Special Session 135: Dynamical Systems in Mathematical Biology: Epidemiology, Population Dynamics, and Reaction Networks

Stoichiometric Ruin Theory: Coupling Balanced Bilinear Epidemics with Cramer-Lundberg Processes

Rim Adenane University Ibn Tofail Morocco Co-Author(s):

Abstract: This work establishes a formal mathematical bridge between the Next-Generation Matrix (NGM) method, the celebrated cornerstone of mathematical epidemiology (ME), and the stochastic ruin theory of the Cramer-Lundberg process. Drawing on recent developments that prove the NGM is a structural outcome of the siphon property fundamental in Chemical Reaction Networks (CRN), we demonstrate how epidemiological thresholds R_0 can be mapped directly onto insurance solvency metrics. By treating the epidemic as a balanced bilinear model, we prove that the stoichiometric dwell times of the infectious compartments, a concept derived from CRN and ME, determine the asymptotic claim intensity and the adjustment coefficient of the insurer's surplus. This synthesis allows for a "stoichiometric stress test" of insurance portfolios, where financial stability is explicitly linked to the biological reaction kinetics of a pathogen.

Understanding recurrent COVID-19 outbreaks under imperfect mask protection and reinfection: a mathematical modeling study

Dipo Aldila Universitas Indonesia Indonesia Co-Author(s):    Dipo Aldila, Livia Owen, Stephen Wirana, Putri Zahra Kamalia

Abstract: Mathematical modeling has played a key role in understanding the spread of COVID-19 and guiding public health interventions. While the effects of medical masks and reinfection have been widely studied, their interaction remains less explored. In particular, how mask usage influences reinfection dynamics can significantly alter disease outcomes but is often overlooked. In this study, we develop a transmission model that incorporates medical mask usage, reinfection, and treatment limitations. Our analysis shows that even when the basic reproduction number $\mathcal{R}_0$ is below one, the disease may still persist due to complex system behavior. This highlights that controlling COVID-19 is not always as straightforward as reducing $\mathcal{R}_0$. Through detailed numerical analysis, we uncover rich dynamics such as oscillatory outbreaks and multiple endemic states, which may explain recurring waves of infection observed in real-world data. Our results demonstrate that reinfection can fundamentally change disease dynamics, while consistent mask usage remains a crucial intervention. These findings suggest that adaptive and sustained strategies are necessary to prevent repeated outbreaks. Beyond COVID-19, this work emphasizes how combining behavioral and epidemiological factors in mathematical models can provide deeper insights for designing effective public health policies.

Compartmental disease models with time-dependent transmission parameters

Fatihcan M. Atay Bilkent University Turkey Co-Author(s):

Abstract: We study the dynamics of compartmental disease models with time-dependent parameters. As a particular disease, we consider bacterial meningitis with two age classes and seasonal exacerbations. The time-dependent transmission parameters may represent the outbreak of meningitis cases after the annual pilgrimage period or uncontrolled inflows of irregular immigrants. We consider periodic functions in the analysis of the parameters, as well as more general non-periodic transmission processes. We derive conditions under which the long-time average values of transmission functions can be used as a stability marker of equilibria. Furthermore, we interpret the basic reproduction number in the case of time-dependent transmission functions.

Computing the competitive exclusion partition along the minimal siphons lattice, for multi-strain mathematical epidemiology models

Florin Avram UPPA (retired) France Co-Author(s):    Rim Adenane, Andrei-Dan Halanay, Andras Horvath, Sei Zhen Khong

Abstract: Our paper started as a review of three related topics. One is a recent proof of the celebrated next generation matrix (NGM) method of mathematical epidemiology (ME), which was shown recently to be an outcome of the fact that the invariance/siphon property fundamental in positive ODEs and in particular in chemical reaction networks (CRN) forces the Jacobian at any reasonable boundary equilibrium to have a triangular block form. The second topic are seven results pertaining to a family of bilinear models with rank one NGM introduced by Fall, Iggidr, Sallet and Bonzi, which utilize the explicit eigenvectors of the NGM to compute the unique endemic equilibrium (EE), and Lyapunov functions at both the disease free equilibrium (DFE) and EE. Here we clarified that the Bonzi-Iggidr-Sallet bilinear models with rank one NGM may be classified in two classes, with slight variations in the eigenvector formulas, and that extensions in the presence of feedback from infectious to susceptible are possible. The third topic are results of Shuai and Van den Driessche (2013) which essentially deal with the same DFE -EE stability exchange in the non-rank one case, when the eigenvectors are not explicit. Beyond the review, we identified another positive ODE/CRN concept, that of minimal siphons lattice, which might be useful in ME, in the direction for studying multi-strain models with multiple boundary equilibria. This work is ongoing, but it yielded already several results, as well as an algorithm implemented in our Mathematica package Epid-CRN at https://github.com/florinav/EpidCRNmodels, which partitions the parameter space into regions where only one boundary point may be locally asymptotically stable (LAS) (the so-called competitive exclusion partition (CEP). All the examples in the paper have accompanying notebooks, available at the same address.

Integrating Behavioral Survey Data into Epidemic ModelsA Data-Driven Modeling Framework

Yogesh Bali Johannes Gutenberg University of Mainz Germany Co-Author(s):    Markus Schepers, Burcu G\{u}rb\{u}z

Abstract: Human behavior plays a central role in shaping infectious disease transmission. As risk changes, people modify their mobility, adopt protective measures, and respond to health policies and rising case numbers. Despite this, most epidemic models still represent behavior only indirectly, either through fixed transmission parameters or by inferring behavioral effects from epidemiological trends alone. In this study, we develop a modeling framework that explicitly incorporates measured behavioral change into epidemic dynamics and enables comparison across alternative behavioral compartmental structures. Using repeated survey data from the COSMO project in Germany, we quantify variation in risk perception and protective behavior, and link these responses to policy interventions using indicators from the Oxford COVID-19 Government Response Tracker. On this basis, we construct three compartmental formulations in which behavioral change is represented through transitions between behavioral states and through behavior-dependent modulation of contact patterns and transmission intensity. Population mixing is modeled using age-structured contact matrices from POLYMOD, rescaled with time-varying mobility data from Google. All model variants are calibrated to weekly COVID-19 mortality data across 16 German states using Approximate Bayesian Computation with Sequential Monte Carlo. Our results show that explicitly incorporating behavioral dynamics improves model fit and captures regional and temporal heterogeneity effectively.

Smoluchowski coagulation equation with a flux of dust particles

Marina Ferreira CNRS, University of Toulouse France Co-Author(s):

Abstract: The Smoluchowski coagulation equation is a classical equation describing the distribution of particle sizes undergoing binary coagulation. It arises in many areas of science, including aerosol science, molecular biology, and ecology. Despite extensive study for over a century, it continues to pose significant analytical challenges, particularly concerning long-time behavior for general coagulation kernels. Recently, an existence theory for nontrivial steady states has been developed for a large class of kernels describing coagulation in open systems. We construct a time-dependent solution that is expected to converge to a nontrivial steady state, and prove this convergence for the constant kernel with zero initial data. The solution satisfies a nonzero flux boundary condition describing a constant input of dust particles. We show that this dust is instantaneously converted into particles, so that none remains in the system, and the total mass grows linearly in time. The construction applies to a broad class of non-gelling kernels for which stationary solutions exist; in the complementary regime, no such type of solutions with flux exist. (Based on a joint work with Aleksis Vuoksenmaa - Sapienza University)

SIRS Dynamics with Waning Immunity and Periodic Revaccination

Burcu Gürbüz Johannes Gutenberg-University Mainz Germany Co-Author(s):

Abstract: In this study, we propose an SIRS-type epidemiological model incorporating imperfect vaccination, waning vaccine-induced immunity, and periodic revaccination. Vaccinated individuals are structured by the time elapsed since their last dose, leading to a vaccination-age dependent PDE coupled to an ODE system for the remaining compartments. A discrete-time formulation yields a high-dimensional ODE model consistent with the continuous description. We analyze the equilibria and stability properties of both formulations and derive the basic reproduction number. The model exhibits backward bifurcations and bistability induced by waning immunity and revaccination, implying that disease persistence may occur even when the reproduction number is below one. Numerical continuation is used to investigate the influence of revaccination schedules and contact reduction measures. The results underline the structural role of immunity loss and demonstrate the necessity of combined vaccination and contact control strategies.

On the Dynamics of a Two-Strain Dengue System with Secondary Infection-Induced Mortality

Aytul Gokce Ordu University Turkey Co-Author(s):    Joseph Paez Chavez, Thomas Gotz, Burcu Gurbuz

Abstract: Dengue fever is among the most prevalent vector-borne diseases worldwide. In this work, we propose and analyze a deterministic two-strain host-vector model for dengue transmission. The human population is structured into primary and secondary infection classes, while the mosquito population is divided into single- and co-infected compartments. The model incorporates temporary cross-immunity, mortality during secondary infections, antibody-dependent enhancement (ADE), and explicit mosquito co-infection. ADE is represented through distinct transmission rates for primary and secondary infections. Using the next-generation matrix approach, we derive the basic reproduction number, R_0, and establish the local stability of the disease-free equilibrium when R_0<1. We show that specific ADE conditions can destabilize one-strain endemic equilibria, enabling invasion by a heterologous strain. Center-manifold analysis and numerical continuation further reveal backward bifurcation, bistability, and Hopf-induced oscillations, emphasizing complex dynamics relevant to dengue control strategies.

Mathematical Modeling of Regulatory Dynamics and Viral Pathogenesis in T-Cell Mediated Immune Responses

Meltem Golgeli TOBB University of Economics and Technology Turkey Co-Author(s):    Kaan Karaser

Abstract: The progression of viral infections is determined by the dynamic interplay between viral replication strategies and the host`s adaptive immune response. Central to this process is the balance between effector T-cell activation and the induction of regulatory mechanisms that, while preventing excessive tissue damage, may inadvertently facilitate viral persistence. Understanding the non-linear transitions within these regulatory feedback loops is essential for identifying the biological triggers of viral pathogenesis. In this talk, we propose a mathematical framework based on a system of non-linear ordinary differential equations (ODEs) to investigate the interactions between viral load, effector cell populations, and regulatory signaling pathways. The model incorporates specific transcription factor-mediated dynamics that govern the suppressive modulation of the immune response throughout the infection process. We conduct a rigorous qualitative analysis, including the determination of steady states and their stability, to identify parameter thresholds where the system undergoes significant regime shifts. Our findings highlight critical parameters, such as the suppression rate of effector populations, which act as primary drivers for the transition between viral clearance and immune escape. This model is specifically applied to and validated against viral pathogenesis data, providing mechanistic insights into potential therapeutic interventions and the complex dynamics of viral-host co-evolution.

Allee-Driven Thresholds and Bifurcation Structure in Cancer Immunoediting.

Eymard Hernandez-Lopez University of Tennessee at Chattanooga USA Co-Author(s):

Abstract: This work explores a mathematical model of tumor-immune interactions that incorporates Allee effects to capture the nuances of cooperative tumor growth. Through bifurcation analysis and numerical continuation, we identify and characterize saddle-node, Hopf, Bautin, and Bogdanov-Takens bifurcations, further establishing a formal proof of a codimension-three bifurcation within a biologically relevant parameter space. The findings provide a theoretical foundation for understanding the critical transitions between the elimination, equilibrium, and escape phases of cancer immunoediting, highlighting the underlying mechanisms that drive clinical outcomes.

New oscillatory regimes for competing predators with Holling type II response

Phillipo Lappicy Universidad Complutense de Madrid Spain Co-Author(s):    K. E. M. Church, J.-Y. Dai, O. H\`enot, A. L\`opez-Nieto, H. Stuke, N. Vassena.

Abstract: Oscillatory regimes typically arise from the presence of periodic orbits in dynamical systems. We present three new results for models of competing predators with Holling type II functional response. First, we introduce a new mechanism that generates periodic orbits, which we call hybrid bifurcations: a classical bifurcation occurring at a bifurcation without parameters. We establish existence and stability criteria for the bifurcating periodic solutions and obtain stable periodic coexistence states far from extinction regimes, where all populations remain bounded away from zero. Second, we prove global continuation and stability of families of periodic orbits with respect to a parameter using a computer-assisted framework. As a consequence, we solve a conjecture of Butler and Waltman (1981) concerning one-parameter families of periodic orbits connecting two extinction regimes. Finally, we analyze a candidate Poincar\`e return map for these systems. Using computer-assisted techniques, we prove the existence of periodic orbits together with associated period-doubling bifurcations, indicating a transition to a chaotic regime.

Controlling dynamics of complex biological systems based on network topology

Atsushi Mochizuki Institute for Life and Medical Sciences, Kyoto University Japan Co-Author(s):    Atsushi Mochizuki

Abstract: Dynamics of gene activities based on gene regulatory networks are the origin of biological functions. To understand dynamics of complex systems, we developed Linkage Logic theory by which important aspects of dynamics are determined from topology of regulatory network alone. The theory assures that i) any dynamical behavior of whole system can be identified/controlled by a subset of nodes in a regulatory network, and ii) the subset is determined from topology of the network as a feedback vertex set (FVS). We applied the theory to gene regulatory network for ascidian development including >90 genes. We verified our prediction by experimental manipulation of six genes, and confirmed deterministic induction of each of all seven tissues, respectively. To expand the practical power of Linkage Logic, we also developed new estimation method for gene regulatory networks called RENGE, where genes are perturbed comprehensively and resulting changes in gene expression are measured as a time series. This method makes it possible to distinguish between direct and indirect regulations. This method was applied to human iPS cells, and a gene network containing 103 genes for pluripotency was estimated. We are currently working on fate control of human iPS cells by manipulating FVS of the network.

On Reaction-Diffusion-Taxis Systems in Eco-Epidemiology

Nishith NM Mohan RPTU Kaiserslautern-Landau Germany Co-Author(s):    Nishith Mohan

Abstract: We investigate the role of taxis mechanisms in eco-epidemiological systems, i.e., models that integrate both ecological interactions and disease dynamics. The inclusion of taxis makes the model more nuanced but introduces significant analytical challenges by imparting a cross-diffusive structure. The mathematical analysis is carried out through the development of an energy-based argument, similar to that for the chemotaxis Keller-Segel system, and we demonstrate that it can be adapted to this broader framework. By exploiting the underlying energy structure, we establish global existence and boundedness of solutions under certain spatial and parametric restrictions. These results highlight the efficacy of energy-like approaches in handling complex coupled systems arising in mathematical biology.

A reaction-diffusion model of resistance development in diploid organisms

Luca Nieding Technical University Braunschweig Germany Co-Author(s):

Abstract: The development of metabolic resistance complicates the treatment of economic plants with herbicides and is not yet fully understood. We present a population-dynamic 2D reaction-diffusion equation as a polygenic fitness model for the development of metabolic resistance. We explore the general dynamics due to inheritance as a reaction term and its interaction with spatial spread. Further, we construct a family of submodels and investigate the hierarchy of the modelled effects. As a consequence to the application in agriculture, we numerically investigate the effects of spatial barriers on the dynamics.

Structural Determination of Bifurcation and Multistability in Chemical Reaction Networks

Takashi Okada Hiroshima University Japan Co-Author(s):

Abstract: In living cells, numerous reactions are interconnected through shared substrates and products, thereby forming complex reaction networks. The dynamics of such networks remain insufficiently understood, largely because the quantitative forms of reaction-rate functions are often unknown. To address this difficulty, one can adopt a structural or topological approach that does not rely on detailed kinetic assumptions or specific parameter values. Here, we present our recent studies on structural methods that enable us to determine bifurcation properties of chemical reaction systems directly from network structure, including which parameters control the onset of bifurcations and which parts of the system exhibit bifurcating behavior. We further discuss multistability, focusing in particular on a structural criterion for identifying the molecular species that should be observed to distinguish and classify coexisting steady states.

An epidemiological model describing co-infection of HIV/AIDS and COVID-19 considering public awareness and prevention

Joseph Paez Chavez Escuela Superior Politecnica del Litoral Ecuador Co-Author(s):    D. Aldila, B. Nugroho, B. Omede, O. James, P. Kamalia

Abstract: This presentation proposes a mathematical model describing the simultaneous transmission of HIV and COVID-19, explicitly incorporating COVID-19 vaccination and public awareness. The model is analytically examined to determine the existence and local stability of equilibria for both single-infection and co-infection scenarios. Results show that each disease persists in isolation when its basic reproduction number exceeds one. For the co-infection framework, the overall reproduction number is governed by the larger of the individual reproduction numbers for HIV and COVID-19. Numerical continuation reveals thresholds that allow both diseases to coexist, while disease-free stability requires both reproduction numbers to be below one. A two-parameter continuation analysis shows that the condition where both reproduction numbers equal one serves as an organizing center for various (co-)infection scenarios.

Computational approaches to inheritance of dynamics in reaction networks

Casian Pantea West Virginia University USA Co-Author(s):

Abstract: Recent work by Banaji and collaborators shows that certain enlargements of reaction networks --through the addition of species and reactions-- preserve key dynamical properties such as multistationarity, oscillations, and bifurcations. This framework enables the use of certificates for specific behaviors (e.g., a supercritical Hopf bifurcation) by reducing analysis to smaller, more tractable subnetworks. In principle, this allows one to answer the question ``Does a network {\mathcal N} exhibit dynamical property {\em X}? by identifying a smaller network {\mathcal M} with property {\em X} and a sequence of enlargements from {\mathcal M} to {\mathcal N}. In this talk, we investigate algorithms for tackling this combinatorially explosive problem and present real-world applications of inherited Hopf bifurcation in large enzymatic networks.

PerTexP: scenario-based exploration of pertussis dynamics under maternal and infant vaccination

Emanuela Penitente University of Naples Federico II Italy Co-Author(s):    Anna Autoriello, Sabrina Averga, Bruno Buonomo, Rossella Della Marca, Alfredo Guarino, Cristina Moracas, Emanuela Penitente, Marco Poeta

Abstract: Despite the widespread availability of effective vaccines, pertussis remains a significant public health concern in many high-income countries, particularly because of its severe impact on infants. In recent decades, several regions have experienced a resurgence of pertussis, with recurrent outbreaks and an overall increase in incidence \cite{yeung2017update}. These patterns highlight the need for modelling tools that are both mathematically rigorous and accessible to health practitioners, supporting the exploration of intervention scenarios and evidence-based planning. To this end, we present PerTexP (Pertussis Time Exploration), an interactive MATLAB tool for scenario-based analysis of pertussis transmission under different vaccination strategies \cite{buonomo2025pertexp}. PerTexP is based on a discrete-time, stage-structured compartmental model with two age classes, infants and non-infants, and explicitly incorporates maternal immunisation, infant vaccination, and booster doses in older individuals. Through a graphical user interface, the tool allows users to compare vaccination scenarios and assess their impact on transmission. Applied to the 2024 Italian pertussis outbreak \cite{poeta2024pertussis}, PerTexP suggests an increasing burden over a five-year horizon and shows that increasing maternal coverage yields a larger reduction in cumulative incidence than an equivalent increase in booster uptake, while elimination requires strengthening both interventions. \bibliographystyle{plain} \begin{thebibliography}{99} \bibitem{buonomo2025pertexp} Autoriello, A. et al. (2026). PerTexP: scenario-based exploration of pertussis dynamics under maternal and infant vaccination. medRxiv, 2026-03. \bibitem{poeta2024pertussis} Poeta, M. et al. (2024). Pertussis outbreak in neonates and young infants across Italy, January to May 2024: implications for vaccination strategies. Eurosurveillance, 29(23), 2400301. \bibitem{yeung2017update} Yeung, K. H. T. et al. (2017). An update of the global burden of pertussis in children younger than 5 years: a modelling study. The Lancet Infectious Diseases, 17(9), 974-980. \end{thebibliography}

Delayed immune response and therapy in tumor-immune dynamics

Ana Jacinta Soares Centre of Mathematics, University of Minho Portugal Co-Author(s):    L. Boudjellal. M. J. Torres.

Abstract: We present and analyse a mathematical model describing tumor-immune interactions. The model incorporates the effects of adoptive cellular immunotherapy and includes a delay term accounting for the time lag in the adaptive immune response following tumor recognition.We also consider a non-autonomous extension modelling time-dependent targeted therapy. We investigate the qualitative behaviour of the model, including well-posedness, equilibrium states and their stability, and analyse how the delay and therapy influence the system dynamics. In particular, we show that the delay may induce stability switches, while time-dependent therapies can significantly affect the long-term behaviour of the solutions. Numerical simulations are presented to illustrate the theoretical results and to investigate the impact of the targeted therapy, supported by parameter estimation from experimental data. This is joint work with Laid Boudjellal and Maria Joana Torres.

Starvation-driven cell patterning: integrating lab experiments and mathematical modelling

Cinzia Soresina University of Trento Italy Co-Author(s):

Abstract: We present a reaction-diffusion model describing the interactions among cells, nutrients, and growth factors, aimed at capturing the emergence of starvation-driven cell pattern formation, a phenomenon recently observed in laboratory experiments under nutrient-limited growth conditions. Experiments and modelling were developed in parallel, enabling progressively more targeted experimental design while enhancing the biological realism of the model. This interdisciplinary feedback loop led to the formulation of new hypotheses and enabled the estimation of several key parameters. Numerical simulations show that the model reproduces pattern formation in both one- and two-dimensional spatial domains. To provide theoretical support for these findings, we performed a Turing instability analysis to investigate the potential for diffusion-driven instability. The analysis indicates that the observed patterns are not driven by chemotaxis; rather, they arise naturally under starvation conditions and display structural similarities to the Klausmeier model for vegetation pattern formation in semi-arid environments, suggesting the robustness of the underlying mechanism across biological scales.

The Influence of Climate Variability on Ebola Spread: A Dynamical Systems Approach with Environmental Reservoir and Viral Ecology

Calvin Tadmon University of Dschang Cameroon Co-Author(s):

Abstract: Ebola virus disease (EVD) is an overwhelming haemorrhagic fever causing serious threats to human health, with outbreaks frequently linked to a spillover from wildlife reservoirs. Climatic factors are suspected to influence EVD transmission. However, the mechanisms by which this proceeds remain poorly understood. The aim of this talk is to quantify the effects of some climatic drivers such as temperature and rainfall on the spread of EVD. We consider direct and indirect routes of contamination between and within human and fruit bat populations, and model the transmission dynamics of the disease as a system of nonlinear ordinary differential equations, where some key climate-dependent parameters are incorporated as functions of temperature and rainfall. The nonautonomous differential system derived is completely analysed. To begin with, we neglect the intra-annual variation of climate, and investigate the corresponding autonomous system obtained. The basic reproduction number is computed, and the existence and stability of equilibria are successfully studied. Sensitivity analyses highlight, among others, the critical role of environmental transmission and cross-species contamination. Secondly, the nonautonomous model is thoroughly investigated by mainly relying on the definition of the basic reproduction number in periodic environments. We prove the existence, uniqueness and global stability of a positive Ebola-free solution. Finally, to illustrate the theoretical findings, we perform some numerical simulations using real climate data from the locality of Beni (Democratic Republic of Congo). Our results reveal that temperature and rainfall can actually influence the spread of EVD. The present investigation provides a quantitative framework linking climate change to Ebola virus ecology, and a valuable tool for public health planning in climate vulnerable regions.

Invading activity fronts stabilize excitable systems against stochastic extinction

Uwe C Tauber Physics Department, Virginia Tech USA Co-Author(s):    Kenneth Distefano, Sara Shabani

Abstract: Stochastic chemical reaction or population dynamics in finite systems often terminates in an absorbing state. Yet in large spatially extended systems, the time to reach species extinction (or fixation) becomes exceedingly long. Tuning control parameters may diminish the survival probability, rendering species coexistence susceptible to stochastic extinction events. In inhomogeneous settings, where a vulnerable subsystem is diffusively coupled to an adjacent stable patch, the former is reanimated through continuous influx from the interfaces, provided the absorbing region sustains spreading activity fronts. We demonstrate this generic elimination of finite-size extinction instabilities via immigration flux in predator-prey, epidemic spreading, and cyclic competition models.

Dynamical consequences of autocatalysis in reaction networks

Nicola Vassena Leipzig University Germany Co-Author(s):

Abstract: Autocatalysis is a fundamental mechanism for self-amplification and positive feedback in reaction networks. Using a structural (i.e., network-based) definition, autocatalysis provides a sufficient condition for a network to admit an unstable equilibrium. More specifically, a Perron-Frobenius argument links autocatalysis to a possible positive growth of the system. Albeit with different wording, bifurcations in epidemiological networks are most naturally a consequence of autocatalysis too (see e.g. works by Adenane and Avram, also participating in this special session). In this talk I will overview such ideas and present examples of reaction networks where multistationarity (including co-existence of stable equilibria) and periodic oscillations are triggered by autocatalysis. I will also discuss how autocatalysis is a natural, but not exhaustive, route to instability, and show examples where non-autocatalytic forms of instability arise.

Non-monotonic dose-response curves in biochemical systems

Polly Y. Yu University of Illinois Urbana-Champaign USA Co-Author(s):    Eduardo D. Sontag

Abstract: A response curve measures the output of a biological system at equilibrium against an input parameter, which could be a rate constant, the dose of a ligand, or the strength of an external signal. While often monotonic, a response curve that is biphasic serves as a mechanism against over-activation. For example, it has been observed that a T-cell`s response to antigen concentration is non-monotonic. It has been conjectured that an incoherent feedforward loop is necessary to explain biphasic response. In this talk, we establish necessary conditions for biphasic response for general non-linear systems. More precisely, we proved that either an incoherent feedforward loop, or a combination of positive and negative feedback loops, is necessary for biphasic response.