Related papers: Behavioral-feedback SIR epidemic model: analysis a…
In the framework of homogeneous susceptible-infected-recovered (SIR) models, we use a control theory approach to identify optimal pandemic mitigation strategies. We derive rather general conditions for reaching herd immunity while…
We study dynamics of a variant of the SIR the model, where we assume that individuals respond differently to dynamics of the epidemic. Their heterogeneous response is modeled by the Preisach hysteresis operator. The degree of heterogeneity…
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…
We propose and study a compartmental model for epidemiology with human behavioral effects. Specifically, our model incorporates governmental prevention measures aimed at lowering the disease infection rate, but we split the population into…
In this paper, we consider an optimal distributed control problem for a reaction-diffusion-based SIR epidemic model with human behavioral effects. We develop a model wherein non-pharmaceutical intervention methods are implemented, but a…
We study the problem of optimal control of the stochastic SIR model. Models of this type are used in mathematical epidemiology to capture the time evolution of highly infectious diseases such as COVID-19. Our approach relies on…
We propose two SIR models which incorporate sociological behavior of groups of individuals. It is these differences in behaviors which impose different infection rates on the individual susceptible populations, rather than biological…
To simplify mathematical models of disease spread, we often assume equal contact rates among hosts, but real-world scenarios differ. Network-based frameworks help capture these complexities and structural variations in actual systems. We…
This paper proposes a feedback design that effectively copes with uncertainties for reliable epidemic monitoring and control. There are several optimization-based methods to estimate the parameters of an epidemic model by utilizing past…
This article is devoted to the analysis of a particle system model for epidemics among a finite population with susceptible, infective and removed individuals (SIR). The infection mechanism depends on the relative distance between…
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 present a detailed set-based analysis of the well-known SIR and SEIR epidemic models subjected to hard caps on the proportion of infective individuals, and bounds on the allowable intervention strategies, such as social distancing,…
We introduce a policy model coupled with the susceptible-infected-recovered (SIR) epidemic model to study interactions between policy-making and the dynamics of epidemics. We consider both single-region policies, as well as game-theoretic…
The Susceptible-Infected-Recovered (SIR) model is the cornerstone of epidemiological models. However, this specification depends on two parameters only, which implies a lack of flexibility and the difficulty to replicate the volatile…
The SIR model is a three-compartment model of the time development of an epidemic. After normalizing the dependent variables, the model is a system of two non-linear differential equations for the susceptible proportion $S$ and the infected…
This paper considers a stochastic SIR (susceptible$\to$infective$\to$removed) epidemic model in which individuals may make infectious contacts in two ways, both within `households' (which for ease of exposition are assumed to have equal…
We present a data-driven optimal control approach which integrates the reported partial data with the epidemic dynamics for COVID-19. We use a basic Susceptible-Exposed-Infectious-Recovered (SEIR) model, the model parameters are…
This paper is concerned with the well-posedness and optimal control problem of a reaction-diffusion system for an epidemic Susceptible-Infected-Recovered-Susceptible (SIRS) mathematical model in which the dynamics develops in a spatially…
The Susceptible-Infectious-Recovered (SIR) equations and their extensions comprise a commonly utilized set of models for understanding and predicting the course of an epidemic. In practice, it is of substantial interest to estimate the…
Susceptibility governs the dynamics of contagion. The classical SIR model is one of the simplest compartmental models of contagion spread, assuming a single shared susceptibility level. However, variation in susceptibility over a population…