# Time delay in disease transmission via interactions of heterogeneous agents in Watts-Strogatz networks

### Abstract

We analyze the effect of heterogeneity η ≡ ∆ρ/<ρ> of infection probability ρ on the transmission dynamics of a susceptible-infected (SI) epidemic model on a static and complex newtork. The different configurations of the complex network is achieved using the Watts-Strogatz network model (N nodes) that uses the rewiring probability p_{r} : a regular (circular) lattice (p_{r} = 0), a small-world network (1/N), and a completely random network (1). We compare the results of these networks to the fully-connected network of the same size N. The time when the infection spread through half of the completely susceptible population is assigned as T_{1/2} indicating how fast infection spreads over the population. We show that T_{1/2} of disease transmission to half of the population becomes delayed for increasing η. We further show that the propagation of disease in a completely homogeneous population η = 0 is significantly different from a completely heterogeneous population by conducting the Kolmogorov-Smirnov statistical test.

*Proceedings of the Samahang Pisika ng Pilipinas*

**36**, SPP-2018-PB-34 (2018). URL: https://paperview.spp-online.org/proceedings/article/view/SPP-2018-PB-34.