Related papers: Mathematical Analysis and Dynamic Active Subspaces…
We develop a general dynamical model as a framework for possible causal interpretation. We first state a criterion of local independence in terms of measurability of processes involved in the Doob-Meyer decomposition of stochastic…
Most engineering models contain several parameters, and the map from input parameters to model output can be viewed as a multivariate function. An active subspace is a low-dimensional subspace of the space of inputs that explains the…
A simple deterministic model is proposed to represent the basic aspects concerning the effects of different antiretroviral treatment schedules on HIV incidence and prevalence of affected populations. The model mimics current treatment…
Causal effect estimation for dynamic treatment regimes (DTRs) contributes to sequential decision making. However, censoring and time-dependent confounding under DTRs are challenging as the amount of observational data declines over time due…
This paper considers the problem of modeling epidemic outbreaks in different regions with a common model, that uses additional information about these regions to adjust its parameters and relieve us of mundanity of data collecting, and…
An increasing amount of geo-referenced mobile phone data enables the identification of behavioral patterns, habits and movements of people. With this data, we can extract the knowledge potentially useful for many applications including the…
This paper introduces a novel hybrid model combining Partial Differential Equations (PDEs) and Ordinary Differential Equations (ODEs) to simulate infectious disease dynamics across geographic regions. By leveraging the spatial detail of…
Highly active antiretroviral therapy (HAART) has proved efficient in increasing CD4 counts in many randomized clinical trials. Because randomized trials have some limitations (e.g., short duration, highly selected subjects), it is…
We introduce a mathematical description of the impact of sociality in the spread of infectious diseases by integrating an epidemiological dynamics with a kinetic modeling of population-based contacts. The kinetic description leads to study…
Understanding dynamics of an outbreak like that of COVID-19 is important in designing effective control measures. This study aims to develop an agent based model that compares changes in infection progression by manipulating different…
Networks of contacts capable of spreading infectious diseases are often observed to be highly heterogeneous, with the majority of individuals having fewer contacts than the mean, and a significant minority having relatively very many…
We analyze damage propagation modeling of turbo-engines in a data-driven approach. We investigate subspace tracking assuming a low dimensional manifold structure and a static behavior during the healthy state of the machines. Our damage…
The integration of longitudinal measurements and survival time in statistical modeling offers a powerful framework for capturing the interplay between these two essential outcomes, particularly when they exhibit associations. However, in…
Intensive longitudinal data (ILD) collected in mobile health (mHealth) studies contain rich information on multiple outcomes measured frequently over time that have the potential to capture short-term and long-term dynamics. Motivated by an…
In this survey we report some recent results in the mathematical modeling of epidemic phenomena through the use of kinetic equations. We initially consider models of interaction between agents in which social characteristics play a key role…
Human immunodeficiency virus (HIV-1 or simply HIV) induces a persistent infection, which in the absence of treatment leads to AIDS and death in almost all infected individuals. HIV infection elicits a vigorous immune response starting about…
In this paper, the mathematical model of HIV infection for CD8+ T-cells is illustrated. The homotopy analysis method and the Laplace transformations are combined for solving this model. Also, the convergence theorem is proved to demonstrate…
Modeling long-range epidemic spreading in a random environment, we consider a quenched disordered, $d$-dimensional contact process with infection rates decaying with the distance as $1/r^{d+\sigma}$. We study the dynamical behavior of the…
We revisit the SICA (Susceptible-Infectious-Chronic-AIDS) mathematical model for transmission dynamics of the human immunodeficiency virus (HIV) with varying population size in a homogeneously mixing population. We consider SICA models…
We investigate the celebrated mathematical SICA model but using fractional differential equations in order to better describe the dynamics of HIV-AIDS infection. The infection process is modelled by a general functional response and the…