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 A mathematical model of infectious disease transmission

2020 ◽  
Vol 34 ◽  
pp. 02002
Author(s):  
Aurelia Florea ◽  
Cristian Lăzureanu
Keyword(s):  
Infectious Disease ◽  
Mathematical Model ◽  
Nonlinear System ◽  
Numerical Simulations ◽  
Disease Transmission ◽  
Three Dimensional ◽  
Type System ◽  
Epidemic Disease ◽  
Infectious Disease Transmission ◽  
The Stability

In this paper we consider a three-dimensional nonlinear system which models the dynamics of a population during an epidemic disease. The considered model is a SIS-type system in which a recovered individual automatically becomes a susceptible one. We take into account the births and deaths, and we also consider that susceptible individuals are divided into two groups: non-vaccinated and vaccinated. In addition, we assume a medical scenario in which vaccinated people take a special measure to quarantine their newborns. We study the stability of the considered system. Numerical simulations point out the behavior of the considered population.

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.

scholarly journals The The Dynamics of a Prey-Predator Model with Infectious Disease in Prey: Role of Media Coverage

2021 ◽  
pp. 4930-4952
Author(s):  
Wassan Hussein ◽  
Huda Abdul Satar
Keyword(s):  
Infectious Disease ◽  
Global Stability ◽  
Numerical Simulations ◽  
Functional Response ◽  
Media Coverage ◽  
Epidemiological Model ◽  
Local Bifurcation ◽  
Predator Model ◽  
Disease In Prey

In this paper, an eco-epidemiological model with media coverage effect is proposed and studied. A prey-predator model with modified Leslie-Gower and functional response is studied. An  -type of disease in prey is considered.  The existence, uniqueness and boundedness of the solution of the model are discussed. The local and global stability of this system are carried out. The conditions for the persistence of all species are established. The local bifurcation in the model is studied. Finally, numerical simulations are conducted to illustrate the analytical results.

scholarly journals Notch signaling and taxis mechanims regulate early stage angiogenesis: A mathematical and computational model

2019 ◽  
Author(s):  
Rocío Vega ◽  
Manuel Carretero ◽  
Rui D.M. Travasso ◽  
Luis L. Bonilla
Keyword(s):  
Mathematical Model ◽  
Wound Healing ◽  
Numerical Simulations ◽  
Notch Signaling ◽  
Blood Vessels ◽  
Crucial Role ◽  
Early Stage ◽  
Tissue Mechanics ◽  
Organ Development

AbstractDuring angiogenesis, new blood vessels sprout and grow from existing ones. This process plays a crucial role in organ development and repair, in wound healing and in numerous pathological processes such as cancer progression or diabetes. Here, we present a mathematical model of early stage angiogenesis that permits exploration of the relative importance of mechanical, chemical and cellular cues. Endothelial cells proliferate and move over an extracellular matrix by following external gradients of Vessel Endothelial Growth Factor, adhesion and stiffness, which are incorporated to a Cellular Potts model with a finite element description of elasticity. The dynamics of Notch signaling involving Delta-4 and Jagged-1 ligands determines tip cell selection and vessel branching. Through their production rates, competing Jagged-Notch and Delta-Notch dynamics determine the influence of lateral inhibition and lateral induction on the selection of cellular phenotypes, branching of blood vessels, anastomosis (fusion of blood vessels) and angiogenesis velocity. Anastomosis may be favored or impeded depending on the mechanical configuration of strain vectors in the ECM near tip cells. Numerical simulations demonstrate that increasing Jagged production results in pathological vasculatures with thinner and more abundant vessels, which can be compensated by augmenting the production of Delta ligands.Author SummaryAngiogenesis is the process by which new blood vessels grow from existing ones. This process plays a crucial role in organ development, in wound healing and in numerous pathological processes such as cancer growth or in diabetes. Angiogenesis is a complex, multi-step and well regulated process where biochemistry and physics are intertwined. The process entails signaling in vessel cells being driven by both chemical and mechanical mechanisms that result in vascular cell movement, deformation and proliferation. Mathematical models have the ability to bring together these mechanisms in order to explore their relative relevance in vessel growth. Here, we present a mathematical model of early stage angiogenesis that is able to explore the role of biochemical signaling and tissue mechanics. We use this model to unravel the regulating role of Jagged, Notch and Delta dynamics in vascular cells. These membrane proteins have an important part in determining the leading cell in each neo-vascular sprout. Numerical simulations demonstrate that increasing Jagged production results in pathological vasculatures with thinner and more abundant vessels, which can be compensated by augmenting the production of Delta ligands.

Concept of Rasayana Therapy in Covid 19

2020 ◽  
Vol 11 (SPL1) ◽  
pp. 857-861
Author(s):  
Tikeshwar Darwate ◽  
Shamli Hiware
Keyword(s):  
Infectious Disease ◽  
Immune System ◽  
Physical Health ◽  
Essential Role ◽  
Vital Role ◽  
State Of Health ◽  
Healthy Individuals ◽  
Prolongation Of Life

An Ayurveda is an ancient system of medicine. The primary purpose of Ayurveda is to maintain the health of healthy individuals and cure the disease of the diseased one. 'Rasayanchikitsa’ plays a vital role in keeping the health of an individual. Rasayanchikitsa also plays an essential role in infectious disease which spreads directly or indirectly from man to man, animal to animal or from the environment to animal or man. Rasayana promotes physical health, improve dhatus (tissues), acts as immunomodulation and rejuvenate the system. Rasayana, by its name, means obtaining good qualities of rasa & nourishing the rasadidhatus(tissues). The excellent quality of rasa directly governs the state of health of individuals. Rasayana therapy deals with the delaying process of ageing, prolongation of life and curing the disease. Acharya Sushruta says, "for better results, Rasayan therapy should be done after Panchakarma procedures like Vaman, Virechan and Basti depending on the individual's Vata, pitta and Kapha predominance. Strength, improving complexion, prolongation of life, energy, enhancing memory, immunity booster, etc. is obtained from Rasayan therapy. Rasayan drugs help by modulating the neuro-endocrine-immune system and also a rich source of antioxidants. Review of the role of rasayan in the prevention of new infectious disease like Covid 19.

scholarly journals Modelling immune system dynamics: the interaction of HIV and recombinant virus

2015 ◽  
Vol 56 ◽  
pp. 30-35
Author(s):  
Ugnė Jankauskaitė ◽  
Olga Štikonienė
Keyword(s):  
Mathematical Model ◽  
Immune System ◽  
Numerical Simulations ◽  
Recombinant Virus ◽  
Time Delays ◽  
Dynamical Behavior ◽  
Hopf Bifurcations ◽  
Stability Switches ◽  
Discrete Delays ◽  
Theoretical Results

We investigate the dynamical behavior of a mathematical model of HIV and recombinant rabies virus (RV), designed to infect only the lymphocytes previously infected by HIV. This model is described by five ordinary differential equations with two discrete delays. The effect of two time delays on stability of the equilibria of the system has been studied. Stability switches and Hopf bifurcations when time delays cross through some critical values are found. Numerical simulations are performed to illustrate the theoretical results.

scholarly journals Modelling the effects of phylogeny and body size on within-host pathogen replication and immune response

2017 ◽  
Vol 14 (136) ◽  
pp. 20170479 ◽  
Author(s):  
Soumya Banerjee ◽  
Alan S. Perelson ◽  
Melanie Moses
Keyword(s):  
Infectious Disease ◽  
Immune Response ◽  
Immune System ◽  
Body Size ◽  
Zoonotic Diseases ◽  
Passerine Species ◽  
Host Pathogen ◽  
Host Phylogeny ◽  
Multiple Species

Understanding how quickly pathogens replicate and how quickly the immune system responds is important for predicting the epidemic spread of emerging pathogens. Host body size, through its correlation with metabolic rates, is theoretically predicted to impact pathogen replication rates and immune system response rates. Here, we use mathematical models of viral time courses from multiple species of birds infected by a generalist pathogen (West Nile Virus; WNV) to test more thoroughly how disease progression and immune response depend on mass and host phylogeny. We use hierarchical Bayesian models coupled with nonlinear dynamical models of disease dynamics to incorporate the hierarchical nature of host phylogeny. Our analysis suggests an important role for both host phylogeny and species mass in determining factors important for viral spread such as the basic reproductive number, WNV production rate, peak viraemia in blood and competency of a host to infect mosquitoes. Our model is based on a principled analysis and gives a quantitative prediction for key epidemiological determinants and how they vary with species mass and phylogeny. This leads to new hypotheses about the mechanisms that cause certain taxonomic groups to have higher viraemia. For example, our models suggest that higher viral burst sizes cause corvids to have higher levels of viraemia and that the cellular rate of virus production is lower in larger species. We derive a metric of competency of a host to infect disease vectors and thereby sustain the disease between hosts. This suggests that smaller passerine species are highly competent at spreading the disease compared with larger non-passerine species. Our models lend mechanistic insight into why some species (smaller passerine species) are pathogen reservoirs and some (larger non-passerine species) are potentially dead-end hosts for WNV. Our techniques give insights into the role of body mass and host phylogeny in the spread of WNV and potentially other zoonotic diseases. The major contribution of this work is a computational framework for infectious disease modelling at the within-host level that leverages data from multiple species. This is likely to be of interest to modellers of infectious diseases that jump species barriers and infect multiple species. Our method can be used to computationally determine the competency of a host to infect mosquitoes that will sustain WNV and other zoonotic diseases. We find that smaller passerine species are more competent in spreading the disease than larger non-passerine species. This suggests the role of host phylogeny as an important determinant of within-host pathogen replication. Ultimately, we view our work as an important step in linking within-host viral dynamics models to between-host models that determine spread of infectious disease between different hosts.

scholarly journals Mathematical Model of Antiviral Immune Response against the COVID-19 Virus

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1356
Author(s):  
Juan Carlos Chimal-Eguia
Keyword(s):  
Mathematical Model ◽  
Immune Response ◽  
Immune System ◽  
Adaptive Immune Response ◽  
Humoral Response ◽  
Antiviral Immune Response ◽  
Infection Dynamics ◽  
Current Outbreak ◽  
Delay Differential

This work presents a mathematical model to investigate the current outbreak of the coronavirus disease 2019 (COVID-19) worldwide. The model presents the infection dynamics and emphasizes the role of the immune system: both the humoral response as well as the adaptive immune response. We built a mathematical model of delay differential equations describing a simplified view of the mechanism between the COVID-19 virus infection and the immune system. We conduct an analysis of the model exploring different scenarios, and our numerical results indicate that some theoretical immunotherapies are successful in eradicating the COVID-19 virus.

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

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