The coronavirus disease 2019 (COVID-19) pandemic is changing and impacting lives on a global scale. In this paper, we introduce a mean-field game model in controlling the propagation of epidemics on a spatial domain. The control variable, the spatial velocity, is first introduced for the classical disease models, such as the SIR model. For this proposed model, we provide fast numerical algorithms based on proximal primal-dual methods. Numerical experiments demonstrate that the proposed model illustrates how to separate infected patients in a spatial domain effectively.
We propose a novel framework to study viral spreading processes in metapopulation models. Large subpopulations (i.e., cities) are connected via metalinks (i.e., roads) according to a metagraph structure (i.e., the traffic infrastructure). The problem of containing the propagation of an epidemic outbreak in a metapopulation model by controlling the traffic between subpopulations is considered. Controlling the spread of an epidemic outbreak can be written as a spectral condition involving the eigenvalues of a matrix that depends on the network structure and the parameters of the model. Based on …
In this research, we develop a framework to analyze the interaction between the economy and the Covid-19 pandemic using an extension of SIR epidemic model. At the outset, we assume there are two health related investments including general medical expenditures and the other for a direct investment for controlling the pandemic. We incorporate the learning dynamics associated with the management of the virus into our model. Given that the labor force in a society depends on the state of the epidemic, we allow birth, death, and vaccination to occur in our model and assume labor force consists of …
We consider a multi-population epidemic model with one or more (almost) isolated communities and one mobile community. Each of the isolated communities has contact within itself and, in addition, contact with the outside world but only through the mobile community. The contact rate between the mobile community and the other communities is assumed to be controlled. We first derive a multidimensional ordinary differential equation (ODE) as a mean-field fluid approximation to the process of the number of infected nodes, after appropriate scaling. We show that the approximation becomes tight as th…
We consider the problem of controlling the propagation of an epidemic outbreak in an arbitrary contact network by distributing vaccination resources throughout the network. We analyze a networked version of the Susceptible-Infected-Susceptible (SIS) epidemic model when individuals in the network present different levels of susceptibility to the epidemic. In this context, controlling the spread of an epidemic outbreak can be written as a spectral condition involving the eigenvalues of a matrix that depends on the network structure and the parameters of the model. We study the problem of finding…
Testing is a crucial control mechanism for an epidemic outbreak because it enables the health authority to detect and isolate the infected cases, thereby limiting the disease transmission to susceptible people, when no effective treatment or vaccine is available. In this paper, an epidemic model that incorporates the testing rate as a control input is presented. The proposed model distinguishes between the undetected infected and the detected infected cases with the latter assumed to be isolated from the disease spreading process in the population. Two testing policies, effective during the on…
In this paper, we continue development of the new epidemiological model HIT, which is suitable for analyzing and predicting the propagation of COVID-19 epidemics. This is a discrete-time model allowing a reconstruction of the dynamics of asymptomatic virus holders using the available daily statistics on the number of new cases. We suggest to use a new indicator, the total infection rate, to distinguish the propagation and recession modes of the epidemic. We check our indicator on the available data for eleven different countries and for the whole world. Our reconstructions are very precise. In…
Motivated by the ongoing pandemic COVID-19, we propose a closed-loop framework that combines inference from testing data, learning the parameters of the dynamics and optimal resource allocation for controlling the spread of the susceptible-infected-recovered (SIR) epidemic on networks. Our framework incorporates several key factors present in testing data, such as the fact that high risk individuals are more likely to undergo testing. We then present two tractable optimization problems to evaluate the trade-off between controlling the growth-rate of the epidemic and the cost of non-pharmaceuti…
This paper investigates epidemic control behavioral synchronization for a class of complex networks resulting from spread of epidemic diseases via pinning feedback control strategy. Based on the quenched mean field theory, epidemic control synchronization models with inhibition of contact behavior is constructed, combining with the epidemic transmission system and the complex dynamical network carrying extra controllers. By the properties of convex functions and Gerschgorin theorem, the epidemic threshold of the model is obtained, and the global stability of disease-free equilibrium is analyze…
We propose a mathematical framework, based on conic geometric programming, to control a susceptible-infected-susceptible viral spreading process taking place in a directed contact network with unknown contact rates. We assume that we have access to time series data describing the evolution of the spreading process observed by a collection of sensor nodes over a finite time interval. We propose a data-driven robust convex optimization framework to find the optimal allocation of protection resources (e.g., vaccines and/or antidotes) to eradicate the viral spread at the fastest possible rate. In …
Many models of virus propagation in Computer Networks inspired by {\bf SIS,SIR,}\\ {\bf SEIR}, etc. epidemic disease propagation mathematical models that can be found in the epidemiology field have been proposed in the last two decades. The purpose of these models has been to determine the conditions under which a virus becomes rapidly extinct in a network. The most common models proposed in the field of virus propagation in networks are inspired by SIS-type models or their variants. In such models, the conditions that lead to a rapid extinction of the spread of a computer virus have been calc…
In this paper, we develop a robust economic model predictive controller for the containment of stochastic Susceptible-Exposed-Infected-Vigilant (SEIV) epidemic processes which drives the process to extinction quickly, while minimizing the rate at which control resources are used. The work we present here is significant in that it addresses the problem of efficiently controlling general stochastic epidemic systems without relying on mean-field approximation, which is an important issue in the theory of stochastic epidemic processes. This enables us to provide rigorous convergence guarantees on …
We consider the problem of controlling an SIR-model epidemic by temporarily reducing the rate of contact within a population. The control takes the form of a multiplicative reduction in the contact rate of infectious individuals. The control is allowed to be applied only over a finite time interval, while the objective is to minimize the total number of individuals infected in the long-time limit, subject to some cost function for the control. We first consider the no-cost scenario and analytically determine the optimal control and solution. We then study solutions when a cost of intervention …
In this paper, we consider the problem of controlling a diffusion process pertaining to an opioid epidemic dynamical model with random perturbation so as to prevent it from leaving a given bounded open domain. Here, we assume that the random perturbation enters only through the dynamics of the susceptible group in the compartmental model of the opioid epidemic dynamics and, as a result of this, the corresponding diffusion is degenerate, for which we further assume that the associated diffusion operator is hypoelliptic. In particular, we minimize the asymptotic exit rate of such a controlled-di…
Nowadays, epidemic models provide an appropriate tool for describing the propagation of biological viruses in human or animal populations, or rumours and other kinds of information in social networks and malware in both computer and ad hoc networks. Commonly, there are exist multiple types of malware infecting a network of computing devices, or different messages can spread over the social network. Information spreading and virus propagation are interdependent processes. To capture such independencies, we integrate two epidemic models into one holistic framework, known as the modified Suscepti…
The optimal control of epidemic-like stochastic processes is important both historically and for emerging applications today, where it can be especially important to include time-varying parameters that impact viral epidemic-like propagation. We connect the control of such stochastic processes with time-varying behavior to the stochastic shortest path problem and obtain solutions for various cost functions. Then, under a mean-field scaling, this general class of stochastic processes is shown to converge to a corresponding dynamical system. We analogously establish that the optimal control of t…
