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For a heterogeneous host population, the basic reproduction number of an infectious disease, $\cR_0$, is defined as the spectral radius of the next generation operator (NGO). The threshold properties of the basic reproduction number are…
A basic reproduction number, $R_0$, is a concept encountered frequently in the study of ecological and epidemiological models. It is routinely used to determine the stability of an extinction or a disease-free fixed point or steady state.…
Recently, Li and Zhao [5] (Bull. Math. Biol., 83(5), 43, 25 pp (2021)) proposed and studied a periodic reaction-diffusion model of Zika virus with seasonality and spatial heterogeneous structure in host and vector populations. They found…
An important issue in theoretical epidemiology is the epidemic threshold phenomenon, which specify the conditions for an epidemic to grow or die out. In standard (mean-field-like) compartmental models the concept of the basic reproductive…
The basic reproduction number ($R_0$) is an epidemiological metric that represents the average number of new infections caused by a single infectious individual in a completely susceptible population. The methodology for calculating this…
Accurate epidemic forecasting requires models that account for the layered and heterogeneous nature of real social interactions. The basic reproduction number $\mathcal R_0$ calculated from models that assume homogeneous mixing or…
Since the last century, deterministic compartmental models have emerged as powerful tools to predict and control epidemic outbreaks, in many cases helping to mitigate their impacts. A key quantity for these models is the so-called Basic…
The effect of diffusion rates on the basic reproduction number of a general compartmental reaction-diffusion epidemic model in a heterogeneous environment is considered. It is shown when the diffusion rates tend to zero, the limit of the…
We study the global stability issue of the reaction-convection-diffusion cholera epidemic PDE model and show that the basic reproduction number serves as a threshold parameter that predicts whether cholera will persist or become globally…
The basic reproduction number $R_0$ is a fundamental quantity in epidemiological modeling, reflecting the typical number of secondary infections that arise from a single infected individual. While $R_0$ is widely known to scientists,…
We study the Suscectible-Infected-Recovered-Susceptible (SIRS) epidemic model on deterministic networks. For connected but otherwise general interaction patterns and heterogeneous recovery and loss-of-immunity rates, we identify a…
We propose a novel approach to approximate the basic reproduction number $R_0$ as spectral radius of the Next-Generation Operator in time-periodic population models by characterizing the latter via evolution semigroups. Once birth/infection…
In this paper, we provide a straightforward approach to defining and deriving the key epidemiological quantity, the basic reproduction number, $R_0$, for Markovian epidemics in structured populations. The methodology derived is applicable…
A reaction-diffusion model is investigated to understand infective environments in a man-environment-man epidemic model. The free boundary is introduced to describe the expanding front of an infective environment induced by fecally-orally…
In this paper we consider epidemic models of directly transmissible SIR (susceptible $\to$ infective $\to$ recovered) and SEIR (with an additional latent class) infections in fully-susceptible populations with a social structure, consisting…
The basic reproduction number R0 -- the number of individuals directly infected by an infectious person in an otherwise susceptible population -- is arguably the most widely used estimator of how severe an epidemic outbreak can be. This…
Recent evidences show that individuals who recovered from COVID-19 can be reinfected. However, this phenomenon has rarely been studied using mathematical models. In this paper, we propose a SEIRE epidemic model to describe the spread of the…
In this paper we describe the dynamics of a vector-borne relapsing disease, such as tick-borne relapsing fever, using the methods of compartmental models. After some motivation, model description, and a brief overview of the theory of…
This paper is concerned with a nonlocal dispersal susceptible-infected-susceptible (SIS) epidemic model with Dirichlet boundary condition, where the rates of disease transmission and recovery are assumed to be spatially heterogeneous. We…
In this work, we revisit the basic reproduction rate $\mathcal{R}_{0}$ definition for analysis of epidemic-non-epidemic phases describing the dynamics of the discrete stochastic version of the epidemic $SIR$ model based on the Master…