Related papers: Stochastic modeling using Adomian method and fract…
Partial differential equation (PDE) models for infectious diseases, while less common than their ordinary differential equation (ODE) counterparts, have found successful applications for many years. Such models are typically of…
Infectious diseases are among the most prominent threats to mankind. When preventive health care cannot be provided, a viable means of disease control is the isolation of individuals, who may be infected. To study the impact of isolation,…
This review maps developments in stochastic modeling, highlighting non-standard approaches and their applications to biology and epidemiology. It brings together four strands: (1) core models for systems that evolve with randomness; (2)…
Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations…
We consider an evolution equation with the regularized fractional derivative of an order $\alpha \in (0,1)$ with respect to the time variable, and a uniformly elliptic operator with variable coefficients acting in the spatial variables.…
An epidemic model with distributed time delay is derived to describe the dynamics of infectious diseases with varying immunity. It is shown that solutions are always positive, and the model has at most two steady states: disease-free and…
We develop a mathematical model for adsorption based on averaging the flow around, and diffusion inside, adsorbent particles in a column. The model involves three coupled partial differential equations for the contaminant concentration both…
In this paper, we are interested in the study of a problem with fractional derivatives having boundary conditions of integral types. The problem represents a Caputo type advection-diffusion equation where the fractional order derivative…
We introduce a model for stochastic transport on a one-dimensional substrate with particles assuming different conformations during their stepping cycles. These conformations correspond to different footprints on the substrate: in order to…
This paper concerns a time fractional version of the conventional Lengyel--Epstein CIMA reaction model. We define the invariant regions of the system and establish sufficient conditions for the unique equilibrium's local and global…
This paper examines the temporal evolution of a two-stage stochastic model for spherical random fields. The model uses a time-fractional stochastic hyperbolic diffusion equation, which describes the evolution of spherical random fields on…
We demonstrate how direct simulation of stochastic, individual-based models can be combined with continuum numerical analysis techniques to study the dynamics of evolving diseases. % Sidestepping the necessity of obtaining explicit…
We consider the design and analysis of multi-factor experiments using fractional factorial and incomplete designs within the potential outcome framework. These designs are particularly useful when limited resources make running a full…
We present a hybrid model of a biological filter, a genetic circuit which removes fast fluctuations in the cell's internal representation of the extra cellular environment. The model takes the classic feed-forward loop (FFL) motif and…
Advances in nanotechnology have allowed scientists to study biological processes on an unprecedented nanoscale molecule-by-molecule basis, opening the door to addressing many important biological problems. A phenomenon observed in recent…
We present a method to infer the arbitrary space-dependent drift and diffusion of a nonlinear stochastic model driven by multiplicative fractional Gaussian noise from a single trajectory. Our method, fractional Onsager-Machlup optimisation…
Fractional Brownian motion (fBm) features both randomness and strong scale-free correlations, challenging generative models to reproduce the intrinsic memory characterizing the underlying stochastic process. Here we examine a zoo of…
We focus on variational inference in dynamical systems where the discrete time transition function (or evolution rule) is modelled by a Gaussian process. The dominant approach so far has been to use a factorised posterior distribution,…
Starting from a particle model we derive a macroscopic aggregation-diffusion equation for the evolution of slime mold under the assumption of propagation of chaos in the large particle limit. We analyze properties of the macroscopic model…
In this paper we study a nonlinear reaction-diffusion system which models an infectious disease caused by bacteria such as those for cholera. One of the significant features in this model is that a certain portion of the recovered human…