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We analyze the Bass and SI models for the spreading of innovations and epidemics, respectively, on homogeneous complete networks, circular networks, and heterogeneous complete networks with two homogeneous groups. We allow the network…
This study presents a mathematical model for optimal vaccination strategies in interconnected metropolitan areas, considering commuting patterns. It is a compartmental model with a vaccination rate for each city, acting as a control…
In this paper we investigate a susceptible-infected-susceptible (SIS) epidemic model describing data dissemination in opportunistic networks with heterogeneous setting of transmission parameters. We obtained the estimation of the final…
This research introduces a new approach utilizing optimal control theory (OCT) to assess the Social Optimum (SO) of a vaccination game, navigating the intricate considerations of cost, availability, and distribution policies. By integrating…
The waning of immunity after recovery or vaccination is a major factor accounting for the severity and prolonged duration of an array of epidemics, ranging from COVID-19 to diphtheria and pertussis. To study the effectiveness of different…
Heterogeneity is an important property of any population experiencing a disease. Here we apply general methods of the theory of heterogeneous populations to the simplest mathematical models in epidemiology. In particular, an SIR…
In this paper, we investigate game-theoretic strategies for containing spreading processes on large-scale networks. Specifically, we consider the class of networked susceptible-infected-susceptible (SIS) epidemics where a large population…
Consider a matching problem on a graph where disjoint sets of vertices are privately owned by self-interested agents. An edge between a pair of vertices indicates compatibility and allows the vertices to match. We seek a mechanism to…
We analyze an optimal control version of a simple SIRS epidemiology model. The policy maker can adopt policies to diminish the contact rate between infected and susceptible individuals, at a specific economic cost. The arrival of a vaccine…
We consider the bi-objective problem of allocating doses of a (perfect) vaccine to an infinite-dimensional metapopulation in order to minimize simultaneously the vaccination cost and the effective reproduction number $R_e$, which is defined…
We consider the problem of the optimal allocation of vaccination and protection measures for the Susceptible-Infected-Recovered-Infected (SIRI) epidemiological model, which generalizes the classical Susceptible-Infected-Recovered (SIR) and…
Developing robust, quantitative methods to optimize resource allocations in response to epidemics has the potential to save lives and minimize health care costs. In this paper, we develop and apply a computationally efficient algorithm that…
This paper investigates optimal vaccination strategies in a metapopulation epidemic model. We consider a linear cost to better capture operational considerations, such as the total number of vaccines or hospitalizations, in contrast to the…
Optimal intervention design is formulated as a hybrid optimal control problem for multiphase homogeneous epidemiological systems. The system extends a foundational compartmental model through intermediate phases that incorporate…
In this work we study the stability properties of the equilibrium points of deterministic epidemic models with nonconstant population size. Models with nonconstant population have been studied in the past only in particular cases, two of…
Incorporating vaccination into mathematical models appears deceptively simple: models integrate vaccine-derived protections, such as reduced susceptibility to infection, using parameters informed by empirical estimates of vaccine efficacy…
This paper studies an optimal control problem for a class of SIR epidemic models, in scenarios in which the infected population is constrained to be lower than a critical threshold imposed by the ICU (intensive care unit) capacity. The…
There are often multiple diseases with cross immunity competing for vaccination resources. Here we investigate the optimal vaccination program in a two-layer Susceptible-Infected-Removed (SIR) model, where two diseases with cross immunity…
Compartmental equations are primary tools in disease spreading studies. Their predictions are accurate for large populations but disagree with empirical and simulated data for finite populations, where uncertainties become a relevant…
Mixture models provide a flexible representation of heterogeneity in a finite number of latent classes. From the Bayesian point of view, Markov Chain Monte Carlo methods provide a way to draw inferences from these models. In particular,…