Related papers: Stochastic and parameter analysis for an integrati…
Demographic noise has profound effects on evolutionary and population dynamics, as well as on chemical reaction systems and models of epidemiology. Such noise is intrinsic and due to the discreteness of the dynamics in finite populations.…
We study an excitable active rotator with slowly adapting nonlinear feedback and noise. Depending on the adaptation and the noise level, this system may display noise-induced spiking, noise-perturbed oscillations, or stochastic busting. We…
The stochastic mutual repressor model is analysed using perturbation methods. This simple model of a gene circuit consists of two genes and three promotor states. Either of the two protein products can dimerize, forming a repressor molecule…
In this paper a stochastic reaction diffusion system is considered, which models the spread of a finite population reacting with a non-renewable resource in the presence of individual based noise. A two-parameter phase diagram is…
In conventional radiotherapy, the probability of controlling tumor growth is quantified using Tumor Control Probability (TCP) models. Instead, the probability of experiencing a side effect after the irradiation of healthy tissues and organs…
We consider the effects of parameter uncertainty on the optimal radiation schedule in the context of the linear-quadratic model. Our interest arises from the observation that if inter-patient variations in OAR and tumor sensitivities to…
The interplay between tumor cells and macrophages plays a central regulatory role in cancer progression. In this study, we developed a mathematical model that incorporates tumor cells, M1 type macrophages, M2 type macrophages and an M3 type…
The intrinsic stochasticity of gene expression can lead to large variability of protein levels across a population of cells. Variability (or noise) in protein distributions can be modulated by cellular mechanisms of gene regulation; in…
This paper investigates the stochastic permanence of malaria and the existence of a stationary distribution for the stochastic process describing the disease dynamics over sufficiently longtime. The malaria system is highly random with…
We analyze the effect of the simultaneous presence of correlated additive and multiplicative noises on the stochastic resonance response of a modulated bistable system. We find that when the correlation parameter is also modulated, the…
A stochastic model is here introduced to investigate the molecular mechanisms which trigger the perception of pain. The action of analgesic drug compounds is discussed in a dynamical context, where the competition with inactive species is…
Theoretical and computational tools that can be used in the clinic to predict neoplastic progression and propose individualized optimal treatment strategies to control cancer growth is desired. To develop such a predictive model, one must…
In this article we provide homotopy solutions of a cancer nonlinear model describing the dynamics of tumor cells in interaction with healthy and effector immune cells. We apply a semi-analytic technique for solving strongly nonlinear…
The interplay of seasonality, the system's nonlinearities and intrinsic stochasticity is studied for a seasonally forced susceptible-exposed-infective-recovered stochastic model. The model is explored in the parameter region that…
Intrinsic noise, the stochastic cell-to-cell fluctuations in mRNAs and proteins, has been observed and proved to play important roles in cellular systems. Due to the recent development in single-cell-level measurement technology, the…
Understanding cancer cell differentiation is essential for advancing its detection, diagnosis, and treatment. Mathematical models significantly contribute to this by providing a theoretical framework to understand the complex interactions…
Modeling stochasticity in gene regulatory networks is an important and complex problem in molecular systems biology. To elucidate intrinsic noise, several modeling strategies such as the Gillespie algorithm have been used successfully. This…
Stochastic transitions between discrete microscopic states play an important role in many physical and biological systems. Often, these transitions lead to fluctuations on a macroscopic scale. A classic example from neuroscience is the…
In this paper, we investigate how stochastic reaction processes are affected by external perturbations. We describe an extension of the deterministic metabolic control analysis (MCA) to the stochastic regime. We introduce stochastic…
In this paper, we studied phase-space analysis of a certain mathematical model of tumor growth with an immune responses and chemotherapy therapy. Mathematical modelling of this process is viewed as a potentially powerful tool in the…