Time scale theory on stability of explicit and implicit discrete epidemic models: applications to Swine flu outbreak.

Time scales theory has been in use since the 1980s with many applications. Only very recently, it has been used to describe within-host and between-hosts dynamics of infectious diseases. In this study, we present explicit and implicit discrete epidemic models motivated by the time scales modeling approach. We use these models to formulate the basic reproduction number, which determines whether an outbreak occurs or the disease dies out. We discuss the stability of the disease-free and endemic equilibrium points using the linearization method and Lyapunov function. Furthermore, we apply our models to swine flu outbreak data to demonstrate that the discrete models can accurately describe the epidemic dynamics. Our comparison analysis shows that the implicit discrete model can best describe the data regardless of the data frequency. In addition, we perform the sensitivity analysis on the key parameters of the models to study how these parameters impact the basic reproduction number.

#stayhome to contain Covid-19: Neuro-SIR - Neurodynamical epidemic modeling of infection patterns in social networks.

An innovative neurodynamical model of epidemics in social networks - the Neuro-SIR - is introduced. Susceptible-Infected-Removed (SIR) epidemic processes are mechanistically modeled as analogous to the activity propagation in neuronal populations. The workings of infection transmission from individual to individual through a network of social contacts, is driven by the dynamics of the threshold mechanism of leaky integrate-and-fire neurons. Through this approach a dynamically evolving landscape of the susceptibility of a population to a disease is formed. In this context, epidemics with varying velocities and scales are triggered by a small fraction of infected individuals according to the configuration of various endogenous and exogenous factors representing the individuals' vulnerability, the infectiousness of a pathogen, the density of a contact network, and environmental conditions. Adjustments in the length of immunity (if any) after recovery, enable the modeling of the Susceptible-Infected-Recovered-Susceptible (SIRS) process of recurrent epidemics. Neuro-SIR by supporting an impressive level of heterogeneities in the description of a population, contagiousness of a disease, and external factors, allows a more insightful investigation of epidemic spreading in comparison with existing approaches. Through simulation experiments with Neuro-SIR, we demonstrate the effectiveness of the #stayhome strategy for containing Covid-19, and successfully validate the simulation results against the classical epidemiological theory. Neuro-SIR is applicable in designing and assessing prevention and control strategies for spreading diseases, as well as in predicting the evolution pattern of epidemics.