相关论文: Global Threshold Dynamics of a Stochastic Differen…
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…
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…
Pairwise models are used widely to model epidemic spread on networks. These include the modelling of susceptible-infected-removed (SIR) epidemics on regular networks and extensions to SIS dynamics and contact tracing on more exotic networks…
A simplified SIS reaction-diffusion-advection model is proposed and investigated to understand the impact of spatial heterogeneity of environment and advection on the persistence and eradication of an infectious disease. The free boundary…
In the world of epidemics, the mathematical modeling of disease co-infection is gaining importance due to its contributions to mathematics and public health. Because the co-infection may have a double burden on families, countries, and the…
We study the Susceptible-Infectious-Susceptible (SIS) model on arbitrary networks. The well-established pair approximation treats neighboring pairs of nodes exactly while making a mean field approximation for the rest of the network. We…
We propose a systematic method to derive the asymptotic behaviour of the persistence distribution, for a large class of stochastic processes described by a general Fokker-Planck equation in one dimension. Theoretical predictions are…
We investigate predictions of stochastic compartmental models on the severity of disease outbreaks. The models we consider are the Susceptible-Infected-Susceptible (SIS) for bacterial infections, and the Susceptible -Infected-Removed (SIR)…
We demonstrate that the susceptible-infected-susceptible (SIS) model on complex networks can have an inactive Griffiths phase characterized by a slow relaxation dynamics. It contrasts with the mean field theoretical prediction that the SIS…
Becker, Greaves-Tunnell, Kontorovich, Miller, Ravikumar, and Shen determined the long term evolution of virus propagation behavior on a hub-and-spoke graph of one central node and $n$ neighbors, with edges only from the neighbors to the hub…
The Susceptible-Infected-Susceptible model is a canonical model for emerging disease outbreaks. Such outbreaks are naturally modeled as taking place on networks. A theoretical challenge in network epidemiology is the dynamic correlations…
We study an SIR epidemic model with a seasonal contact rate and saturated treatment function. It is shown that the basic reproduction number $(\mathcal {R}_0)$ cannot be acted as a threshold that predicts the spread of an infection. Based…
We study the class of SIS epidemics on temporal networks and propose a new activity-driven and adaptive epidemic model that captures the impact of asymptomatic and infectious individuals in the network. In the proposed model, referred to as…
We consider the classical two-dimensional Rosenzweig-MacArthur prey-predator model with a degenerate noise, whereby only the prey variable is subject to small environmental fluctuations. This model has already been introduced in…
The extinction and persistence of infective individuals are closely related to the random change of the environment. In this paper, via the random/stochastic SIRS models, we analyze qualitatively and quantitatively the impact caused by the…
This paper considers a susceptible-infected-susceptible (SIS) epidemic reaction-diffusion model with no-flux boundary conditions and varying total population. The interaction of the susceptible and infected people is describe by the…
In this manuscript, we develop a mobility-based Susceptible-Infectious-Recovered (SIR) model to elucidate the dynamics of pandemic propagation. While traditional SIR models within the field of epidemiology aptly characterize transitions…
A comparative stochastic and deterministic study of a family of SEIRS epidemic dynamic models for malaria is presented. The family type is determined by the qualitative behavior of the nonlinear incidence rates of the disease. Furthermore,…
We study the spread of discrete-time epidemics over arbitrary networks for well-known propagation models, namely SIS (susceptible-infected-susceptible), SIR (susceptible-infected-recovered), SIRS (susceptible-infected-recovered-susceptible)…
There are many processes in cell biology that can be modelled in terms of an actively switching particle. The continuous degrees of freedom evolve according to a hybrid stochastic differential equation (hSDE) whose drift term depends on a…