# Dynamics of disease spread. Effect of the characteristic times

## TL;DR

This study investigates how the characteristic times of infection, latency, and recovery influence disease spread dynamics in a heterogeneous population using a stochastic SEIR model on a Small World Network, revealing exponential growth, oscillations, and survey biases.

## Contribution

It introduces a dynamic SEIR model incorporating realistic disease parameters and analyzes how characteristic times affect epidemic behavior and observational accuracy.

## Key findings

- Exponential increase in infected individuals when latency is shorter than infection time.
- Oscillatory infection dynamics emerge when latency exceeds infection time.
- Periodic surveys can misestimate infection spread if not aligned with characteristic times.

## Abstract

Dynamic properties of spreading infection through a heterogeneous population are studied numerically and analytically using a dynamic variant of Watts and Strogatz Small World Network-based stochastic Susceptible-Exposed-Infectious-Removed (SEIR) epidemic model. This model includes the main realistic parameters usually characterizing transmissible diseases, such as the force of infection, latency and infection times. As far as the latency time remains smaller than that of infection, the proportion of infected individuals increases exponentially with time, otherwise an oscillatory behavior appears. This may explain the periodic behaviors in time observed by the health prevention services. It is also shown that periodic epidemiological surveys overestimate or underestimate the dynamics of infection if the survey periods do not exactly correspond to the characteristic times of the infection. Further discussion is provided on the diffusion and relaxation processes involved in this model, and their relation to the infection characteristic time.