Related papers: Dynamical epidemic suppression using stochastic pr…

Why are the epidemic patterns of COVID-19 so different among different cities or countries which are similar in their populations, medical infrastructures, and people's behavior? Why are forecasts or predictions made by so-called experts…

In this paper a stochastic reaction diffusion system is considered, which models the spread of a finite population reacting with a non-renewable resource in the presence of individual based noise. A two-parameter phase diagram is…

Catastrophic transitions, where a system shifts abruptly between alternate steady states, are a generic feature of many nonlinear systems. Recently these regime shift were suggested as the mechanism underlies many ecological catastrophes,…

Many socio-economic and biological processes can be modeled as systems of interacting individuals. The behaviour of such systems can be often described within game-theoretic models. In these lecture notes, we introduce fundamental concepts…

Time delay in general leads to instability in some systems, while a specific feedback with delay can control fluctuated motion in nonlinear deterministic systems to a stable state. In this paper, we consider a non-stationary stochastic…

The paper considers a stabilizing stochastic control which can be applied to a variety of unstable and even chaotic maps. Compared to previous methods introducing control by noise, we relax assumptions on the class of maps, as well as…

The basic reproduction number, $R_0$, is a well-known quantifier of epidemic spread. However, a class of existing methods for estimating $R_0$ from incidence data early in the epidemic can lead to an over-estimation of this quantity. In…

Both for the theoretical and practical treatment of Inverse Problems, the modeling of the noise is a crucial part. One either models the measurement via a deterministic worst-case error assumption or assumes a certain stochastic behavior of…

In this chapter, we focus on the problem of containing the spread of diseases taking place in both temporal and adaptive networks (i.e., networks whose structure `adapts' to the state of the disease). We specifically focus on the problem of…

Age structure is incorporated in many types of epidemic model. Often it is convenient to assume that such models converge to early asymptotic behaviour quickly, before the susceptible population has been appreciably depleted. We make use of…

A natural phenomenon occurring in a living system is an outcome of the dynamics of the specific biological network underlying the phenomenon. The collective dynamics have both deterministic and stochastic components. The stochastic nature…

Previously, we developed a population model incorporating the Allee effect and periodic environmental fluctuations, in which organisms alternate between nomadic and colonial behaviours. This switching strategy is regulated by biological…

Species populations often modify their environment as they grow. When environmental feedback operates more slowly than population growth, the system can undergo boom-bust dynamics, where the population overshoots its carrying capacity and…

We study the effects of switching social contacts as a strategy to control epidemic outbreaks. Connections between susceptible and infective individuals can be broken by either individual, and then reconnected to a randomly chosen member of…

Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class…

In this paper, we focus on the hitting times of a stochastic epidemic model presented by \cite{Gray}. Under the help of the auxiliary stopping times, we investigate the asymptotic limits of the hitting times by the variations of calculus…

Health-policy planning requires evidence on the burden that epidemics place on healthcare systems. Multiple, often dependent, datasets provide a noisy and fragmented signal from the unobserved epidemic process including transmission and…

For a stochastic COVID-19 model with jump-diffusion, we prove the existence and uniqueness of the global positive solution. We also investigate some conditions for the extinction and persistence of the disease. We calculate the threshold of…

In this paper we make the first steps to bridge the gap between classic control theory and modern, network-based epidemic models. In particular, we apply nonlinear model predictive control (NMPC) to a pairwise ODE model which we use to…

The importation and subsequent establishment of novel pathogenic strains in a population is subject to a large degree of uncertainty due to the stochastic nature of the disease dynamics. Mathematical models need to take this stochasticity…