MODELLING EPIDEMICS AND VIRUS MUTATIONS BY METHODS OF THE MATHEMATICAL KINETIC THEORY FOR ACTIVE PARTICLES

2009 ◽  
Vol 19 (supp01) ◽  
pp. 1405-1425 ◽  
Author(s):  
S. DE LILLO ◽  
M. DELITALA ◽  
M. C. SALVATORI
Keyword(s):  
Immune System ◽  
Kinetic Theory ◽  
Numerical Simulations ◽  
Mathematical Approach ◽  
Heterogeneous Distribution ◽  
Active Particles

The present study is devoted to modelling the onset and the spread of epidemics. The mathematical approach is based on the generalized kinetic theory for active particles. The modelling includes virus mutations and the role of the immune system. Moreover, the heterogeneous distribution of patients is also taken into account. The structure allows the derivation of specific models and of numerical simulations related to real systems.

FROM THE MODELING OF THE IMMUNE HALLMARKS OF CANCER TO A BLACK SWAN IN BIOLOGY

2013 ◽  
Vol 23 (05) ◽  
pp. 949-978 ◽  
Author(s):  
ABDELGHANI BELLOUQUID ◽  
ELENA DE ANGELIS ◽  
DAMIAN KNOPOFF
Keyword(s):  
Immune System ◽  
Kinetic Theory ◽  
Biological Function ◽  
Early Stage ◽  
Black Swan ◽  
Mathematical Approach ◽  
Hallmarks Of Cancer ◽  
Active Particles ◽  
Scalar Variable ◽  
Large Systems

This paper deals with the modeling of the early stage of cancer phenomena, namely mutations, onset, progression of cancer cells, and their competition with the immune system. The mathematical approach is based on the kinetic theory of active particles developed to describe the dynamics of large systems of interacting cells, called active particles. Their microscopic state is modeled by a scalar variable which expresses the main biological function. The modeling focuses on an interpretation of the immune-hallmarks of cancer.

INTERLEUKIN MATHEMATICAL MODEL OF AN IMMUNE SYSTEM

1995 ◽  
Vol 03 (03) ◽  
pp. 889-902 ◽  
Author(s):  
URSULA FORYS
Keyword(s):  
Infectious Disease ◽  
Mathematical Model ◽  
Immune System ◽  
Numerical Simulations ◽  
Basic Properties

Some generalizations of Marchuk's model of an infectious disease with respect to the role of interleukins are presented in this paper. Basic properties of the models are studied. Results of numerical simulations with different coefficients corresponding to the different forms of the disease are shown.

scholarly journals What is life? A perspective of the mathematical kinetic theory of active particles

2021 ◽  
pp. 1-46
Author(s):  
Nicola Bellomo ◽  
Diletta Burini ◽  
Giovanni Dosi ◽  
Livio Gibelli ◽  
Damian Knopoff ◽  
...  
Keyword(s):  
Kinetic Theory ◽  
Case Studies ◽  
General Framework ◽  
Living Systems ◽  
Mathematical Approach ◽  
Collective Behaviors ◽  
Research Perspectives ◽  
Active Particles ◽  
Look Ahead

The modeling of living systems composed of many interacting entities is treated in this paper with the aim of describing their collective behaviors. The mathematical approach is developed within the general framework of the kinetic theory of active particles. The presentation is in three parts. First, we derive the mathematical tools, subsequently, we show how the method can be applied to a number of case studies related to well defined living systems, and finally, we look ahead to research perspectives.

Influence of drivers ability in a discrete vehicular traffic model

2017 ◽  
Vol 28 (03) ◽  
pp. 1750030 ◽  
Author(s):  
D. Burini ◽  
S. De Lillo ◽  
G. Fioriti
Keyword(s):  
Kinetic Theory ◽  
Numerical Simulations ◽  
Traffic Flow ◽  
Stochastic Games ◽  
Traffic Model ◽  
Driving Ability ◽  
Experimental Measurements ◽  
Nonlinear Interactions ◽  
Vehicular Traffic ◽  
Active Particles

A vehicular traffic model is presented, based on the so-called Kinetic Theory of Active Particles. Vehicles are characterized by a lattice of discrete speeds and by the driving ability of the drivers. The evolution of the system is modeled through nonlinear interactions, whose output is described by stochastic games. The results of numerical simulations are consistent with experimental measurements of traffic flow.

scholarly journals A contribution to the mathematical modeling of immune-cancer competition

2018 ◽  
Vol 9 (2) ◽  
pp. 76-90
Author(s):  
Najat M. Omar Dabnoun ◽  
Maria Stella Mongiovì
Keyword(s):  
Mathematical Modeling ◽  
Immune System ◽  
Kinetic Theory ◽  
Cancer Cells ◽  
Immune Cells ◽  
Cell Populations ◽  
Spatial Homogeneity ◽  
Active Particles ◽  
Free Parameters ◽  
Discrete Values

Abstract This paper deals with the modeling of interactions between the immune system and cancer cells, in the framework of the mathematical kinetic theory for active particles. The work deepens a previous paper of Belloquid et al. that assumes spatial homogeneity and discrete values of the activity of cancer and immune cells. A number of simulations are made with the aim to investigate how the state of the various cell populations evolves in time depending on the choice of the free parameters.

scholarly journals A Continuous–Time Markov Chain Modeling Cancer–Immune System Interactions

2018 ◽  
Vol 9 (2) ◽  
pp. 106-118 ◽  
Author(s):  
Diletta Burini ◽  
Elena De Angelis ◽  
Miroslaw Lachowicz
Keyword(s):  
Markov Chain ◽  
Immune System ◽  
Kinetic Theory ◽  
Mathematical Models ◽  
Tumor Cells ◽  
Continuous Time ◽  
Microscopic Level ◽  
Continuous Time Markov Chain ◽  
Active Particles ◽  
Mesoscopic Level

Abstract In the present paper we propose two mathematical models describing, respectively at the microscopic level and at the mesoscopic level, a system of interacting tumor cells and cells of the immune system. The microscopic model is in terms of a Markov chain defined by the generator, the mesoscopic model is developed in the framework of the kinetic theory of active particles. The main result is to prove the transition from the microscopic to mesoscopic level of description.

On the modeling of epidemics under the influence of risk perception

2017 ◽  
Vol 28 (04) ◽  
pp. 1750051 ◽  
Author(s):  
S. De Lillo ◽  
G. Fioriti ◽  
M. L. Prioriello
Keyword(s):  
Risk Perception ◽  
Kinetic Theory ◽  
Numerical Simulations ◽  
Stochastic Games ◽  
Initial Conditions ◽  
Nonlinear Interactions ◽  
Epidemic Spreading ◽  
Spreading Model ◽  
Active Particles

An epidemic spreading model is presented in the framework of the kinetic theory of active particles. The model is characterized by the influence of risk perception which can reduce the diffusion of infection. The evolution of the system is modeled through nonlinear interactions, whose output is described by stochastic games. The results of numerical simulations are discussed for different initial conditions.

FROM METHODS OF THE MATHEMATICAL KINETIC THEORY FOR ACTIVE PARTICLES TO MODELING VIRUS MUTATIONS

2011 ◽  
Vol 21 (supp01) ◽  
pp. 843-870 ◽  
Author(s):  
M. DELITALA ◽  
P. PUCCI ◽  
M. C. SALVATORI
Keyword(s):  
Immune System ◽  
Kinetic Theory ◽  
Qualitative Analysis ◽  
General Framework ◽  
Mathematical Problem ◽  
System Control ◽  
Well Posedness ◽  
Virus Prevalence ◽  
Active Particles ◽  
Different Levels

The paper presents a model of virus mutations and evolution of epidemics in a system of interacting individuals, where the intensity of the pathology, described by a real discrete positive variable, is heterogeneously distributed, and the virus is in competition with the immune system or therapeutical actions. The model is developed within the framework of the Kinetic Theory of Active Particles. The paper also presents a qualitative analysis developed to study the well-posedness of the mathematical problem associated to the general framework. Finally, simulations show the ability of the model to predict some interesting emerging phenomena, such as the mutation to a subsequent virus stage, the heterogeneous evolution of the pathology with the co-presence of individual carriers of the virus at different levels of progression, and the presence of oscillating time phases with either virus prevalence or immune system control.

PERAN IBU DALAM PENINGKATAN SISTEM IMUN ANAK DENGAN INFEKSI SALURAN PERNAFASAN AKUT

2019 ◽  
Vol 11 (2) ◽  
pp. 79-86
Author(s):  
Cindy Ayustin Noya ◽  
Angkit Kinasih ◽  
Venti Agustina ◽  
R.Rr Maria Dyah Kurniasari
Keyword(s):  
Immune System ◽  
Acute Respiratory Infection ◽  
Lower Respiratory Tract ◽  
Research Method ◽  
Respiratory Infections ◽  
Acute Respiratory Infections ◽  
Clean Environment ◽  
History Of ◽  
Qualitative Descriptive

Infeksi saluran pernafasan akut atau yang sering disebut ISPA merupakan infeksi pada saluran pernafasan baik saluran pernafasan atas atau bawah.ISPA juga kebanyakan terjadi pada anak balita karena daya tahan tubuh mereka tidak kuat dalam menghadapi penyakit ISPA. ISPA mengakibatkan kematiansekitar15%-20% per tahun pada usia balita di Negara berkembang. Tujuan penelitian ini adalah untuk mengetahui dan menganalisa peran ibu dalam meningkatkan sistem imun anak dengan ISPA.Metode penelitian yang digunakan dalam penelitian ini adalah kualitatif deskriptif dengan sampel purposive sampling.Populasi dan sampel penelitian ini adalah ibu yang mempunyai anak dengan riwayat dan saat ini menderita penyakit ISPA di Batu Gajah Kota Ambon.Partisipan dalam penelitian ini berjumlah 5 orang. Hasil dari penelitian mendapati 4 kategori yaitu pemberian nutrisi pada anak untuk memenuhi kebutuhan agar sistem imunnya terjaga, kebersihan lingkungan, peran ibu dalam melakukan pencegahan pada anaknya yang mengalami ISPA, dan  peran ibu dalam menjaga dan mempertahankan kesehatan anaknya.   Kata kunci: peran ibu, sistem imun, ispa THE ROLE OF MOTHERS IN INCREASING IMMUNE SYSTEM OF CHILDREN WITH ACUTE RESPIRATORY INFECTION    ABSTRACT Acute respiratory infections or often called ARI is an infection of the upper or lower respiratory tract. ARI occurs mostly in children under the age of five because their endurance is not strong in dealing with ARI. ARI results in deaths of around 15%-20% per year at the age of under-five in developing countries. The purpose of this study was to determine and analyze the role of mothers in improving the immune system of children against ARI. The research method used in this study was qualitative descriptive with a purposive sampling sample. Respondents and samples of this study were five mothers who had children with a history of ARI and currently suffering from the disease in Batu Gajah, Ambon City. The results of the study found 4 categories, namely providing nutrition to children to meet their needs so that their immune systems are maintained, clean environment, mother's role in preventing children with ARI, and mother's role to preserve and maintain the health of their children. The findings indicated that in terms of coping or improving the immune system of a child to avoid ARI, it is necessary to have role the of mothers in providing nutrition so that the immune system is boosted, besides that the mother can prevent and protect her child from various diseases, especially ARI. Keywords: role of mothers, immune system, acute respiratory infections

Sign in / Sign up

Export Citation Format

Share Document