# Local vs. long-range infection in unidimensional epidemics

## TL;DR

This paper investigates how local and long-range interactions influence the spread of epidemics in a one-dimensional lattice, revealing that long-range transmissions do not significantly change critical behavior.

## Contribution

It introduces a unidimensional contact process model incorporating both local and long-range infection mechanisms, confirming earlier theoretical predictions through numerical analysis.

## Key findings

- Long-range interactions do not significantly alter critical exponents.
- Numerical results support early field-theoretic predictions.
- The model captures vector-mediated transmission effects.

## Abstract

We study the effects of local and distance interactions in the unidimensional contact process (CP). In the model, each site of a lattice is occupied by an individual, which can be healthy or infected. As in the standard CP, each infected individual spreads the disease to one of its first-neighbors with rate $\lambda$, and with unitary rate, it becomes healthy. However, in our model, an infected individual can transmit the disease to an individual at a distance $\ell$ apart. This step mimics a vector-mediated transmission. We observe the host-host interactions do not alter the critical exponents significantly in comparison to a process with only L\'evy-type interactions. Our results confirm, numerically, early field-theoretic predictions.