arXiv subjects

Erida Gjini

Publications and source records attributed to Erida Gjini.

6 recordsLinked to original sources

arXiv2026

Backward bifurcations in spatial replicator models:when invasion criteria fail to predict coexistence

The replicator equation is a central framework for studying frequency--dependent selection in ecology and evolutionary game theory. In well-mixed populations, the long-term outcome of a two-species system is determined by the signs of the pairwise invasion fitnesses, leading to dominance, coexistence, or bistability. However, many ecological systems are spatially structured, with environmental heterogeneity and dispersal shaping local interactions. How these spatial effects modify the classical replicator regimes remains incompletely understood. In this work, we study a spatially heterogeneous extension of the two-species replicator equation in which pairwise invasion fitnesses vary across space, and frequencies evolve under diffusion and advection. In this setting, the classical invasion fitnesses are replaced by spatial invasion rates given by the principal eigenvalues of the associated linearized operators. Using bifurcation theory, we show that these spatial invasion rates do not fully determine the qualitative dynamics of the system. In particular, spatial heterogeneity can induce a backward bifurcation, generating stable coexistence states even in parameter regimes where the well-mixed replicator predicts competitive exclusion. We derive an explicit local condition for this mechanism, characterizing when such coexistence states arise. These results show that spatial structure can fundamentally alter classical replicator dynamics and provide a concrete mechanism through which coexistence may emerge.

math.DS↗

arXiv2026

Multi-strain SIS dynamics with coinfection under host population structure

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.

q-bio.PE↗

arXiv2025

Derivation of a spatial replicator system with environmental heterogeneity from a co-colonization SIS model with N strains and P patches

The interplay between local and regional processes in the dynamics of ecological communities remains a challenge to model, analyze and predict. This is especially notable in infectious diseases with multiple strains, where several layers of heterogeneity can interact, including strain biological traits and environmental heterogeneity among locations where disease can spread. Motivated by this challenge, here we study a Susceptible-Infected-Susceptible (SIS) model with co-colonization and multiple interacting strains where hosts move between a set of inter-connected patches. Under strain similarity and slow migration rate, we derive a fast-slow approximation of the global metacommunity dynamics, resulting in a spatial replicator system for N strains across P patches. In contrast to a discretization approach on the spatial slow-fast PDE originally derived in(Le and Madec, 2023), here the slow-fast reduction is managed ab-initio by a new approach using strongly the Perron-Frobenius Theorem for Metzler matrices, which simplifies and clarifies the structure of the co-colonization system.

math.DS↗

arXiv2025

Understanding the invader-driven replicator dynamics

In this paper, we study a special case of the invasion fitness matrix in a replicator equation: the invader-driven case. In this replicator, each species is defined by its unique active invasiveness potential (initial growth rate when rare), upon invading any other species, independently of the partner. We derive explicit expressions and theorems to fully characterize the steady-states of this system, including its unique interior coexistence regime, reached for positive species traits, or alternative boundary exclusion states, reached for negative species traits. We study the internal stability of coexistence steady-states, and the system's stability to outsider invasion, relevant for system assembly. We provide detailed analytical results for critical diversity thresholds, and for the special case of random uniform species traits, we analytically compute the probability of stable $k-$species coexistence in a random pool of size $N$, and show that the mean number of co-existing species can be approximated as $\mathbb{E}[n] \sim \sqrt{2N}$. We also derive explicit mathematical conditions for invader traits and invasion outcomes (augmentation, rejection, and replacement), dependent on the history of system assembly. Finally, by outlining links of this replicator case with corresponding (rank-1) Lotka-Volterra ecological systems and specific epidemiological multi-strain SIS models with coinfection, we highlight the relevance of applying these mathematical principles to improve the theoretical and empirical understanding of multi-species coexistence.

math.DS↗

arXiv2022

Pneumococcus and the stress-gradient hypothesis: a trade-off links $R_0$ and susceptibility to co-colonization across countries

Modern molecular technologies have revolutionized our understanding of bacterial epidemiology, but reported data across different settings remain under-integrated in common theoretical frameworks. Pneumococcus serotype co-colonization, caused by the polymorphic bacteria Streptococcus pneumoniae, has been increasingly investigated in recent years. While the global genomic diversity and serotype distribution of S. pneumoniae are well-characterized, there is limited information on how co-colonization patterns vary globally, critical for understanding bacterial evolution and dynamics. Gathering a rich dataset of cross-sectional pneumococcal colonization studies in the literature, we quantified patterns of transmission intensity and co-colonization prevalence in children populations across 17 geographic locations. Fitting these data to an SIS model with co-colonization under the assumption of similarity among interacting strains, our analysis reveals strong patterns of negative co-variation between transmission intensity ($R_0$) and susceptibility to co-colonization ($k$). In support of the stress-gradient hypothesis in ecology (SGH), pneumococcus serotypes appear to compete more in high-transmission settings and less in low-transmission settings, a trade-off which ultimately leads to a conserved ratio of single to co-colonization $μ=1/(R_0-1)k$. Within our mathematical model, such conservation suggests preservation of 'stability-diversity-complexity' regimes in multi-strain coexistence. We find no major study differences in serotype composition, pointing to underlying adaptation of the same set of serotypes across environments. Our work highlights that understanding pneumococcus transmission patterns from global epidemiological data can benefit from simple analytical approaches that account for quasi-neutrality among strains, co-colonization, as well as variable environmental adaptation.

q-bio.PE↗

arXiv2021

Quasi-neutral Dynamics in a Coinfection System with N Strains and Asymmetries along Multiple Traits

Understanding the interplay of different traits in a co-infection system with multiple strains has many applications in ecology and epidemiology. Because of high dimensionality and complex feedbacks between traits manifested in infection and co-infection, the study of such systems remains a challenge. In the case where strains are similar (quasi-neutrality assumption), we can model trait variation as perturbations in parameters, which simplifies analysis. Here, we apply singular perturbation theory to many strain parameters simultaneously, and advance analytically to obtain their explicit collective dynamics. We consider and study such a quasi-neutral model of susceptible-infected-susceptible (SIS) dynamics among N strains which vary in 5 fitness dimensions: transmissibility, clearance rate of single-and co-infection, transmission probability from mixed coinfection, and co-colonization vulnerability factors encompassing cooperation and competition. This quasi-neutral system is analyzed with a singular perturbation method through an appropriate slow-fast decomposition. The fast dynamics correspond to the embedded neutral system, while the slow dynamics are governed by an N-dimensional replicator equation, describing the time evolution of strain frequencies. The coefficients of this replicator system are pairwise invasion fitnesses between strains, which, in our model, are an explicit weighted sum of pairwise asymmetries along all trait dimensions. Remarkably these weights depend only on the parameters of the neutral system. Such model reduction highlights the centrality of the neutral system for dynamics at the edge of neutrality, and exposes critical features for maintenance of diversity.

math.DS↗