[Paper Review] Multi-strain SIS dynamics with coinfection under host population structure

Sten Madec, Nicola Cinardi+1 more|arXiv (Cornell University)|Jan 30, 2026

Evolution and Genetic Dynamics0 citations

TL;DR

The paper develops a structured-host, multi-strain SIS model with coinfection and derives a global replicator equation to describe strain coexistence and selection under host heterogeneity.

ABSTRACT

Coinfection phenomena are common in nature, yet there is a lack of analytical approaches for coinfection systems with a high number of circulating and interacting strains. In this paper, we investigated a coinfection SIS framework applied to N strains, co-circulating in a structured host population. Adopting a general formulation for fixed host classes, defined by arbitrary epidemiological traits such as class-specific transmission rates, susceptibilities, clearance rates, etc., our model can be easily applied in different frameworks: for example, when different host species share the same pathogen, in classes of vaccinated or non-vaccinated hosts, or even in classes of hosts defined by the number of contacts. Using the strain similarity assumption, we identify the fast and slow variables of the epidemiological dynamics on the host population, linking neutral and non-neutral strain dynamics, and deriving a global replicator equation. This global replicator equation allows to explicitly predict coexistence dynamics from mutual invasibility coefficients among strains. The derived global pairwise invasion fitness matrix contains explicit traces of the underlying host population structure, and of its entanglement with the strain interaction and trait landscape. Our work thus enables a more comprehensive study and efficient simulation of multi-strain dynamics in endemic ecosystems, paving the way to deeper understanding of global persistence and selection forces, jointly shaped by pathogen and host diversity.

Motivation & Objective

• Introduce a fixed-host-class, multi-strain SIS framework with coinfection
• Incorporate arbitrary host population structure across classes and traits
• Develop a slow-fast reduction under strain similarity to obtain a global replicator equation
• Characterize invasion fitness and coexistence through a structured next-generation approach
• Apply the framework to vaccination and network-like host structures to study strain selection

Proposed method

• Formulate a general SIS coinfection model with host classes and N strains (I_k^i and D_k^{i,j} compartments)
• Define Theta_k as the total infection probability for class k and derive the next-generation matrix with R0=ρ(diag(R)Q)
• Use strain similarity to identify fast and slow variables and derive a global replicator equation for strain frequencies
• Define neutrality and quasi-neutrality to connect strain dynamics to a replicator system with invasion fitness matrix
• Provide explicit results for special cases (two hosts, vaccination structure, and mean-field networks) and prove the neutral/quasi-neutral reductions
• Prove global stability results for disease-free and endemic equilibria and derive expressions for S_k^*, I_k^*, D_k^* under R0>1

Experimental results

Research questions

• RQ1 How does host population structure influence multi-strain coinfection dynamics?
• RQ2 Can a global replicator equation capture strain coexistence and competitive outcomes under structured hosts?
• RQ3 How do vaccination or contact-structure heterogeneity modify invasion fitness and strain selection?
• RQ4 What are the conditions for disease-free versus endemic equilibria in a structured N-strain SIS-coinfection model?
• RQ5 How do neutral and quasi-neutral dynamics relate to aggregate host-strain interactions?

Key findings

• A structured N-strain SIS-coinfection model reduces to a replicator equation for strain frequencies under quasi-neutrality
• The disease-free equilibrium is globally stable when R0≤1 and a unique endemic equilibrium exists and is globally stable when R0>1
• Endemic prevalence across host classes is bounded and determined by a fixed-point Theta^* solving a class-structured equation
• Heterogeneity in host classes reduces overall endemic prevalence compared to a homogeneous system with the same R0
• Special cases yield explicit expressions for S_k^*, T_k^*, I_k^*, D_k^* in terms of Theta^*
• The framework accommodates applications to two-host systems, vaccination-induced structure, and heterogeneous contact networks