Related papers: Solution of Fuzzy Growth and Decay Model
The rate at which individual bacterial cells grow depends on the concentrations of cellular components such as ribosomes and proteins. These concentrations continuously fluctuate over time and are inherited from mother to daughter cells,…
Single-cell experiments revealed substantial variability in generation times, growth rates but also in birth and division sizes between genetically identical cells. Understanding how these fluctuations determine the fitness of the…
We investigate the structure and stability of the steady states for a bacterial colony model with density-suppressed motility. We treat the growth rate of bacteria as a bifurcation parameter to explore the local and global structure of the…
We consider a discrete model of population with interaction where the birth and death rates are non linear functions of the population size. After proceeding to renormalization of the model parameters, we obtain in the limit of large…
Many mathematical models utilize limit processes. Continuous functions and the calculus, differential equations and topology, all are based on limits and continuity. However, when we perform measurements and computations, we can achieve…
We present an explicit solution to a classic model of cell-population growth introduced by Luria and Delbrueck 70 years ago to study the emergence of mutations in bacterial populations. In this model a wild-type population is assumed to…
We show, in this report, how a population balance model differential equation describing batch crystal growth from solution can be solved in closed form for the case of diffusion limited growth with and without modeling the effects of…
Cell division times in microbial populations display significant fluctuations, that impact the population growth rate in a non-trivial way. If fluctuations are uncorrelated among different cells, the population growth rate is predicted by…
Modelling, analysing and inferring triggering mechanisms in population reproduction is fundamental in many biological applications. It is also an active and growing research domain in mathematical biology. In this chapter, we review the…
In this paper, experimental data is presented and a simple model is developed for the time evolution of a F-amp \textit{E. Coli} culture population. In general, the bacteria life cycle as revealed by monitoring a culture's population…
In this study, we consider a linear differential equation with fuzzy boundary values. We express the solution of the problem in terms of a fuzzy set of crisp real functions. Each real function from the solution set satisfies differential…
We present a model for a biological reactor in which bacteria tend to aggregate in flocs, as encountered in wastewater treatment plants. The influence of this flocculation on the growth dynamics of the bacteria is studied. We argue that a…
We study the interplay of population growth and evolutionary dynamics using a stochastic model based on birth and death events. In contrast to the common assumption of an independent population size, evolution can be strongly affected by…
Epidemic models play a crucial role in population dynamics, offering valuable insights into disease transmission while aiding in epidemic prediction and control. In this paper, we analyze the mathematical model of the time-fractional Zika…
The controversy concerning both the definition of the species and methods for inferring the boundaries and numbers of species has occupied biologists for centuries, and the debate itself has become known as the species problem. The modern…
We formulate dynamical rate equations for physical processes driven by a combination of diffusive growth, size fragmentation and fragment coagulation. Initially, we consider processes where coagulation is absent. In this case we solve the…
We propose a model of chemostat where the bacterial population is individually-based, each bacterium is explicitly represented and has a mass evolving continuously over time. The substrate concentration is represented as a conventional…
Modeling human ratings data subject to raters' decision uncertainty is an attractive problem in applied statistics. In view of the complex interplay between emotion and decision making in rating processes, final raters' choices seldom…
We show that a simple nonlinear differential equation (originally studied in the physics of disordered systems) is able to mathematically describe the global population growth over the past 12000 years. Different regimes of population…
We study the mathematical properties of a model of cell division structured by two variables, the size and the size increment, in the case of a linear growth rate and a self-similar fragmentation kernel. We first show that one can construct…