Global Dynamics of Infectious Disease with Arbitrary Distributed Infectious Period on Complex Networks

Abstract

Most of the current epidemic models assume that the infectious period follows an exponential distribution. However, due to individual heterogeneity and epidemic diversity, these models fail to describe the distribution of infectious periods precisely. We establish a SIS epidemic model with multistaged progression of infectious periods on complex networks, which can be used to characterize arbitrary distributions of infectious periods of the individuals. By using mathematical analysis, the basic reproduction numberR0for the model is derived. We verify that theR0depends on the average distributions of infection periods for different types of infective individuals, which extend the general theory obtained from the single infectious period epidemic models. It is proved that ifR0<1, then the disease-free equilibrium is globally asymptotically stable; otherwise the unique endemic equilibrium exists such that it is globally asymptotically attractive. Finally numerical simulations hold for the validity of our theoretical results is given.

An analysis on epidemiological characteristics of brucellosis based on the regression analysis

“…Vector quantities are typed in layer m; matrixes are calculated in layer n; vector quantities are printed in layer l. Dimensions of the parameter matrix are set that θ 1 is the first array and θ 2 is the second array. Parameters {θ 1 , θ 2 ,…θ n } are link coefficients between typed vector quantities and the intermediate calculated matrix as well as link coefficients between the intermediate calculated matrix and printed vector quantities [3] . After the construction of the network structure, the network should be calculated forward and cost function should be printed and output.…”

“…After the calculation, calculate j l  layer by layer and point by point to obtain the difference value Features hidden in the data can be mined through the construction of a deep learning model. After the construction of the network [3] , the model can be solved through MATLAB program. Data can be divided into a training set, a verifying set and a testing set.…”

“…Carry out the forward calculation so as to obtain values of the next group {z (2) , a (2) , z (3) , a (3) }. The stability can be ensured by adding bias.…”