Related papers: Persistence, extinction and spatio-temporal synchr…
A significant proportion of the infections driving the current {SARS-CoV-2} pandemic are transmitted asymptomatically. Here we introduce and study a simple epidemic model with separate compartments comprising asymptomatic and symptomatic…
This paper is concerned with spatial spreading dynamics of a nonlocal dispersal population model in a shifting environment where the favorable region is shrinking. It is shown that the species will become extinct in the habitat once the…
A diffusive epidemic model with an infection-dependent recovery rate is formulated in this paper. Multiple constant steady states and spatially homogeneous periodic solutions are first proven by bifurcation analysis of the reaction…
We present a model for evolution and extinction in large ecosystems. The model incorporates the effects of interactions between species and the influences of abiotic environmental factors. We study the properties of the model by approximate…
The stochastic extinction and stability in the mean of a family of SEIRS malaria models with a general nonlinear incidence rate is presented. The dynamics is driven by independent white noise processes from the disease transmission and…
Sexual partnerships that overlap in time (concurrent relationships) may play a significant role in the HIV epidemic, but the precise effect is unclear. We derive edge-based compartmental models of disease spread in idealized dynamic…
Stochastic differential equations characterized by uncertainty are effective in modelling virus dynamics and provide an alternative to traditional deterministic models. Epidemic models are inevitably subjected to the randomness within the…
We explore how heterogeneity in the intensity of interactions between people affects epidemic spreading. For that, we study the susceptible-infected-susceptible model on a complex network, where a link connecting individuals $i$ and $j$ is…
Dynamic extinction colonisation models (also called contact processes) are widely studied in epidemiology and in metapopulation theory. Contacts are usually assumed to be possible only through a network of connected patches. This network…
Persistence in spatially extended dynamical systems (like coarsening systems and other nonequilibrium systems) is reviewed. We discuss, in particular, the spatial correlations in the persistent regions and their evolution in time in these…
We investigate the role of global mixing in epidemic processes. We first construct a simplified model of the SIR epidemic using a realistic population distribution. Using this model, we examine possible mechanisms for destruction of spatial…
A family of discrete non-autonomous SIRVS models with general incidence is obtained from a continuous family of models by applying Mickens non-standard discretization method. Conditions for the permanence and extinction of the disease and…
In wireless sensor networks (WSNs), main task of each sensor node is to sense the physical activity (i.e., targets or disaster conditions) and then to report it to the control center for further process. For this, sensor nodes are attached…
We consider the edge-based compartmental models for epidemic spread developed in Part I. We show conditions under which simpler models may be substituted for more detailed models, and in so doing we define a hierarchy of epidemic models. In…
We introduce a theoretical framework that highlights the impact of physical distancing variables such as human mobility and physical proximity on the evolution of epidemics and, crucially, on the reproduction number. In particular, in…
Recently, different dispersion strategies in population models subject to geometric catastrophes have been considered as strategies to improve the chance of po\-pu\-lation's survival. Such dispersion strategies have been contrasted with the…
Epidemic modelling on complex networks has been studied intensively all the time. The majority of relative research assumes that the time scale of the underlying network evolution is much larger compared to the propagation dynamics on it,…
The basic and effective reproduction numbers are widely used metrics for characterizing the dynamics of infectious disease epidemics. However, the interpretation of these numbers is based on the assumption of homogeneous mixing and may not…
When a new infectious disease (or a new strain of an existing one) emerges, as in the recent COVID-19 pandemic, different types of mobility restrictions are considered to slow down or mitigate the spread of the disease. The measures to be…
The main aim of the work is to present a general class of two time scales discrete-time epidemic models. In the proposed framework the disease dynamics is considered to act on a slower time scale than a second different process that could…