Related papers: Epidemic control via stochastic optimal control
We study a stochastic phase-field model for tumor growth dynamics coupling a stochastic Cahn-Hilliard equation for the tumor phase parameter with a stochastic reaction-diffusion equation governing the nutrient proportion. We prove strong…
We study a class of backward stochastic differential equations (BSDEs) driven by a random measure or, equivalently, by a marked point process. Under appropriate assumptions we prove well-posedness and continuous dependence of the solution…
The spread of COVID-19 has been thwarted in most countries through non-pharmaceutical interventions. In particular, the most effective measures in this direction have been the stay-at-home and closure strategies of businesses and schools.…
We study first order necessary conditions for an optimal control problem of a Susceptible-Infected-Recovered (SIR) model with limitations on the duration of the quarantine. The control is done by means of the reproduction number, i.e., the…
We study a family of optimal control problems under a set of controlled-loss constraints holding at different deterministic dates. The characterization of the associated value function by a Hamilton-Jacobi-Bellman equation usually calls for…
The SIR model is the cornerstone model for mathematical epidemiology, explaining key epidemic features such as the second-order transition between disease-free and epidemic states, the initial exponential growth of outbreaks or the…
The COVID-19 pandemic has had worldwide devastating effects on human lives, highlighting the need for tools to predict its development. Dynamics of such public-health threats can often be efficiently analysed through simple models that help…
We introduce a stochastic version of the optimal transport problem. We provide an analysis by means of the study of the associated Hamilton-Jacobi-Bellman equation, which is set on the set of probability measures. We introduce a new…
One of the main challenges of the measures against the COVID-19 epidemic is to reduce the amplitude of the epidemic peak without increasing without control its timescale. We investigate this problem using the SIR model for the epidemic…
This paper revisits a longstanding problem of interest concerning the distributed control of an epidemic process on human contact networks. Due to the stochastic nature and combinatorial complexity of the problem, finding optimal policies…
The COVID-19 pandemic has posed a policy making crisis where efforts to slow down or end the pandemic conflict with economic priorities. This paper provides mathematical analysis of optimal disease control policies with idealized…
During a pandemic, there are conflicting demands arising from public health and economic cost. Lockdowns are a common way of containing infections, but they adversely affect the economy. We study the question of how to minimise the economic…
We develop a new methodology for the efficient computation of epidemic final size distributions for a broad class of Markovian models. We exploit a particular representation of the stochastic epidemic process to derive a method which is…
We show how the standard field theoretical language based on creation and annihilation operators may be used for a straightforward derivation of closed master equations describing the population dynamics of multivariate stochastic epidemic…
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…
We study optimal stochastic control problems of general coupled systems of forward-backward stochastic differential equations with jumps. By means of the It\^o-Ventzell formula the system is transformed to a controlled backward stochastic…
We consider a stochastic optimal control problem where the controller can anticipate the evolution of the driving noise over some dynamically changing time window. The controlled state dynamics are understood as a rough differential…
This paper is concerned with providing the maximum principle for a control problem governed by a stochastic evolution system on a separable Hilbert space. In particular, necessary conditions for optimality for this stochastic optimal…
The aim of this paper is to provide a rigorous mathematical analysis of an optimal control problem of a SIR epidemic on an infinite horizon. A state constraint related to intensive care units (ICU) capacity is imposed and the objective…
Some recent works reveal that there are models of differential equations for the mean and variance of infected individuals that reproduce the SIS epidemic model at some point. This stochastic SIS epidemic model can be interpreted as a…