An SIR pairwise epidemic model with infection age and demography

Abstract

The demography and infection age play an important role in the spread of slowly progressive diseases. To investigate their effects on the disease spreading, we propose a pairwise epidemic model with infection age and demography on dynamic networks. The basic reproduction number of this model is derived. It is proved that there is a disease-free equilibrium which is globally asymptotically stable if the basic reproduction number is less that unity. Besides, sensitivity analysis is performed and shows that increasing the variance in recovery time and decreasing the variance in infection time can effectively control the diseases. The complex interaction between the death rate and equilibrium prevalence suggests that it is imperative to correctly estimate the parameters of demography in order to assess the disease transmission dynamics accurately. Moreover, numerical simulations show that the endemic equilibrium is globally asymptotically stable.

An SIR rumor pairwise model with spreading age

“…In many cases, we realize demography and infection age are important factors in the epidemic disease model [9,21]. However, in the literature [10], it found that the most of the researcher ignored the important effect of the spreading age on the spreading process of the rumor.…”

“…Obviously, these are not consistent with the reality [14,17]. To make the rumor model more accurate and truthful, after investigating the modern epidemic dynamics models and documents [9,14,21], we introduce the risk function instead of the recovery rate, where the recovery rate depend on the spreading age. Numerical simulations are used to verify the accuracy of the model and ensure the model in line with the reality.…”

“…Numerical simulations are used to verify the accuracy of the model and ensure the model in line with the reality. In numerical simulations, Jing et al [9] and Zhang et al [21] discovered that the different recovery time distributions could lead to different effects on the spreading process. Neil et al [14] studied the rumor models on scale-free network by performing Monte Carlo simulations and made numerical solutions of the mean-field equations.…”

“…Neil et al [14] studied the rumor models on scale-free network by performing Monte Carlo simulations and made numerical solutions of the mean-field equations. Furthermore, Wilkinsion et al [16] provided an upper bound for the expected epidemic scale at any fixed time t > 0 and Jing et al [9] found that increasing the variance in the recovery time or decreasing the variance in infection period could effectively control the diseases.…”

A Discrete Numerical Solution of The SIR Model with Horizontal and Vertical Transmission

“…This method give a good approximation in many works, such as in [5] and [6]. In [5] the method was applied to approximate SIRS epidemic model while in [6] it was applied to find the numerical solution of SIR Pairwise Epidemic model. Euler method is a simple scheme, but only works for a small step-size.…”