# The role of disease cycles in the endemicity of infectious diseases

## TL;DR

This paper presents a simple epidemiological model demonstrating how reservoir cycles influence disease endemicity, highlighting that focusing solely on vectors or reservoirs may be insufficient for disease control.

## Contribution

The study introduces a network-based model with a bifurcation parameter to explain disease endemicity driven by reservoir cycles, even when individual reservoir cycles are weak.

## Key findings

- Reservoir cycles with small reproductive numbers can sustain endemicity.
- Endemic states can occur without strong reservoir cycles when considering the full reservoir network.
- Control strategies should target both vectors and reservoirs, not just one.

## Abstract

Vector-borne diseases with reservoir cycles are complex to understand because new infections come from contacts of the vector with humans and different reservoirs. In this scenario, the basic reproductive number $\mathcal{R}^h_0$ of the system where the reservoirs are not included could turn out to be less than one, yet, an endemic equilibrium be observed. Indeed, when the reservoirs are taken back into account, the basic reproductive number $\mathcal{R}_0^r$, of only vectors and reservoirs, explains the endemic state. Furthermore, reservoirs cycles with a small basic reproductive number could contribute to reach an endemic state in the human cycle. Therefore, when controlling for the spread of a disease, it could not be enough to focus on specific reservoir cycles or only on the vector. In this work, we created a simple epidemiological model with a network of reservoirs where $\mathcal{R}_0^r$ is a bifurcation parameter of the system, explaining disease endemicity in the absence of a strong reservoir cycle. This simple model may help to explain transmission dynamics of diseases such as Chagas, Leishmaniasis and Dengue.