Dynamical analysis of an SIS epidemic model with migration and residence time

Abstract

Migration can be divided into temporary and permanent migration, which is related to the residence time of people in the patch, thus we consider an SIS epidemic model with migration and residence time in a patchy environment. If [Formula: see text], the disease-free equilibrium is globally asymptotically stable and the disease dies out. With the same migration rate of susceptible and infectious individuals and without disease-induced death, when [Formula: see text], the endemic equilibrium is unique and globally asymptotically stable. Numerical simulations are carried out to show the effects of residence time and the migration rate on disease prevalence.

Stochastic Dynamics Analysis of Epidemic Models Considering Negative Feedback of Information

“…Setting Ω b = {ω 0 : τ b ≤ T}, for any ω ∈ Ω b , by (7), we have P(Ω b ) ≥ ε, then at least one of x(min{τ b (ω 0 ), T}), y(min{τ b (ω 0 ), T}), z(min{τ b (ω 0 ), T}), w(min{τ b (ω 0 ), T}) is equal to 1 b or equal to b, thus…”

“…Through dynamic analysis of infectious disease models, they dynamically simulate the development of infectious diseases, make predictions based on actual infection data, and based on the conclusions drawn from the research, corresponding recommendations for infectious disease prevention and control are proposed. Many infectious disease models are deterministic [4][5][6][7][8][9], including various features such as time delay, immunity, multi-group, network, etc., making the established mathematical models close to the natural propagation process. However, deterministic models have to some extent simplified the model of transmission process of infectious diseases.…”

Research on disaster information dissemination based on social sensor networks

“…Existing propagation models, such as susceptible infected (SI), susceptible infected susceptible (SIS), and susceptible infected removed (SIR), simplify the real situation to some extent and cannot meet the research needs under the quick development of social metworks. [22][23][24] Therefore, researchers have further divided the stages of information dissemination based on the analysis of individual attributes according to the specific research field and established many new information dissemination models, such as susceptible exposed infectious recovered (SEIR) and susceptible contacted infected removed (SCIR). 25,26 PP Shu et al 27 constructed a group emergent model with scale-free characteristics of group emergent information dissemination network model based on the fact that the information dissemination behavior among group members is actually influenced by both meritocratic and stochastic action mechanisms.…”

“…Existing propagation models, such as susceptible infected (SI), susceptible infected susceptible (SIS), and susceptible infected removed (SIR), simplify the real situation to some extent and cannot meet the research needs under the quick development of social metworks. 22–24 Therefore, researchers have further divided the stages of information dissemination based on the analysis of individual attributes according to the specific research field and established many new information dissemination models, such as susceptible exposed infectious recovered (SEIR) and susceptible contacted infected removed (SCIR). 25,26…”