Complete global analysis of a two-scale network SIRS epidemic dynamic model with distributed delay and random perturbations

The stochastic extinction and stability conditions for nonlinear malaria epidemics

“…In general, these models are classified as SIS, SIR, SIRS, SEIRS, and SEIR etc. [33,34,19,37,16,59,55,25] epidemic dynamic models depending on the compartments of the disease classes directly involved in the general disease dynamics. Some of these studies devote interest to SEIRS and SEIR models [37,16,38,17,25,4], which account for the compartment of individuals who are exposed to the disease, E, that is, infected but noninfectious individuals.…”

“…The immunity delay represents the period of effective naturally acquired immunity against the disease after successful recovery from infection. See [55,56,66,33,25,14,20,47,13,49].…”

“…The presence of noise in an epidemiological process may directly impact the state of the system -known as demographic white noise, or indirectly influence other driving parameters of the infectious system-known as environmental white noise. For example, in [55,59,56], environmental white noise is studied, where the noise represents the random fluctuations in the disease transmission rate. In [33], the white noise process represents the variability in the natural death rate of the population.…”

“…It is assumed in the formulation of this incidence rate that the number of infectious vectors at time t interacting and effectively transmitting infection to susceptible individuals, S, after β number of effective contacts per unit time per infective is proportional to the infectious human population, I, at earlier time t − T . Cook's method of effectively studying the dynamics of a vector-borne disease in a human population without directly including the vector population dynamics has been utilized by several other authors, for example [49,39,55,33,51]. demic dynamic models for malaria with three distributed delays:…”

Online Social Network Emergency Public Event Information Propagation and Nonlinear Mathematical Modeling

“…The model was also used to examine social network effects to better understand the topological structure of social contact and the impact of its properties. An improved susceptible-infected-susceptible (SIS) epidemic 2 Complexity spreading model is proposed in order to provide a theoretical method to analyze and predict the spreading of diseases [16][17][18][19][20]. This model is based on the following idea: in social networks, the contact probability between nodes is decided by their social distances and their active degrees.…”