I present a new dose-survival equation for fitting clonogenic assay data collected for irradiated cells, one motivated by the hypothesis that all cellular activities can be partitioned into two states (“state R” and “state Q”) which differ in their sensitivity to low-LET radiation. The LQ model can be derived from it by taking a Taylor expansion. The empirical observation that rapidly proliferating cancer cells have a straighter dose-survival relationship, while slowly proliferating cancer cells and normal cells have a curvier one featuring a shoulder region, is explained in terms of state R and state Q. The new equation (1) provides a convention for classifying cells as radioresistant, (2) provides a means of reducing, or possibly eliminating, cell cycle phase as a variable in treatment outcome, and (3) may enable standardization of the results reported for clonogenic assays. Finally, a novel hypothesis is offered for the “oxygen enhancement ratio” phenomenon.

In this work, we investigate the existence of multistationarity for a triple-site mixed phosphorylation network, where the phosphorylation part contains distributive and processive components, while the dephosphorylation part is purely distributive. We obtain a simple inequality which defines a region in parameter space such that the parametric ordinary differential equations (ODE) system modeling the mixed network is multistationary, i.e., it has multiple positive steady states. We obtain a sufficient condition for uniqueness of the steady state in the form of parametric inequalities. Lastly, we show that the emergence of multistationarity is enabled by the catalytic constants regardless of the position of the processive part in the triple-site mixed mechanism phosphorylation network.

This work constructs, analyzes and simulates the SIR-IH model, a modified SIR epidemiological model for the spread of a disease, in which the infection rate and hospitalization ratio are system variables. The motivation, in part, of making the infection rate a state variable comes from the observations that the infectivity of a disease, such as COVID-19, has been changing with the evolution of the disease, and not necessarily by the appearance of new variants. Moreover, it may change in time if more than one variant are present. The addition of a hospitalization rate is done to make the model more applied for those who need to make decisions on the preparedness of the health system, in particular the hospitals, in case of a pandemic. The model consists of a coupled system of differential equations, and its analysis shows the existence, positivity and boundedness of the solutions. Then, computer simulations depict some typical or interesting dynamic behaviors, and the way the system approaches the steady states.

Stability analysis of nonlinear age-of-infection and -immunity structured SVLIAR-type model of susceptible, vaccinated, latent, COVID-19 infected, asymptomatic and recovered sub-classes of population dynamics is carried out in this paper. The SVLIAR model uses five age variables - age of vaccine immunity of vaccinated individuals, age of virus infection in organism during incubation period of latent individuals, “age” of infectious disease treatment of infected individuals, age of asymptomatic infectious dis-ease of asymptomatic individuals, “age” of immunity of organism after recovering of recovered individuals. Individuals can move from one subclass to another when these age variables take some fixed values, that is the processes in sub-classes are adjusted and synchronized by age variables. The conditions for the existence of disease-free and unique endemic equilibria and their local asymptotic stability were obtained. The local asymptotic stability/instability of endemic equilibrium of SVLIAR model is defined by criterion, which relates the demographic characteristics of population, infection disease characteristics (disease-induced death rate, death rate induced by the complications after disease), characteristics of vaccination (fraction of fully vaccinated susceptibles per unit of time, vaccination efficacy) and characteristics of age variables (their maximum values) of sub-classes. These theoretical results help understand better the conditions of transmission dynamics of the COVID-19 induced disease.

This study investigates the impact of melting/binding rates (referred to hereafter as the parameters) over the polymers and monomers on the dynamics of carbon-monoxide-mediated sickle cell hemoglobin (HbS) de-polymerization. Two approaches, namely the traditional sensitivity analysis (TSA) and the multi-parameter sensitivity analysis (MPSA), have been developed and applied to the mathematical model system to quantify the sensitivities of polymers and monomers to the parameters. The Runge-Kutta method and the Monte-Carlo simulation are employed for the implementation of the sensitivity analyses. The TSA utilizes the traditional sensitivity functions (TSFs). The MPSA enumerates the overall effect of the model input parameters on the output by perturbing the model input parameters simultaneously within large ranges. All four concentrations (namely, de-oxy HbS monomers, CO-bound HbS monomers, de-oxy Hbs polymer and CO-bound HbS polymer) as model outputs, and all four binding/melting rates (namely, the CO binding and melting rates for polymers and monomers) as input parameters are considered in this study. The sensitivity results suggest that TSA and MPSA are essentially consistent.

We investigate a model of the early stage of the COVID-19 epidemic comprising undetected infected individuals as well as behavioural change towards the use of self-protection measures. The model is fitted to China data reported between 22 January and 29 June 2020. Using fitting results, we then consider model responses to varying screening intensities.

This paper presents the current situation and how to minimize its effect in India through a mathematical model of infectious Coronavirus disease (COVID-19). This model consists of six compartments to population classes consisting of susceptible, exposed, home quarantined, government quarantined, infected individuals in treatment, and recovered class. The basic reproduction number is calculated, and the stabilities of the proposed model at the disease-free equilibrium and endemic equilibrium are observed. The next crucial treatment control of the Covid-19 epidemic model is presented in India's situation. An objective function is considered by incorporating the optimal infected individuals and the cost of necessary treatment. Finally, optimal control is achieved that minimizes our anticipated objective function. Numerical observations are presented utilizing MATLAB software to demonstrate the consistency of present-day representation from a realistic standpoint.

We consider a mathematical model of human immunodeficiency virus (HIV) infection dynamics of T lymphocyte (T cell), infected T cell, and viral populations under reverse transcriptase inhibitor (RTI) andprotease inhibitor (PI) treatment. Existence, uniqueness, and characterization of optimal treatment profiles which minimize total amount of drug used, viral, and infected T cell populations, while maximizing levels of T cells are determined analytically. Numerical optimal control experiments are also performed to illustrate how burst rate of infected T cells and shedding rate of virions impact optimal treatment profiles. Finally, a sensitivity analysis is performed to detect how model input parameters contribute to output variance.

The paper considers the sigmoid function definedthrough the hyper-log-logistic model introduced by Blumberg. We study the Hausdorff distance of this sigmoid to the Heaviside function, which characterises the shape of switching from 0 to 1. Estimates of the Hausdorff distance in terms of the intrinsic growth rate are derived. We construct a family of recurrence generated sigmoidal functions based on the hyper-log-logistic function. Numerical illustrations are provided.

Effective methods of fluid transport vary across scale. A commonly used dimensionless number for quantifying the effective scale of fluid transport is the frequency based Reynolds number, Re, which gives the ratio of inertial to viscous forces in a fluid flow. What may work well for one Re regime may not produce significant flows for another. These differences in scale have implications for many organisms, ranging from the mechanics of how organisms move through their fluid environment to how hearts pump at various stages in development. Some organisms, such as soft pulsing corals, actively contract their tentacles to generate mixing currents that enhance photosynthesis. Their unique morphology and the intermediate Re regime at which they function, where both viscous and inertial forces are significant, make them a unique model organism for understanding fluid mixing. In this paper, 3D fluid-structure interaction simulations of a pulsing soft coral are used to quantify fluid transport and describe fluid mixing across a wide range of Re. The results show that net transport is negligible for Re<10, and continuous upward flow is produced for Re≥10. Sustained net transport is necessary to bring in new fluid for sampling and to remove waste. As the Re is increased well above 10, the slow region of mixing necessary for gas exchange between the tentacles is reduced. Since corals live at Re between about 8 and 36, the flows they produce are defined by sustained net transport of fluid away from the coral in a continuous upward jet and a slow region of mixing between the tentacles necessary for gas exchange.Supplementary material:1.В Movie of velocity and vorticity of flow field around pulsing coral at Re = 0.52.В Movie of velocity and vorticity of flow field around pulsing coral at Re = 103.В Movie of velocity and vorticity of flow field around pulsing coral at Re = 80В