Moment closure of infectious diseases model on heterogeneous metapopulation network

Abstract

The global transmission of infectious diseases poses huge threats to human. Traditional heterogeneous mean-field models on metapopulation networks ignore the heterogeneity of individuals who are in different disease states in subpopulations with the same degree, resulting in inaccuracy in predicting the spread of disease. In this paper, we take heterogeneity of susceptible and infectious individuals in subpopulations with the same degree into account, and propose a deterministic unclosed general model according to Markov process on metapopulation networks to curve the global transmission of diseases precisely. Then we make the general model closed by putting forward two common assumptions: a two-dimensional constant distribution and a two-dimensional log-normal distribution, where the former is equivalent to the heterogeneous mean-field model, and the latter is a system of weighted ordinary differential equations. Further we make a stability analysis for two closed models and illustrate the results by numerical simulations. Next, we conduct a series of numerical simulations and stochastic simulations. Results indicate that our general model extends and optimizes the mean-field model. Finally, we investigate the impacts of total mobility rate on disease transmission and find that timely and comprehensive travel restriction in the early stage is an effective prevention and control of infectious diseases.

Infectious diseases spreading on a metapopulation network coupled with its second-neighbor network

“…The threshold value R 0 depends only on disease parameters β and γ but not on mobility rate δ or transfer rate q , thus, mobility of individuals has no impact on the basic reproduction number. However, movements of individuals between subpopulations accelerates the global spread of infectious diseases on metapopulation networks [24] .…”

A stability analysis on a smoking model with stochastic perturbation

“…Recently, the stochastic epidemic models are increasingly investigated by many authors (Zhou and Zhang, 2016;Zhang et al, 2017;Liu et al, 2020;Seraphin Djaoue et al, 2020;Applebaum, 2009;Duan, 2015;Bao and Zhang, 2017;Tilahun et al, 2020;Tesfay et al, 2020) and different methods are adopted for the solution of non-linear systems in integer and fractional order see (Abbasbandy et al, 2017;Arqub, 2019;Joachimiak, 2020;Alchikh and Khuri, 2019;Bougoffa et al, 2016;Djilali, 2019;Djilali, 2018;Djilali, 2020a;Djilali, 2020b;Djilali et al, XXXX;Bentout et al, 2021;Djilali and Ghanbari, 2021). Moreover, moment closure techniques, supported by precise determinacy criteria and evolutive partial differential equations, are as well suitable instruments used in the analysis of similar systems see (Feng and Jin, 2018;Infusino and Kuna, 2020;Infusino et al, 2021;Li et al, 2019;Li and Viglialoro, 2021;Viglialoro and Woolley, 2020). Motivated by the above research studies, the main object of this study is to establish how the dynamics behaviors are affected by the environmental noise, i.e.…”

Exploring the Epidemic Spreading in a Multilayer Metapopulation Network by considering Individuals’ Periodic Travelling

“…Since the small-world [2] and scale-free networks [3] are presented, many scholars have studied the epidemic spreading using dynamic analysis method based on complex network model [4][5][6][7][8][9] and obtained a lot of better prediction results for the spread of infectious diseases. e use of mathematical models in the study of epidemic dynamics and their mechanisms and their prevention and control provided valuable insights and contributed to draw up the global picture of epidemics occurrence, patterns, and management [10][11][12][13]. However, considering the impact of mathematical models in epidemiology, it is important to build them on realistic assumptions [14][15][16].…”