Alberto D'Onofrio- PhD in Medical Computer Science
- Professor (Associate) at University of Trieste
Alberto D'Onofrio
- PhD in Medical Computer Science
- Professor (Associate) at University of Trieste
Computer Science for Complex Systems
About
205
Publications
42,184
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6,865
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Introduction
I work on multi-agents systems and machine learning, with applications to Behavioral Modeling of Infectious Diseases, on Tumor Population Dynamics and on Quantm Mechanics (new entry).
Current institution
Additional affiliations
March 2022 - February 2025
Position
- Senior Researcher
Description
- I have a lot of fun with math, phys and computer science !
September 2017 - July 2020
October 1995 - April 1997
Education
November 1985 - April 1993
Field of study
- Control Theory, Electrical Engineering, Applied Mathematics and Physics
September 1981 - July 1985
Liceo Scientifico Zaleuco
Field of study
- Sciences (mathematics, physics, chemistry, cell biology, anatomy, geology) and Humanities (latin, philosophy, history, italian and french literature)
Publications
Publications (205)
Most available behavioral epidemiology models have linked the behavioral responses of individuals to infection prevalence. However, this is a crude approximation of reality because prevalence is typically an unobserved quantity. This work considers a general endemic SIR epidemiological model where behavioral responses are incidence-based i.e., the...
We investigated the behavior of a Susceptible-Infected-Recovered seasonally forced model for endemic childhood infectious diseases in the case where the target population is not isolated and, moreover, fast weekly fluctuations of the social contacts occur. We considered some key scenarios of interplay of Susceptible subjects with the external world...
Human behavior, and in particular vaccine hesitancy, is a critical factor for the control of childhood infectious disease. Here we propose a spatio-temporal behavioral epidemiology model where the vaccine propensity depends on information that is non-local in space and in time. The properties of the proposed model are analysed under different hypot...
After the many failures in the control of the COVID-19 pandemic, identifying robust principles of epidemic control will be key in future preparedness. In this work, we propose an optimal control model of an age-of-infection transmission model under a two-phase control regime where social distancing is the only available control tool in the first ph...
The International Conference on Mathematical Analysis and Applications in Science and Engineering –ICMA2SC’24 will take place at the beautiful city of Porto, Portugal, in June 20th-June 22nd 2024.
This conference is dedicated to the memory of Prof JA Tenreiro Machado, who passed away in October 2021.
Its aim is to bring together researchers in ev...
Copy number alterations (CNAs) are among the most important genetic events in cancer, but their detection from sequencing data is challenging because of unknown sample purity, tumor ploidy, and general intra-tumor heterogeneity. Here, we present CNAqc, an evolution-inspired method to perform the computational validation of clonal and subclonal CNAs...
Superspreading events (SSEs) play a critical role in the propagation of infectious disease outbreaks, often leading to extensive transmissions that significantly complicate containment efforts. Although prior research has highlighted the importance of transmission heterogeneity and employed a combination of genomic analysis, contact tracing, and ep...
Single-cell RNA and ATAC sequencing technologies enable the examination of gene expression and chromatin accessibility in individual cells, providing insights into cellular phenotypes. In cancer research, it is important to consistently analyze these states within an evolutionary context on genetic clones. Here we present CONGAS+, a Bayesian model...
We consider a SIR-like reaction-diffusion epidemic model which embeds opinion-driven human behavioural changes. We assume that the contagion rate is theoretically saturated with respect to the density of the disease prevalence. The model extends the general reaction-diffusion epidemic model proposed in 1993 by Capasso and Di Liddo. We study the non...
Given the key role that quantum tunneling plays in a wide range of applications, a crucial objective is to maximize the probability of tunneling from one quantum state/level to another, while keeping the resources of the underlying physical system fixed. In this work, we demonstrate that an effective solution to this challenge can be achieved by co...
Geometric Semantic Geometric Programming (GSGP) is one of the most prominent Genetic Programming (GP) variants, thanks to its solid theoretical background, the excellent performance achieved, and the execution time significantly smaller than standard syntax-based GP. In recent years, a new mutation operator, Geometric Semantic Mutation with Local S...
Despite their impressive performance in classification, neural networks are known to be vulnerable to adversarial attacks. These attacks are small perturbations of the input data designed to fool the model. Naturally, a question arises regarding the potential connection between the architecture, settings, or properties of the model and the nature o...
Single-cell RNA and ATAC sequencing technologies allow one to probe expression and chromatin accessibility states as a proxy for cellular phenotypes at the resolution of individual cells. A key challenge of cancer research is to consistently map such states on genetic clones, within an evolutionary framework. To this end we introduce CONGAS+, a Bay...
In contemporary society, social networks accelerate decision dynamics causing a rapid switch of opinions in a number of fields, including the prevention of infectious diseases by means of vaccines. This means that opinion dynamics can nowadays be much faster than the spread of epidemics. Hence, we propose a Susceptible-Infectious-Removed epidemic m...
Human behavior, and in particular vaccine hesitancy, is a critical factor for the control of childhood infectious disease. Here we propose a spatio-temporal behavioral epidemiology model where the vaccine propensity depends on information that is non-local in space and in time. The properties of the proposed model are analysed under different hypot...
Symmetries in the data and how they constrain the learned weights of modern deep networks is still an open problem. In this work we study the simple case of fully connected shallow non-linear neural networks and consider two types of symmetries: full dataset symmetries where the dataset
X
is mapped into itself by any transformation
g
, i.e.
gX...
Tiered social distancing policies have been adopted by many governments to mitigate the harmful consequences of COVID-19. Such policies have a number of well-established features, i.e. they are short-term, adaptive (to the changing epidemiological conditions), and based on a multiplicity of indicators of the prevailing epidemic activity. Here, we u...
The COVID-19 epidemic highlighted the necessity to integrate dynamic human behaviour change into infectious disease transmission models. The adoption of health protective behaviour, such as handwashing or staying at home, depends on both epidemiological and personal variables. However, only a few models have been proposed in the recent literature t...
Social distancing has been enacted in order to mitigate the spread of COVID-19. Like many authors, we adopt the classic epidemic SIR model, where the infection rate is the control variable. Its differential flatness property yields elementary closed-form formulae for open-loop social distancing scenarios, where, for instance, the increase of the nu...
We consider a behavioral SIR epidemic model to describe the action of the public health system aimed at enhancing the social distancing during an epidemic outbreak. An optimal control problem is proposed where the control acts in a specific way on the contact rate. We show that the optimal control of social distancing is able to generate a period d...
Moving from the study of plasmonic materials with relaxation, in this work we propose a fractional Abraham–Lorentz-like model of the complex permittivity of conductor media. This model extends the Ciancio–Kluitenberg, based on the Mazur–de Groot non-equilibrium thermodynamics theory (NET). The approach based on NET allows us to link the phenomenolo...
Moving from the study of plasmonic materials with relaxation, in this work we propose a fractional Abraham–Lorentz-like model of the complex permittivity of conductor media. This model extends the Ciancio–Kluitenberg, based on the Mazur–de Groot non-equilibrium thermodynamics theory (NET). The approach based on NET allows us to link the phenomenolo...
Background
The combined effects of biological variability and measurement-related errors on cancer sequencing data remain largely unexplored. However, the spatio-temporal simulation of multi-cellular systems provides a powerful instrument to address this issue. In particular, efficient algorithmic frameworks are needed to overcome the harsh trade-o...
A continuously time-varying transmission rate is suggested by many control-theoretic investigations on non-pharmaceutical interventions for mitigating the COVID-19 pandemic. However, such a continuously varying rate is impossible to implement in any human society. Here, we significantly extend a preliminary work (M. Fliess, C. Join, A. d’Onofrio, F...
Persistent epidemic can lead to the emergence of new virus strains due to virus mutations. This work is devoted to the SIR model with strain-dependence of infected individuals due to virus mutations and a continuous strain variable. Characterization of epidemic progression is obtained for a strain-dependent infectivity function in numerical simulat...
A continuously time-varying transmission rate is suggested by many control-theoretic investigations on non-pharmaceutical interventions for mitigating the COVID-19 pandemic. However, such a continuously varying rate is impossible to implement in any human society. Here, we significantly extend a preliminary work (M. Fliess, C. Join, A. d’Onofrio, F...
Responsible Research and Innovation (RRI) associated with public health emergency preparedness (PHEP) and response pose major challenges to the scientific community and civil society because a multistakeholder and interdisciplinary methodology is needed to foster public engagement. In 2017, within “Action plan on Science in Society related issues i...
![The memoryless case for p=1\documentclass[12pt]{minimal}...](publication/359248297/figure/fig2/AS:11431281360910447@1744112000060/The-memoryless-case-for-p1documentclass12ptminimal-usepackageamsmath_Q320.jpg)
![The memoryless case for p=1\documentclass[12pt]{minimal}...](publication/359248297/figure/fig3/AS:11431281361046672@1744112000282/The-memoryless-case-for-p1documentclass12ptminimal-usepackageamsmath_Q320.jpg)
In the behavioral epidemiology (BE) of infectious diseases, little theoretical effort seems to have been devoted to understand the possible effects of individuals’ behavioral responses during an epidemic outbreak in small populations. To fill this gap, here we first build general, behavior implicit, SIR epidemic models including behavioral response...
Social distancing has been enacted in order to mitigate the spread of COVID-19. Like many authors, we adopt the classic epidemic SIR model, where the infection rate is the control variable. Its differential flatness property yields ele mentary closed-form formulae for open-loop social distancing scenarios, where, for instance, the increase of the n...
We introduce a compartmental epidemic model to describe the spread of COVID–19 within a population, assuming that a vaccine is available, but vaccination is not mandatory. The model takes into account vaccine hesitancy and the refusal of vaccination by individuals, which take their decision on vaccination based on both the present and past informat...
We propose a mathematical model to investigate the effects of information–dependent vaccination behavior on meningitis transmission. The information is represented by means of information index as early proposed by d'Onofrio et al. (Theor. Popul. Biol., 2007). We perform a qualitative analysis based on stability theory, focusing to the global stabi...
We consider an ensemble of active particles, i.e., of agents endowed by internal variables u(t). Namely, we assume that the nonlinear dynamics of u is perturbed by realistic bounded symmetric stochastic perturbations acting nonlinearly or linearly. In the absence of birth, death and interactions of the agents (BDIA) the system evolution is ruled by...
Background
In Italy, in recent years, vaccination coverage for key immunizations as MMR has been declining to worryingly low levels, with large measles outbreaks. As a response in 2017, the Italian government expanded the number of mandatory immunizations introducing penalties to unvaccinated children’s families. During the 2018 general elections c...
To mitigate the harmful effects of the COVID-19 pandemic, world countries have resorted - though with different timing and intensities - to a range of interventions. These interventions and their relaxation have shaped the epidemic into a multi-phase form, namely an early invasion phase often followed by a lockdown phase, whose unlocking triggered...
In this paper we introduce a compartmental epidemic model describing the transmission of the COVID-19 disease in presence of non-mandatory vaccination.
The model takes into account the hesitancy and refusal of vaccination. To this aim, we employ the information index, which mimics the idea that individuals take their decision on vaccination based n...
In modern societies the main sources of information are Internet–based social networks. Thus, the opinion of citizens on key topics, such as vaccines, is very volatile. Here, we explore the impact of volatility on the modelling of public response to vaccine awareness campaigns for favouring vaccine uptake. We apply a quasi–steady–state approximatio...
The COVID-19 pandemic is spreading worldwide. Italy emerged early on as the country with the largest outbreak outside Asia. The outbreak in Northern Italy demonstrates that it is fundamental to contain the virus' spread at a very early stage of diffusion. At later stages, no containment measure, even if strict, can prevent the saturation of the hos...
This work considers the propagation of a tumor from the stage of a small avascular sphere in a host tissue and the progressive onset of a tumor neovasculature stimulated by a pro-angiogenic factor secreted by hypoxic cells.
The way new vessels are formed involves cell sprouting from pre-existing vessels and following a trail via a chemotactic mecha...
Background. In many European countries and the US, the burden of Covid-19 epidemic could be much lower if Governments had been able to learn from the China and Lombardy stories and to declare full lockdown without delays.
Methods. We use a simple game-theoretic framework for the strategic interaction between the Government, political oppositions an...
We propose a mathematical model to investigate the effects of information-dependent vaccination behavior on meningitis transmission. The information is represented by means of information index as early proposed in (d'Onofrio et al., Theor. pop. biol., 2007). We perform a qualitative analysis based on stability theory, focusing to the global stabil...
The onset in the last 15 years of behavioral epidemiology has opened many new avenues for epidemiological modelers. In this manuscript we first review two classes of behavioral epidemiology models for vaccine preventable diseases, namely behaviour-implicit SIR models with prevalence-dependent vaccination (at birth and among older individuals), and...
In December 2019, the first case of infection with a new virus COVID-19 (SARS-CoV-2), named coronavirus, was reported in the city of Wuhan, China. At that time, almost nobody paid any attention to it. The new pathogen, however, fast proved to be extremely infectious and dangerous, resulting in about 3–5% mortality. Over the few months that followed...
Background
The COVID-19 pandemic is spreading worldwide. Italy emerged early on as the country with the largest outbreak outside Asia. The outbreak in Northern Italy demonstrates that it is fundamental to contain the virus’ spread at a very early stage of diffusion. At later stages, no containment measure, even if strict, can prevent the saturation...
The onset in the last 15 years of behavioral epidemiology has opened many new avenues for epidemiological modelers. In this manuscript we first review two classes of behavioral epidemiology models for vaccine preventable diseases, namely behaviour-implicit SIR models with prevalence-dependent vaccination (at birth and among older individuals), and...
Reducing risky behaviour and/or avoiding sites where the risk of infection is perceived as higher-i.e. social and spatial distancing-represent the two main forms of non-pharmaceutical behavioral responses of humans to the threats of infectious diseases. Here we investigate, within a reaction-diffusion setting, a family of new models for an endemic...
Realistic stochastic modeling is increasingly requiring the use of bounded noises. In this work, properties and relationships of commonly employed bounded stochastic processes are investigated within a solid mathematical ground. Four families are object of investigation: the Sine-Wiener (SW), the Doering–Cai–Lin (DCL), the Tsallis–Stariolo–Borland...
Under voluntary vaccination, a critical role in shaping the level and trends of vaccine uptake is played by the type and structure of information that is received and used by parents of children eligible for vaccination. In this article we investigate the feedbacks of spatial mobility and the spatial structure of information on vaccination dynamics...
In this paper we consider an SIRS epidemic model under a general assumption of density-dependent mortality. We prove the global stability of the disease-free equilibrium and propose a Lyapunov function that allows to demonstrate the global stability of the (unique) endemic state under broad conditions.
![Parameters of case C1 (k=1/10\documentclass[12pt]{minimal}...](publication/328701277/figure/fig1/AS:11431281360702226@1744088903576/Parameters-of-case-C1-k1-10documentclass12ptminimal-usepackageamsmath_Q320.jpg)
![Parameters of case C2 (k=1/90\documentclass[12pt]{minimal}...](publication/328701277/figure/fig2/AS:11431281360702227@1744088903734/Parameters-of-case-C2-k1-90documentclass12ptminimal-usepackageamsmath_Q320.jpg)
![Parameters of case C3 (k=9/10\documentclass[12pt]{minimal}...](publication/328701277/figure/fig3/AS:11431281360375598@1744088903892/Parameters-of-case-C3-k9-10documentclass12ptminimal-usepackageamsmath_Q320.jpg)
In order to seek the optimal time-profiles of public health systems (PHS) Intervention to favor vaccine propensity, we apply optimal control (OC) to a SIR model with voluntary vaccination and PHS intervention. We focus on short-term horizons, and on both continuous control strategies resulting from the forward–backward sweep deterministic algorithm...
Hesitancy and refusal of vaccines preventing childhood diseases are spreading due to 'pseudo-rational' behaviours: parents overweigh real and imaginary side effects of vaccines. Nonetheless, the 'Public Health System' (PHS) may enact public campaigns to favour vaccine uptake. To determine the optimal time profiles for such campaigns, we apply the o...
We investigate the role of time heterogeneity of public health systems efforts in favoring the propensity of parents to vaccinate their newborns against a target childhood disease. The starting point of our investigation is the behavioral-epidemiology model proposed by d’Onofrio et al. (PLoS ONE 7:e45653, 2012), where the PHS effort was assumed to...
Epidemics and pandemics are natural events recurring over the time: their impact can be appropriately minimised but most countries only rely on emergency response. The European Decision 1082/2013 on serious cross-border threats to health is innovative in recognising risk communication as an essential tool in coping with public health emergencies of...
In this work we consider, from a statistical mechanics point of view, the effects of bounded stochastic perturbations of the protein decay rate for a bistable biomolecular network module. Namely, we consider the perturbations of the protein decay/binding rate constant (DBRC) in a circuit modeling the positive feedback of a transcription factor (TF)...
We provide a review of some key literature results on the influence of seasonality and other time heterogeneities of contact rates, and other parameters, such as vaccination rates, on the spread of infectious diseases. This is a classical topic where highly theoretical methodologies have provided new insight on the seemingly random behavior observe...
We extend here the game-theoretic investigation made by d'Onofrio et al (2012) on the interplay between private vaccination choices and actions of the public health system (PHS) to favor vaccine propensity in SIR-type diseases. We focus here on three important features. First, we consider a SEIR--type disease. Second, we focus on the role of season...
The mathematical and computational modelling of the spread of infectious diseases is a research field in applied mathematics that in the same time was both able to give an impetum to various areas of the dynamical systems theory and mathematical analysis, and to give an important contribution to the biological and epidemiological understanding of t...
In this paper, we consider a SEIR epidemiological model with information-related changes in contact patterns. One of the main features of the model is that it includes an information variable, a negative feedback on the behavior of susceptible subjects, and a function that describes the role played by the infectious size in the information dynamics...
An apparently ideal way to generate continuous bounded stochastic processes is to consider the stochastically perturbed motion of a point of small mass in an infinite potential well, under overdamped approximation. Here, however, we show that the aforementioned procedure can be fallacious and lead to incorrect results. We indeed provide a counter-e...
DOI:https://doi.org/10.1103/PhysRevE.94.059905
In this review we illustrate our view on the epidemiological relevance of geographically mapping cancer mortality.
In the first part of this work, after delineating the history of cancer mapping with a view on interpretation of Cancer Mortality Atlases, we briefly illustrate the ‘art’ of cancer mapping. Later we summarise in a non-mathematical way...
Historically, infectious diseases caused considerable damage to human societies, and they continue to do so today. To help reduce their impact, mathematical models of disease transmission have been studied to help understand disease dynamics and inform prevention strategies. Vaccination - one of the most important preventive measures of modern time...
Historically, infectious diseases caused considerable damage to human societies, and they continue to do so today. To help reduce their impact, mathematical models of disease transmission have been studied to help understand disease dynamics and inform prevention strategies. Vaccination - one of the most important preventive measures of modern time...
![Model 1, single cell response to DRUG(t)=1\documentclass[12pt]{minimal}...](publication/304582519/figure/fig11/AS:961841022902283@1606332178147/Model-1-single-cell-response-to-DRUGt1documentclass12ptminimal_Q320.jpg)
In this paper we analyze the impact of the stochastic fluctuation of genes between their ON and OFF states on the pharmacodynamics of a potentially large class of drugs. We focus on basic mechanisms underlying the onset of in vitro experimental dose-response curves, by investigating two elementary molecular circuits. Both circuits consist in the tr...
Several new vaccines have the characteristic of being “imperfect” that is their protection wanes over time and supplies only partial protection from infection. On the other hand recent research has shown that the agents’ behavioral responses have the potential to dramatically affect the dynamics and control of infections. In this paper we investiga...
Gene switching dynamics is a major source of randomness in genetic networks, also in the case of large concentrations of the transcription factors. In this work, we consider a common network motif - the positive feedback of a transcription factor on its own synthesis - and assess its response to extrinsic noises perturbing gene deactivation in a va...
Objective:
To review and quantify the association between endogenous and exogenous testosterone and prostate specific antigen (PSA) and prostate cancer.
Methods:
Literature searches were performed following the PRISMA guidelines. Prospective cohort studies that reported data on the associations between endogenous testosterone and prostate cancer...
This paper proposes and analyzes a discrete-time deterministic SIR model with information dependent immunization behaviour, where vaccination coverage at birth during any period of time is a general phenomenological function of the risk of infection that is perceived at the beginning of the period. Results on existence of equilibria, their local st...
Author Summary
P53 is an antitumor gene regulating vital cellular functions such as repair of DNA damage, cellular suicide, and cell proliferation: in many tumors p53 is lowly expressed and/or mutated. Drugs targeting the biomolecular network of p53 are becoming important. The network includes the key proteins Mdm2 and PTEN, whose production is reg...
In the first part of this invited paper we review the role of both extrinsic and intrinsic stochasticity in shaping the dynamics of biomolecular networks. In particular, we stress the use of bounded stochastic processes as a model of extrinsic random perturbations. In the second part, we propose three examples of molecular circuits under the influe...
To study the effects of a delayed immune-response on the growth of an immunogenic neoplasm we introduce Stochastic Hybrid Automata with delayed transitions as a representation of hybrid biochemical systems with delays. These transitions abstractly model unknown dynamics for which a constant duration can be estimated, i.e. a delay. These automata ar...
With chapters on free boundaries, constitutive equations, stochastic dynamics, nonlinear diffusion–consumption, structured populations, and applications of optimal control theory, this volume presents the most significant recent results in the field of mathematical oncology. It highlights the work of world-class research teams, and explores how dif...
This paper outlines the major components and function of the Technologically Integrated Oncosimulator developed primarily within the ACGT (Advancing Clinico Genomic Trials on Cancer) project. The Oncosimulator is defined as an information technology system simulating in vivo tumor response to therapeutic modalities within the clinical trial context...
The focus of the growing discipline of behavioral epidemiology (BE) of infectious diseases is on individual behavior as a key determinant of infection trajectories. This overview departs from the central, but static, role of human behavior in traditional mathematical models of infection to motivate the importance of including behavior into epidemio...
Three behavioral-epidemic models (i.e., epidemic systems including feedbacks (FB) that the information about an infectious disease has on its spreading) are introduced. Two relevant FB are explicitly considered: the pseudo-rational exemption to vaccination and the information-related changes in contact patterns by healthy subjects. The global stabi...
A main research area in the behavioural epidemiology (BE) of infectious diseases deals with the modelling of vaccinating behaviour under voluntary immunisation. We attempt to provide a broad overview of our research work on the subject, by separately analysing a general prevalence-based framework, where vaccine uptake is taken as a function of the...
This volume summarizes the state-of-the-art in the fast growing research area of modeling the influence of information-driven human behavior on the spread and control of infectious diseases. In particular, it features the two main and inter-related “core” topics: behavioral changes in response to global threats, for example, pandemic influenza, and...
The volume is organized in four parts. The first part presents the main kinds of bounded noises and their applications in theoretical physics. The theory of bounded stochastic processes is intimately linked to its applications to mathematical and statistical physics, and it would be difficult and unnatural to separate the theory from its physical a...
Cell polarization (cued or uncued) is a fundamental mechanism in cell biology. As an alternative to the classical Turing bifurcation, it has been proposed that the onset of cell polarity might arise by means of the well-known phenomenon of wave-pinning [Gamba et al., Proc. Natl. Acad. Sci. USA 102, 16927 (2005)]. A particularly simple and elegant d...
Tumors are a family of high-mortality diseases, each differing from the other, but all exhibiting a derangement of cellular proliferation and characterized by a remarkable lack of symptoms [52] and by time courses that, in a broad sense, may be classified as nonlinear. As a consequence, despite the enormous strides in prevention and, to a certain e...
A challenge to disease control in modern societies is the spread of pseudo-rational exemption to vaccination, as a consequence of a comparison between the steadily declining risk of infection, and the perceived risk of side effects from the vaccine. Here we consider rational exemption in an SEIR model with information dependent vaccination where in...
We consider the problem of a rational politician who gains benefit from both being popular and corrupt. In 1994, Feichtinger and Wirl studied this trade-off by means of an infinite-horizon optimal control approach. We reconsider the problem over a finite time horizon, to model the dilemma of a politician who stays in office for a limited period of...
After being considered as a nuisance to be filtered out, it became increasingly clear that noises play a complex role, often fully functional, for biochemical networks. The influence of intrinsic and extrinsic noises on these networks has intensively been investigated in the last 10 years, though contributions on the co-presence of both are sparse....
Recent deterministic models suggest that for solid and nonsolid tumors the delivery of constant continuous infusion therapy may induce multistability in the tumor size. In other words, therapy, when not able to produce tumor eradication, may at least lead to a small equilibrium that coexists with a far larger one. However, bounded stochastic fluctu...
In this work, we introduce three spatiotemporal colored bounded noises, based on the zero-dimensional Cai–Lin, Tsallis–Borland, and sine-Wiener noises. Then we study and characterize the dependence of the defined stochastic processes on both a temporal correlation parameter τ and a spatial coupling parameter λ. In particular, we found that varying...
Questions
Questions (2)
I have read some papers where chaos theory has been applied to modelling tumour dynamics. However, I do not know examples of review papers on the real use of chaos theory in Mathematical Oncology. With "real use" I mean that I am searching a review paper that is focused on published literature using chaos theory in Mathematical Oncology, not a review paper that illustrates potential applications to Mathematical Oncology of this important branch of dynamical systems theory.
Thanks in advance
Alberto
I do not know examples of review papers on the real use of chaos theory in Systems Biology. With "real use" I mean that I am searching a review paper that is focused on published literature using chaotic theory in systems Biology, not a review paper that illustrates potential applications to Systems Biology of this important branch of dynamical systems theory.
Thanks in advance
Alberto
