Related papers: Existence, multiplicity and stability of endemic s…
We present an SI epidemic model whereby a continuous variable captures variability in proliferative potential and resistance to infection among susceptibles. The occurrence of heritable, spontaneous changes in these phenotype and the…
Infectious disease outbreaks have precipitated a profusion of mathematical models. Epidemic curves predicted by these models are typically qualitatively similar, despite distinct model assumptions, but there is no theoretical explanation…
This work proposes and analyzes a family of spatially inhomogeneous epidemic models. This is our first effort to use stochastic partial differential equations (SPDEs) to model epidemic dynamics with spatial variations and environmental…
The impact of spatial structure on the spread of an epidemic is an important issue in the propagation of infectious diseases. Recent studies, both deterministic and stochastic, have made it possible to understand the importance of the…
Physiological stress fundamentally alters disease susceptibility in aquatic environments. In this paper, we develop a stress-structured epidemiological model where host vulnerability is dynamically driven by water quality. Analytically, we…
Network-based models of epidemic spread have become increasingly popular in recent decades. Despite a rich foundation of such models, few low-dimensional systems for modeling SIS-type diseases have been proposed that manage to capture the…
In this paper, we study an analytically tractable SIS model with a non-linear incidence rate for the number of infectious individuals described through a stochastic differential equation (SDE). We guarantee the existence of a positive…
The dynamics of many epidemic models for infectious diseases that spread in a single host population demonstrate a threshold phenomenon. If the basic reproduction number R0 is below unity, the disease-free equilibrium P0 is globally stable…
We study an SAIRS-type epidemic model with vaccination, where the role of asymptomatic and symptomatic infectious individuals are explicitly considered in the transmission patterns of the disease. We provide a global stability analysis for…
In this paper we study the appearance of bifurcations of limit cycles in an epidemic model with two types of aware individuals. All the transition rates are constant except for the alerting decay rate of the most aware individuals and the…
We extend a recent investigation by Meehan et al. (2019) regarding the global stability properties of the general Kermack-McKendrick (renewal) model to the multi-strain case. We demonstrate that the basic reproduction number of each strain…
This paper is concerned with the global dynamics of a hybrid parabolic-hyperbolic model describing populations with distinct dispersal and sedentary stages. We first establish the global well-posedness of solutions, prove a comparison…
The principle of linearized stability is established for age-structured diffusive populations incorporating nonlinear death and birth processes. More precisely, asymptotic exponential stability is shown for equilibria for which the…
We present an analysis of six deterministic models for epidemic spreading. The evolution of the number of individuals of each class is given by ordinary differential equations of the first order in time, which are set up by using the laws…
We study the role of demographic fluctuations in typical endemics as exemplified by the stochastic SIRS model. The birth-death master equation of the model is simulated using exact numerics and analysed within the linear noise…
We develop a mechanistic model that classifies individuals both in terms of epidemiological status (SIR) and vaccination attitude (willing or unwilling), with the goal of discovering how disease spread is influenced by changing opinions…
A network epidemic model is studied. The underlying social network has two different types of group structures, households and workplaces, such that each individual belongs to exactly one household and one workplace. The random network is…
We study an individual-based stochastic SIR epidemic model with infection-age dependent infectivity on a large random graph, capturing individual heterogeneity and non-homogeneous connectivity. Each individual is associated with particular…
We show that disease transmission models in a spatially heterogeneous environment can have a large number of coexisting endemic equilibria. A general compartmental model is considered to describe the spread of an infectious disease in a…
We investigate a two-strain disease model with amplification to simulate the prevalence of drug-susceptible (s) and drug-resistant (m) disease strains. We model the emergence of drug resistance as a consequence of inadequate treatment, i.e.…