Related papers: A two-strain reaction-diffusion malaria model with…
This paper studies a distributed continuous-time bi-virus model in which two competing viruses spread over a network consisting of multiple groups of individuals. Limiting behaviors of the network are characterized by analyzing the…
The contact process is a non-equilibrium Hamiltonian model that, even in one dimension, lacks an exact solution and has been extensively studied via Monte Carlo simulations, both in steady-state and time-dependent scenarios. Although the…
This study presents a seasonally forced cholera model that incorporates imperfect vaccination as a control strategy. The model captures the temporal dynamics of susceptible, vaccinated, infected, and recovered individuals, as well as the…
In this study, we develop and analyze a deterministic two-strain host-vector model for dengue transmission that incorporates key immuno-epidemiological mechanisms, including temporary cross-immunity, antibody-dependent enhancement (ADE),…
We study the influence of a randomly switching reproduction-predation rate on the survival behavior of the non-spatial cyclic Lotka-Volterra model, also known as the zero-sum rock-paper-scissors game, used to metaphorically describe the…
We consider a simple deterministic model which describes an asymmetric competition between an immune system with a specific and powerful response, and a virus with a broad toxicity and fast mutations. Interest in this model relies on the…
Stochastic discrete-time SIS and SIR models of endemic diseases are introduced and analyzed. For the deterministic, mean-field model, the basic reproductive number $R_0$ determines their global dynamics. If $R_0\le 1$, then the frequency of…
We propose and analyze an epidemiological model for vector borne diseases that integrates a multi-stage vector population and several host sub-populations which may be characterized by a variety of compartmental model types: subpopulations…
I discuss the so-called SuperSpreader epidemic, for which SARS is the canonical examples (and, perhaps, MERS will be another). I use simulation by an agent-based model as well as the mathematics of multi-type branching-processes to…
Recent work from public health experts suggests that incorporating human behavior is crucial in faithfully modeling an epidemic. We present a reaction-diffusion partial differential equation SIR-type population model for an epidemic…
We introduce a stochastic SIR-type partial differential equation model incorporating random diffusion, reinfection, vital dynamics, and a randomly varying transmission rate. For the associated random dynamical system, we prove the existence…
Clustered observations are ubiquitous in controlled and observational studies and arise naturally in multi-centre trials or longitudinal surveys. We present a novel model for the analysis of clustered observations where the marginal…
We study how the interplay between the memory immune response and pathogen mutation affects epidemic dynamics in two related models. The first explicitly models pathogen mutation and individual memory immune responses, with contacted…
Assume that $N_m(x)$ denotes the density of the population at a point $x$ at the beginning of the reproductive season in the $m$th year. We study the following impulsive reaction-diffusion model for any $m\in \mathbb Z^+$…
In this paper, we consider a compartmental SIRS epidemic model with asymptomatic infection and seasonal succession, which is a periodic discontinuous differential system. The basic reproduction number $\mathcal{R}_0$ is defined and valuated…
An SIR epidemic model with free boundary is investigated. This model describes the transmission of diseases. The behavior of positive solutions to a reaction-diffusion system in a radially symmetric domain is investigated. The existence and…
We show that the basic reproduction number of an SIS patch model with standard incidence is either strictly decreasing and strictly convex with respect to the diffusion coefficient of infected subpopulation if the patch reproduction numbers…
This paper is devoted to the analysis of a reaction-diffusion system with strong competition and spatial heterogeneities modelling the interaction between two species of mosquitoes. In particular, we propose a mathematical model that…
We give a comprehensive study of the analytic properties and long-time behavior of solutions of a reaction-diffusion system in a bounded domain in the case where the nonlinearity satisfies the standard monotonicity assumption. We pay the…
In this paper, we develop a family of bivariate beta distributions that encapsulate both positive and negative correlations, and which can be of general interest for Bayesian inference. We then invoke a use of these bivariate distributions…