# Diversity of hysteresis in a fully cooperative coinfection model

## TL;DR

This paper introduces a fully cooperative coinfection model demonstrating three novel types of hysteresis in disease spread, with detailed analysis and numerical validation on network structures.

## Contribution

It identifies and characterizes three new types of hysteresis in a fully cooperative coinfection model, expanding understanding of epidemic transitions.

## Key findings

- Three types of hysteresis ($C$, $S_l$, $S_r$) identified in the model.
- Discontinuous outbreak and eradication transitions characterized.
- Hysteresis types analyzed in well-mixed and network-based approaches.

## Abstract

We propose a fully cooperative coinfection model in which singly infected individuals are more likely to acquire a second disease than those who are susceptible, and doubly infected individuals are also assumed to be more contagious than those infected with one disease. The dynamics of such fully cooperative coinfection model between two interacting infectious diseases is investigated through well-mixed and network-based approaches. We show that the former approach exhibits three types of hysteresis, namely, $C$, $S_l$ and $S_r$ types, where the last two types have not been identified before. The first (resp., the second and the third) type exhibits (resp., exhibit) discontinuous outbreak transition from the disease free (resp., low prevalence) state to the high prevalence state when a transmission rate crosses a threshold from the below. Moreover, the third (resp., the first and the second) type possesses (resp., possess) discontinuous eradication transition from the high prevalence state to the low prevalence (resp., disease free) state when the transmission rate reaches a threshold from the above. Complete characterization of these three types of hysteresis in term of parameters measuring the uniformity of the model is also provided. Finally, we assess numerically this epidemic dynamics in random networks.