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This is an expository article on the score-based diffusion models, with a particular focus on the formulation via stochastic differential equations (SDE). After a gentle introduction, we discuss the two pillars in the diffusion modeling --…
Stochastic differential equations (SDEs) using jump-diffusion processes describe many natural phenomena at the microscopic level. Since they are commonly used to model economic and financial evolutions, the calibration and optimal control…
Dengue is a notifiable communicable disease in Sri Lanka since 1996. Dengue fever spread rapidly among people living in most of the districts of Sri Lanka. The present notification system of dengue communicable diseases which is enforced by…
Modeling spreading processes in complex random networks plays an essential role in understanding and prediction of many real phenomena like epidemics or rumor spreading. The dynamics of such systems may be represented algorithmically by…
Stochastic differential equations (SDEs) provide a flexible framework for modeling temporal dynamics in partially observed systems. A central task is to calibrate such models from data, which requires inferring latent trajectories and…
Irregular sampling intervals and missing values in real-world time series data present challenges for conventional methods that assume consistent intervals and complete data. Neural Ordinary Differential Equations (Neural ODEs) offer an…
Dynamic properties of spreading infection through a heterogeneous population are studied numerically and analytically using a dynamic variant of Watts and Strogatz Small World Network-based stochastic Susceptible-Exposed-Infectious-Removed…
There is great interest in ecology to understand how wild animals are affected by anthropogenic disturbances, such as sounds. Behavioural response studies are an important approach to quantify the impact of naval activity on marine mammals.…
In this work, we explore modeling change points in time-series data using neural stochastic differential equations (neural SDEs). We propose a novel model formulation and training procedure based on the variational autoencoder (VAE)…
This work proposes stochastic partial differential equations (SPDEs) as a practical tool to replicate clustering effects of more detailed particle-based dynamics. Inspired by membrane-mediated receptor dynamics on cell surfaces, we…
The rapid worldwide spread of the severe acute respiratory syndrome (SARS) demonstrated the potential threat an infectious disease poses in a closely interconnected and interdependent world. Here we introduce a probabilistic model which…
We study a stochastic spatial epidemic model where the $N$ individuals carry two features: a position and an infection state, interact and move in $\R^d$. In this Markovian model, the evolution of the infection states are described with the…
In this article, we introduce a system of stochastic differential equations (SDEs) consisting of time-dependent covariates and consider both fixed and random effects set-ups. We also allow the functional part associated with the drift…
Standard epidemic models based on compartmental differential equations are investigated under continuous parameter change as external forcing. We show that seasonal modulation of the contact parameter superimposed a monotonic decay needs a…
We consider the problem of variational Bayesian inference in a latent variable model where a (possibly complex) observed stochastic process is governed by the solution of a latent stochastic differential equation (SDE). Motivated by the…
We describe a map-based model which reproduces many of the behaviors seen in partial differential equations (PDE's). Like PDE's, we show that this model can support an infinite number of stationary solutions, traveling solutions, breathing…
Dengue is a viral vector-borne infectious disease that affects many countries worldwide, infecting around 390 million people per year. The main outbreaks occur in subtropical and tropical countries. We study here the influence of climate on…
A multi-patch and multi-group modeling framework describing the dynamics of a class of diseases driven by the interactions between vectors and hosts structured by groups is formulated. Hosts' dispersal is modeled in terms of patch-residence…
Epidemiological models may give some basic guidelines for public health practitioners, allowing to analyze issues that can influence the strategies to prevent and fight a disease. To be used in decision-making, however, a mathematical model…
Stochastic differential equations (SDEs) are of utmost importance in various scientific and industrial areas. They are the natural description of dynamical processes whose precise equations of motion are either not known or too expensive to…