Spatiotemporal Evolution of Coinfection Dynamics: A Reaction–Diffusion Model

Le, Thi Minh Thao; Madec, Sten

doi:10.1007/s10884-023-10285-z

Cited by 2 publications

(1 citation statement)

References 31 publications

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“…With theoretical extensions ongoing, to increase model scope and generality, for example adding space [59], or more trait dimensions for species differences [31,39], including growth and clearance biases besides interactions, possibly relevant to more biological scenarios [60], we show the backbone of the replicator equation formalism stays the same. This constitutes a big advantage as results on replicator dynamics [8] can be readily harnessed.…”

Section: Discussionmentioning

confidence: 91%

Towards a mathematical understanding of invasion resistance in multispecies communities

Gjini,

Madec

2023

R. Soc. open sci.

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Multispecies community composition and dynamics are key to health and disease across biological systems, a prominent example being microbial ecosystems. Explaining the forces that govern diversity and resilience in the microbial consortia making up our body’s defences remains a challenge. In this, theoretical models are crucial, to bridge the gap between species dynamics and underlying mechanisms and to develop analytic insight. Here we propose a replicator equation framework to model multispecies dynamics where an explicit notion of invasion resistance of a system emerges and can be studied explicitly. For illustration, we derive the conceptual link between such replicator equation and N microbial species’ growth and interaction traits, stemming from micro-scale environmental modification. Within this replicator framework, mean invasion fitness arises, evolves dynamically, and may undergo critical predictable shifts with global environmental changes. This mathematical approach clarifies the key role of this resident system trait for invader success, and highlights interaction principles among N species that optimize their collective resistance to invasion. We propose this model based on the replicator equation as a powerful new avenue to study, test and validate mechanisms of invasion resistance and colonization in multispecies microbial ecosystems and beyond.

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Section: Discussionmentioning

confidence: 91%

Towards a mathematical understanding of invasion resistance in multispecies communities

Gjini,

Madec

2023

R. Soc. open sci.

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Modeling spatial evolution of multi-drug resistance under drug environmental gradients

Freire,

Hu,

Wood

et al. 2023

Preprint

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Multi-drug combinations to treat bacterial populations are at the forefront of approaches for infection control and prevention of antibiotic resistance. Although the evolution of antibiotic resistance has been theoretically studied with mathematical population dynamics models, extensions to spatial dynamics remain rare in the literature, including in particular spatial evolution of multi-drug resistance. In this study, we propose a reaction-diffusion system that describes the multi-drug evolution of bacteria, based on a rescaling approach (Gjini and Wood, 2021). We show how the resistance to drugs in space, and the consequent adaptation of growth rate is governed by a Price equation with diffusion. The covariance terms in this equation integrate features of drug interactions and collateral resistances or sensitivities to the drugs. We study spatial versions of the model where the distribution of drugs is homogeneous across space, and where the drugs vary environmentally in a piecewise-constant, linear and nonlinear manner. Applying concepts from perturbation theory and reaction-diffusion equations, we propose an analytical characterization ofaverage mutant fitnessin the spatial system based on the principal eigenvalue of our linear problem. This enables an accurate translation from drug spatial gradients and mutant antibiotic susceptibility traits, to the relative advantage of each mutant across the environment. Such a mathematical understanding allows to predict the precise outcomes of selection over space, ultimately from the fundamental balance between growth and movement traits, and their diversity in a population.

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Spatiotemporal Evolution of Coinfection Dynamics: A Reaction–Diffusion Model

Cited by 2 publications

References 31 publications

Towards a mathematical understanding of invasion resistance in multispecies communities

Towards a mathematical understanding of invasion resistance in multispecies communities

Modeling spatial evolution of multi-drug resistance under drug environmental gradients

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