# Markovian approach to tackle the interaction of simultaneous diseases

## TL;DR

This paper introduces a Markovian framework to analyze how multiple diseases interact within a population, revealing conditions for abrupt outbreaks, dominance, or coexistence, with implications for understanding complex epidemic dynamics.

## Contribution

It presents a novel, versatile benchmark model for studying cooperative and competitive interactions among multiple pathogens using Markovian processes.

## Key findings

- Identifies critical cooperation levels for explosive epidemic transitions.
- Derives analytical transition points for disease dominance and coexistence.
- Analyzes how weakening competition affects epidemic thresholds.

## Abstract

The simultaneous emergence of several abrupt disease outbreaks or the extinction of some serotypes of multi-strain diseases are fingerprints of the interaction between pathogens spreading within the same population. Here, we propose a general and versatile benchmark to address the unfolding of both cooperative and competitive interacting diseases. We characterize the explosive transitions between the disease-free and the epidemic regimes arising from the cooperation between pathogens, and show the critical degree of cooperation needed for the onset of such abrupt transitions. For the competing diseases, we characterize the mutually exclusive case and derive analytically the transition point between the full-dominance phase, in which only one pathogen propagates, and the coexistence regime. Finally, we use this framework to analyze the behavior of the former transition point as the competition between pathogens is relaxed.