A cell growth model revisited

In this paper a stochastic model for the simultaneous growth and division of a cell-population cohort structured by size is formulated. This probabilistic approach gives straightforward proof of the existence of the steady-size distribution and a simple derivation of the functional-differential equation for it. The latter one is the celebrated pantograph equation (of advanced type). This firmly establishes the existence of the steady-size distribution and gives a form for it in terms of a sequence of probability distribution functions. Also it shows that the pantograph equation is a key equation for other situations where there is a distinct stochastic framework

A model for phenotype change in a stochastic framework

some species, an inducible secondary phenotype will develop some time after the environmental change that evokes it. Nishimura (2006) [4] showed how an individual organism should optimize the time it takes to respond to an environmental change ("waiting time''). If the optimal waiting time is considered to act over the population, there are implications for the expected value of the mean fitness in that population. A stochastic predator-prey model is proposed in which the prey have a fixed initial energy budget. Fitness is the product of survival probability and the energy remaining for non-defensive purposes. The model is placed in the stochastic domain by assuming that the waiting time in the population is a normally distributed random variable because of biological variance inherent in mounting the response. It is found that the value of the mean waiting time that maximises fitness depends linearly on the variance of the waiting time

Optimal nutritional intake for fetal growth

View online at publisher's website: http://www.aimsciences.org/journals/displayArticles.jsp?paperID=6249The regular nutritional intake of an expectant mother clearly affects the weight development of the fetus. Assuming the growth of the fetus follows a deterministic growth law, like a logistic equation, albeit dependent on the nutritional intake, the ideal solution is usually determined by the birth-weight being pre-assigned, for example, as a percentage of the mother's average weight. This problem can then be specified as an optimal control problem with the daily intake as the control, which appears in a Michaelis-Menten relationship, for which there are well-developed procedures to follow. The best solution is determined by requiring minimum total intake under which the preassigned birth weight is reached. The algorithm has been generalized to the case where the fetal weight depends in a detailed way on the cumulative intake, suitably discounted according to the history. The optimality system is derived and then solved numerically using an iterative method for the specific values of parameter. The procedure is generic and can be adapted to any growth law and any parameterisation obtained by the detailed physiology

A prenylated dsRNA sensor protects against severe COVID-19

Inherited genetic factors can influence the severity of COVID-19, but the molecular explanation underpinning a genetic association is often unclear. Intracellular antiviral defenses can inhibit the replication of viruses and reduce disease severity. To better understand the antiviral defenses relevant to COVID-19, we used interferon-stimulated gene (ISG) expression screening to reveal that OAS1, through RNase L, potently inhibits SARS-CoV-2. We show that a common splice-acceptor SNP (Rs10774671) governs whether people express prenylated OAS1 isoforms that are membrane-associated and sense specific regions of SARS-CoV-2 RNAs, or only express cytosolic, nonprenylated OAS1 that does not efficiently detect SARS-CoV-2. Importantly, in hospitalized patients, expression of prenylated OAS1 was associated with protection from severe COVID-19, suggesting this antiviral defense is a major component of a protective antiviral response

Lyapunov functions and global stability for SIR, SIRS, and SIS epidemiological models

Lyapunov functions for classical SIR, SIRS, and SIS epidemiological models are introduced. Global stability of the endemic equilibrium states of the models is thereby established

Equations of Heat Conduction with Slow Combustion

A study is made of the equations of heat conduction with slow combustion. A mathematical model is established from an interpretation of the physical model, with a few simplifying assumptions. This gives rise to a coupled pair of partial differential equations which are the direct concern of this thesis, the dependent variables being the temperature and reactant concentration as functions of position and time. The model is shown to possess a unique solution for which some properties, such as Lipschitz conditions etc., are established. An investigation into the use of a comparison theorem is given, in which it is shown that no direct comparison theorem is possible for this and related systems. However, it is also shown that it is possible to obtain upper and lower estimates by appealing to the physical model. A discussion of the boundary layer is given and this is followed by a detailed discussion of stability. The latter has been one of the main concerns of earlier authors on this system. Their use of a space-averaging process to establish a criterion for stability is also discussed. Probably one of the most interesting features of this system is the subclass of problems for which the reactant is exhausted in a finite time. These hare been named the "cut-off" problems and they can be likened to the free boundary problems in fluid dynamics. A discussion of the cut-off problem is given with particular examples chosen to illustrate the main features. This thesis, contains no material which has been accepted for the award of any other degree or diploma in any University and to the best of my knowledge and belief, the thesis contains no material previously published or written by another person, except where due reference is made in the text of the thesis

Equations of Heat Conduction with Slow Combustion

A study is made of the equations of heat conduction with slow combustion. A mathematical model is established from an interpretation of the physical model, with a few simplifying assumptions. This gives rise to a coupled pair of partial differential equations which are the direct concern of this thesis, the dependent variables being the temperature and reactant concentration as functions of position and time. The model is shown to possess a unique solution for which some properties, such as Lipschitz conditions etc., are established. An investigation into the use of a comparison theorem is given, in which it is shown that no direct comparison theorem is possible for this and related systems. However, it is also shown that it is possible to obtain upper and lower estimates by appealing to the physical model. A discussion of the boundary layer is given and this is followed by a detailed discussion of stability. The latter has been one of the main concerns of earlier authors on this system. Their use of a space-averaging process to establish a criterion for stability is also discussed. Probably one of the most interesting features of this system is the subclass of problems for which the reactant is exhausted in a finite time. These hare been named the "cut-off" problems and they can be likened to the free boundary problems in fluid dynamics. A discussion of the cut-off problem is given with particular examples chosen to illustrate the main features. This thesis, contains no material which has been accepted for the award of any other degree or diploma in any University and to the best of my knowledge and belief, the thesis contains no material previously published or written by another person, except where due reference is made in the text of the thesis

Equations of Heat Conduction with Slow Combustion

A study is made of the equations of heat conduction with slow combustion. A mathematical model is established from an interpretation of the physical model, with a few simplifying assumptions. This gives rise to a coupled pair of partial differential equations which are the direct concern of this thesis, the dependent variables being the temperature and reactant concentration as functions of position and time. The model is shown to possess a unique solution for which some properties, such as Lipschitz conditions etc., are established. An investigation into the use of a comparison theorem is given, in which it is shown that no direct comparison theorem is possible for this and related systems. However, it is also shown that it is possible to obtain upper and lower estimates by appealing to the physical model. A discussion of the boundary layer is given and this is followed by a detailed discussion of stability. The latter has been one of the main concerns of earlier authors on this system. Their use of a space-averaging process to establish a criterion for stability is also discussed. Probably one of the most interesting features of this system is the subclass of problems for which the reactant is exhausted in a finite time. These hare been named the "cut-off" problems and they can be likened to the free boundary problems in fluid dynamics. A discussion of the cut-off problem is given with particular examples chosen to illustrate the main features. This thesis, contains no material which has been accepted for the award of any other degree or diploma in any University and to the best of my knowledge and belief, the thesis contains no material previously published or written by another person, except where due reference is made in the text of the thesis