# Effect of Infection Hubs in District-Based Network Epidemic Spread Model +
###### Abstract  
A network model of epidemic spread accounting for inhomogeneous population district division is investigated. Motivated by the COVID-19 pandemic, we analyze the effects of infection development in the area, for example, of a city divided into several population districts. The districts are characterized by a certain intensity of contact inside and with inter-district communication that can be generally controlled by the authorities. Specifically, we consider the effect of the central district, which is the hub of infection. We investigate how the interaction strength influences the city's level of epidemic development. We obtained that the final infected amount in the district rises with an increasing degree of connection with the hub. However, the model situation was not limited by the first outbreak but included the subsequent waves of infection. We obtained that the appearance and disappearance of subsequent waves of infection essentially depended on the intensity of communication with the infected hub. Our results suggest the mechanism where stricter communication policy can negatively affect the subsequent infection waves. SIR model; COVID-19; network; infection hub; communication +
Footnote †: This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ([[https://creativecommons.org/licenses/py/4.0/](https://creativecommons.org/licenses/py/4.0/)]([https://creativecommons.org/licenses/py/4.0/](https://creativecommons.org/licenses/py/4.0/))). Footnote †: This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons. dynamics. In terms of epidemic prediction, the classical SIR approach [3]. considering homogeneous populations cannot be directly applied to the current pandemic. During more than two years of the pandemic, many mathematical models describing qualitatively and quantitatively COVID-19 development have been proposed [4; 5; 6; 7; 8]. Models demonstrate their satisfactory performance, especially for limited areas [9], although there are other points of view [10]. It should be noted that the modified SIR models require more complex data for development, and due to the presence of little information and lack of reliable data regarding this newly emerged disease, the simple SIR model has been the choice of many investigators [11]. These over-simplified models ignore the factors that have a great effect on the course of the disease and cannot reproduce such effects as secondary and subsequent waves. The other issue affecting the spread of the virus is the behavioral changes considerably related to the social and cultural context of the population [10; 12; 13]. [PERSON] et al. [14] simulated disease spread using SI and SIR models on an empirical temporal network of sexual contacts. To simulate models in an empirical network of sexually transmitted infections, the authors mapped the sampled network onto a time-ordered list. Their results indicate that the network was not dense enough to support sexually transmitted infection outbreaks. Another similar approach was used in the work [15]. The authors defined a multitype, stochastic SIR dynamical epidemic model on a strongly connected graph. The stochastic SIR model for the spread of an epidemic within and between nodes showed a standard finite-time convergence result for a branching process. One of the most unique techniques was shown in the work [16]. The model contains a mix of discrete and continuous times with interaction described as a Bernoulli process of a finite number of binary random variables. [PERSON] et al. [17] presented another type of hybrid model that is based on a SIRD model for two age classes using eight populations and a spatial model where these populations are distributed in space and time between places. Among the most recent research, a spatio-temporal modeling framework was used in the work [18].