coherent states

It is known that the standard and the inverted harmonic oscillator are different. Replacing thus ω by iω in the regular oscillator is necessary going to give the inverted oscillator Hr. This replacement would lead to anti-PT -symmetric harmonic oscillator Hamiltonian (iHos). The pseudo-hermiticity relation has been used here to relate the anti-PT -symmetric harmonic Hamiltonian to the inverted oscillator. By using a simple algebra, we introduce the ladder operators describing the inverted harmonic oscillator to reproduce the analytical solutions.We construct the inverted coherent states which minimize the quantum mechanical uncertainty between the position and the momentum. This paper is dedicated to the memory of Omar Djemli and Nouredinne Mebarki who died due to covid 19. © 2023,Revista Mexicana de Fisica.All Rights Reserved.

Repulsive Scaling Replica Exchange Molecular Dynamics in Modeling Protein-Glycosaminoglycan Complexes.

Glycosaminoglycans are long linear periodic anionic polysaccharides consisting of disaccharide units exhibiting different sulfation patterns forming a highly heterogeneous group of molecules. Due to their flexibility, length, high charge, and periodicity, they are challenging for computational approaches. Despite their biological significance in terms of the important role in various diseases (e.g., Alzheimer, cancer, SARS-CoV-2) and proper cell functioning (e.g., proliferation, maturation), there is a lack of effective molecular docking tools designed specifically for glycosaminoglycans due to their challenging physical-chemical nature. In this chapter we present protocols for the Repulsive Scaling Replica Exchange Molecular Dynamics (RS-REMD) methods to dock glycosaminoglycans with both implicit and explicit solvent models implemented. This novel molecular dynamics-based replica exchange technique should help to elevate our current knowledge on the complexes and interactions between glycosaminoglycans and their protein receptors.

On exact integrability of a Covid‐19 model: SIRV

In this study, the integrability conditions and the exact analytical solutions of the initial‐value problem defined for the prominent SIRV model used for the pandemic Covid‐19 are investigated by using the partial Hamiltonian approach based on the theory of Lie groups. Two different cases are considered with respect to the model parameters. In addition, the integrability properties and the associated approximate and exact analytical solutions to the SIRV model are analyzed and investigated by considering two different phase spaces. Furthermore, the graphical representations of susceptible, infected, recovered, and vaccinated population fractions evolving with time for subcases are introduced and discussed. [ FROM AUTHOR]

Scalable Bayesian phylogenetics.

Recent advances in Bayesian phylogenetics offer substantial computational savings to accommodate increased genomic sampling that challenges traditional inference methods. In this review, we begin with a brief summary of the Bayesian phylogenetic framework, and then conceptualize a variety of methods to improve posterior approximations via Markov chain Monte Carlo (MCMC) sampling. Specifically, we discuss methods to improve the speed of likelihood calculations, reduce MCMC burn-in, and generate better MCMC proposals. We apply several of these techniques to study the evolution of HIV virulence along a 1536-tip phylogeny and estimate the internal node heights of a 1000-tip SARS-CoV-2 phylogenetic tree in order to illustrate the speed-up of such analyses using current state-of-the-art approaches. We conclude our review with a discussion of promising alternatives to MCMC that approximate the phylogenetic posterior. This article is part of a discussion meeting issue 'Genomic population structures of microbial pathogens'.

Darboux polynomials and first integrals of polynomial Hamiltonian systems

We consider an autonomous polynomial Hamiltonian differential system of n degrees of freedom. In this Letter we study relationships between the existence of Darboux polynomials and additional Darboux polynomials for polynomial Hamiltonian systems. Also we extend some ideas of the Darboux theory of integrability for polynomial differential systems to general polynomial Hamiltonian systems taking into account the multiplicity of Darboux polynomials.

Analysis of Household Pulse Survey Public-Use Microdata via Unit-Level Models for Informative Sampling

The Household Pulse Survey, recently released by the U.S. Census Bureau, gathers information about the respondents’ experiences regarding employment status, food security, housing, physical and mental health, access to health care, and education disruption. Design-based estimates are produced for all 50 states and the District of Columbia (DC), as well as 15 Metropolitan Statistical Areas (MSAs). Using public-use microdata, this paper explores the effectiveness of using unit-level model-based estimators that incorporate spatial dependence for the Household Pulse Survey. In particular, we consider Bayesian hierarchical model-based spatial estimates for both a binomial and a multinomial response under informative sampling. Importantly, we demonstrate that these models can be easily estimated using Hamiltonian Monte Carlo through the Stan software package. In doing so, these models can readily be implemented in a production environment. For both the binomial and multinomial responses, an empirical simulation study is conducted, which compares spatial and non-spatial models. Finally, using public-use Household Pulse Survey micro-data, we provide an analysis that compares both design-based and model-based estimators and demonstrates a reduction in standard errors for the model-based approaches.

CONTROLLING THE TRANSMISSION DYNAMICS OF COVID-19

The outbreak of COVID-19 caused by SARS-CoV-2 in Wuhan and other cities in China in 2019 has become a global pandemic as declared by the World Health Organization (WHO) in the first quarter of 2020. The delay in diagnosis, limited hospital resources and other treatment resources led to the rapid spread of COVID-19. Optimal control dynamical models with time-dependent functions are very powerful mathematical modeling tools to investigate the transmission of infectious diseases. In this study, we have introduced and studied a new mathematical model for COVID-19 disease using personal protection, hospitalization and treatment of infectious individuals with early diagnosis, hospitalization and treatment of infectious individuals with delayed diagnosis and spraying of the environment as time-dependent control functions. This new non-autonomous deterministic epidemic model for the 2019 coronavirus disease is an extension of a recently constructed and analyzed data-driven non-optimal control model. We investigated three control strategies for our model problem. From the numerical illustrations of the various control strategies, we realized that the third strategy, which captures all the four time-dependent control functions, yields better results. © 2022 the author(s).

Binding free energy predictions in host-guest systems using Autodock4. A retrospective analysis on SAMPL6, SAMPL7 and SAMPL8 challenges.

We systematically tested the Autodock4 docking program for absolute binding free energy predictions using the host-guest systems from the recent SAMPL6, SAMPL7 and SAMPL8 challenges. We found that Autodock4 behaves surprisingly well, outperforming in many instances expensive molecular dynamics or quantum chemistry techniques, with an extremely favorable benefit-cost ratio. Some interesting features of Autodock4 predictions are revealed, yielding valuable hints on the overall reliability of docking screening campaigns in drug discovery projects.

Optimal control for COVID-19 pandemic with quarantine and antiviral therapy.

In the absence of a proper cure for the disease, the recent pandemic caused by COVID-19 has been focused on isolation strategies and government measures to control the disease, such as lockdown, media coverage, and improve public hygiene. Mathematical models can help when these intervention mechanisms find some optimal strategies for controlling the spread of such diseases. We propose a set of nonlinear dynamic systems with optimal strategy including practical measures to limit the spread of the virus and to diagnose and isolate infected people while maintaining consciousness for citizens. We have used Pontryagin's maximum principle and solved our system by the finite difference method. In the end, several numerical simulations have been executed to verify the proposed model using Matlab. Also, we pursued the resilience of the parameters of control of the nonlinear dynamic systems, so that we can easily handle the pandemic situation.

The Molecular Theory of Liquid Nanodroplets Energetics in Aerosols.

Studies of the coronavirus SARS-CoV-2 spread mechanisms indicate that the main mechanism is associated with the spread in the atmosphere of micro- and nanodroplets of liquid with an active agent. However, the molecular theory of aerosols of microdroplets in gases remains poorly developed. In this work, the energy properties of aerosol nanodroplets of simple liquids suspended in a gas were studied within the framework of molecular theory. The three components of the effective aerosol Hamiltonian were investigated: (1) the interaction energy of an individual atom with a liquid nanodroplet; (2) the surface energy of liquid nanodroplet; and (3) the interaction energy of two liquid nanodroplets. The size dependence of all contributions was investigated. The pairwise interparticle interactions and pairwise interparticle correlations were accounted for to study the nanodroplet properties using the Fowler approximation. In this paper, the problem of the adhesion energy calculation of a molecular complex and a liquid nanodroplet is discussed. The derived effective Hamiltonian is generic and can be used for the cases of multicomponent nano-aerosols and to account for particle size distributions.

Optimal surveillance mitigation of COVID'19 disease outbreak: Fractional order optimal control of compartment model.

In present time, the whole world is in the phase of war against the deadly pandemic COVID'19 and working on different interventions in this regard. Variety of strategies are taken into account from ground level to the state to reduce the transmission rate. For this purpose, the epidemiologists are also augmenting their contribution in structuring such models that could depict a scheme to diminish the basic reproduction number. These tactics also include the awareness campaigns initiated by the stakeholders through digital, print media and etc. Analyzing the cost and profit effectiveness of these tactics, we design an optimal control dynamical model to study the proficiency of each strategy in reducing the virulence of COVID'19. The aim is to illustrate the memory effect on the dynamics of COVID'19 with and without prevention measures through fractional calculus. Therefore, the structure of the model is in line with generalized proportional fractional derivative to assess the effects at each chronological change. Awareness about using medical mask, social distancing, frequent use of sanitizer or cleaning hand and supportive care during treatment are the strategies followed worldwide in this fight. Taking these into consideration, the optimal objective function proposed for the surveillance mitigation of COVID'19, is contemplated as the cost function. The effect analysis is supported through graphs and tabulated values. In addition, sensitivity inspection of basic reproduction number is also carried out with respect to different values of fractional index and cost function. Ultimately, social distancing and supportive care of infected are found to be significant in decreasing the basic reproduction number more rapidly.

Hamiltonian structure of compartmental epidemiological models.

Any epidemiological compartmental model with constant population is shown to be a Hamiltonian dynamical system in which the total population plays the role of the Hamiltonian function. Moreover, some particular cases within this large class of models are shown to be bi-Hamiltonian. New interacting compartmental models among different populations, which are endowed with a Hamiltonian structure, are introduced. The Poisson structures underlying the Hamiltonian description of all these dynamical systems are explicitly presented, and their associated Casimir functions are shown to provide an efficient tool in order to find exact analytical solutions for epidemiological models, such as the ones describing the dynamics of the COVID-19 pandemic.