Relevant bibliographies by topics / Disease-free equilibrium

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Disease-free equilibrium'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Disease-free equilibrium"

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Xu, Jinhu, Wenxiong Xu, and Yicang Zhou. "Analysis of a delayed epidemic model with non-monotonic incidence rate and vertical transmission." International Journal of Biomathematics 07, no. 04 (2014): 1450041. http://dx.doi.org/10.1142/s1793524514500417.

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A delayed SEIR epidemic model with vertical transmission and non-monotonic incidence is formulated. The equilibria and the threshold of the model have been determined on the bases of the basic reproduction number. The local stability of disease-free equilibrium and endemic equilibrium is established by analyzing the corresponding characteristic equations. By comparison arguments, it is proved that, if R0 < 1, the disease-free equilibrium is globally asymptotically stable. Whereas, the disease-free equilibrium is unstable if R0 > 1. Moreover, we show that the disease is permanent if the b
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Moghadas, S. M., and A. B. Gumel. "An epidemic model for the transmission dynamics of HIV and another pathogen." ANZIAM Journal 45, no. 2 (2003): 181–93. http://dx.doi.org/10.1017/s1446181100013250.

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AbstractA five-dimensional deterministic model is proposed for the dynamics between HIV and another pathogen within a given population. The model exhibits four equilibria: a disease-free equilibrium, an HIV-free equilibrium, a pathogen-free equilibrium and a co-existence equilibrium. The existence and stability of these equilibria are investigated. A competitive finite-difference method is constructed for the solution of the non-linear model. The model predicts the optimal therapy level needed to eradicate both diseases.
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Chukwu, C. W., and F. Nyabadza. "A Theoretical Model of Listeriosis Driven by Cross Contamination of Ready-to-Eat Food Products." International Journal of Mathematics and Mathematical Sciences 2020 (March 9, 2020): 1–14. http://dx.doi.org/10.1155/2020/9207403.

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Cross contamination that results in food-borne disease outbreaks remains a major problem in processed foods globally. In this paper, a mathematical model that takes into consideration cross contamination of Listeria monocytogenes from a food processing plant environment is formulated using a system of ordinary differential equations. The model has three equilibria: the disease-free equilibrium, Listeria-free equilibrium, and endemic equilibrium points. A contamination threshold ℛwf is determined. Analysis of the model shows that the disease-free equilibrium point is locally stable for ℛwf<1
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Lu, Jinna, Xiaoguang Zhang, and Rui Xu. "Global stability and Hopf bifurcation of an eco-epidemiological model with time delay." International Journal of Biomathematics 12, no. 06 (2019): 1950062. http://dx.doi.org/10.1142/s1793524519500621.

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In this paper, an eco-epidemiological model with time delay representing the gestation period of the predator is investigated. In the model, it is assumed that the predator population suffers a transmissible disease and the infected predators may recover from the disease and become susceptible again. By analyzing corresponding characteristic equations, the local stability of each of feasible equilibria and the existence of Hopf bifurcations at the disease-free and coexistence equilibria are established, respectively. By means of Lyapunov functionals and LaSalle’s invariance principle, sufficie
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Ah, Nurul Imamah, Wuryansari Muharini Kusumawinahyu, Agus Suryanto, and Trisilowati Trisilowati. "The Dynamics of a Predator-Prey Model Involving Disease Spread In Prey and Predator Cannibalism." Jambura Journal of Biomathematics (JJBM) 4, no. 2 (2023): 119–25. http://dx.doi.org/10.37905/jjbm.v4i2.21495.

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In this article, dynamics of predator prey model with infection spread in prey and cannibalism in predator is analyzed. The model has three populations, namely susceptible prey, infected prey, and predator. It is assumed that there is no migration in both prey and predator populations. The dynamical analysis shows that the model has six equilibria, namely the trivial equilibrium point, the prey extinction point, the disease free and predator extinction equilibrium point, the disease-free equilibrium point, the predator extinction equilibrium point, and the coexistence equilibrium point. The fi
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Lotfi, El Mehdi, Mehdi Maziane, Khalid Hattaf, and Noura Yousfi. "Partial Differential Equations of an Epidemic Model with Spatial Diffusion." International Journal of Partial Differential Equations 2014 (February 10, 2014): 1–6. http://dx.doi.org/10.1155/2014/186437.

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The aim of this paper is to study the dynamics of a reaction-diffusion SIR epidemic model with specific nonlinear incidence rate. The global existence, positivity, and boundedness of solutions for a reaction-diffusion system with homogeneous Neumann boundary conditions are proved. The local stability of the disease-free equilibrium and endemic equilibrium is obtained via characteristic equations. By means of Lyapunov functional, the global stability of both equilibria is investigated. More precisely, our results show that the disease-free equilibrium is globally asymptotically stable if the ba
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A. Sabarmathi, C. Pooja ,. "A Fractional Order Approach in the Eco-epidemiological Model of Sugarcane Grassy Shoot Disease Using Controls." Tuijin Jishu/Journal of Propulsion Technology 44, no. 4 (2023): 5909–15. http://dx.doi.org/10.52783/tjjpt.v44.i4.2024.

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In this paper, an eco-epidemiological model for grassy shoot disease with controls is formed and analyzed using Fractional Differential Equations. The infection-free and endemic equilibriums of the model are obtained. Using the Next generation matrix approach, the basic reproduction number is calculated. The local stability of infection-free equilibrium for integer and fractional order is analyzed. The global stability of the equilibria is found using the Lyapunov function. The sensitive parameters which spread the grassy shoot disease are identified using sensitivity analysis.
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Mangongo Tinda, Yves, Jean-Pierre Lueteta Mulenda, and Josaphat Di-Phanzu Ndelo. "ANALYSIS OF THE DYNAMICS OF HELICOBACTER PYLORI IN THE PRESENCE OF CONCENTRATION OF CO2 AND IMMUNE SYSTEM." Journal Africain des Sciences 1, no. 1 (2024): 46–50. http://dx.doi.org/10.70237/jafrisci.2024.v1.i1.05.

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In this paper, we present a mathematical model describing the dynamics of Helicobacter pylori population in the presence of 〖CO〗_2 and the immune system. We analyze the mathematical and biological meaningful of the model. We analyze the equilibrium of the model. This analysis shows the presence of two types of equilibrium. The first one occurs in the absence of the immune response and when there is no 〖CO〗_2 in the stomach, called “disease-free equilibrium”. The second equilibriums, called “endemic equilibriums”, occur in the presence of immune response and when the concentration of 〖CO〗_2 is
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LIU, YIPING, and JING-AN CUI. "THE IMPACT OF MEDIA COVERAGE ON THE DYNAMICS OF INFECTIOUS DISEASE." International Journal of Biomathematics 01, no. 01 (2008): 65–74. http://dx.doi.org/10.1142/s1793524508000023.

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In this paper, we give a compartment model to discuss the influence of media coverage to the spreading and controlling of infectious disease in a given region. The model exhibits two equilibria: a disease-free and a unique endemic equilibrium. Stability analysis of the models shows that the disease-free equilibrium is globally asymptotically stable if the reproduction number (ℝ0), which depends on parameters, is less than unity. But if ℝ0 > 1, it is shown that a unique endemic equilibrium appears, which is asymptotically stable. On a special case, the endemic equilibrium is globally stable.
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Khan, Muhammad Altaf, Yasir Khan, Sehra Khan, and Saeed Islam. "Global stability and vaccination of an SEIVR epidemic model with saturated incidence rate." International Journal of Biomathematics 09, no. 05 (2016): 1650068. http://dx.doi.org/10.1142/s1793524516500686.

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This study considers SEIVR epidemic model with generalized nonlinear saturated incidence rate in the host population horizontally to estimate local and global equilibriums. By using the Routh–Hurwitz criteria, it is shown that if the basic reproduction number [Formula: see text], the disease-free equilibrium is locally asymptotically stable. When the basic reproduction number exceeds the unity, then the endemic equilibrium exists and is stable locally asymptotically. The system is globally asymptotically stable about the disease-free equilibrium if [Formula: see text]. The geometric approach i
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Dissertations / Theses on the topic "Disease-free equilibrium"

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Seatlhodi, Thapelo. "Mathematical modelling of HIV/AIDS with recruitment of infecteds." University of the Western Cape, 2015. http://hdl.handle.net/11394/4744.

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>Magister Scientiae - MSc<br>The influx of infecteds into a population plays a critical role in HIV transmission. These infecteds are known to migrate from one region to another, thereby having some interaction with a host population. This interactive mobility or migration causes serious public health problems. In a very insightful paper by Shedlin et al. [51], the authors discover risk factors but also beneficial factors with respect to fighting human immunodeficiency virus (HIV) transmission, in the lifestyles of immigrants from different cultural backgrounds. These associated behavioral fac
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Nemaranzhe, Lutendo. "A mathematical modeling of optimal vaccination strategies in epidemiology." University of the Western Cape, 2010. http://hdl.handle.net/11394/3065.

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Magister Scientiae - MSc<br>We review a number of compartmental models in epidemiology which leads to a nonlinear system of ordinary differential equations. We focus an SIR, SEIR and SIS epidemic models with and without vaccination. A threshold parameter R0 is identified which governs the spread of diseases, and this parameter is known as the basic reproductive number. The models have at least two equilibria, an endemic equilibrium and the disease-free equilibrium. We demonstrate that the disease will die out, if the basic reproductive number R0 < 1. This is the case of a disease-free state,
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Vyambwera, Sibaliwe Maku. "Mathematical modelling of the HIV/AIDS epidemic and the effect of public health education." Thesis, University of Western Cape, 2014. http://hdl.handle.net/11394/3360.

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>Magister Scientiae - MSc<br>HIV/AIDS is nowadays considered as the greatest public health disaster of modern time. Its progression has challenged the global population for decades. Through mathematical modelling, researchers have studied different interventions on the HIV pandemic, such as treatment, education, condom use, etc. Our research focuses on different compartmental models with emphasis on the effect of public health education. From the point of view of statistics, it is well known how the public health educational programs contribute towards the reduction of the spread of HIV/AIDS
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Maku, Vyambwera Sibaliwe. "Mathematical modeling of TB disease dynamics in a crowded population." University of the Western Cape, 2020. http://hdl.handle.net/11394/7357.

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Philosophiae Doctor - PhD<br>Tuberculosis is a bacterial infection which is a major cause of death worldwide. TB is a curable disease, however the bacterium can become resistant to the first line treatment against the disease. This leads to a disease called drug resistant TB that is difficult and expensive to treat. It is well-known that TB disease thrives in communities in overcrowded environments with poor ventilation, weak nutrition, inadequate or inaccessible medical care, etc, such as in some prisons or some refugee camps. In particular, the World Health Organization discovered that
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Batistela, Cristiane Mileo. "Modelo dinâmico de propagação de ví­rus em redes de computadores." Universidade de São Paulo, 2018. http://www.teses.usp.br/teses/disponiveis/3/3139/tde-28082018-081239/.

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Desde que os vírus de computadores tornaram-se um grave problema para sistemas individuais e corporativos, diversos modelos de disseminação de vírus têm sido usados para explicar o comportamento dinâmico da propagação desse agente infeccioso. Como estratégias de prevenção de proliferação de vírus, o uso de antivírus e sistema de vacinação, têm contribuído para a contenção da proliferação da infecção. Outra forma de combater os vírus é estabelecer políticas de prevenção baseadas nas operações dos sistemas, que podem ser propostas com o uso de modelos populacionais, como os usados em estudos epi
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Owusu, Frank K. "Mathematical modelling of low HIV viral load within Ghanaian population." Thesis, 2020. http://hdl.handle.net/10500/26903.

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Comparatively, HIV like most viruses is very minute, unadorned organism which cannot reproduce unaided. It remains the most deadly disease which has ever hit the planet since the last three decades. The spread of HIV has been very explosive and mercilessly on human population. It has tainted over 60 million people, with almost half of the human population suffering from AIDS related illnesses and death finally. Recent theoretical and computational breakthroughs in delay differential equations declare that, delay differential equations are proficient in yielding rich and plausible dynamic
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Podder, Chandra Nath. "Mathematics of HSV-2 Dynamics." 2010. http://hdl.handle.net/1993/4082.

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The thesis is based on using dynamical systems theories and techniques to study the qualitative dynamics of herpes simplex virus type 2 (HSV-2), a sexually-transmitted disease of major public health significance. A deterministic model for the interaction of the virus with the immune system in the body of an infected individual (in vivo) is designed first of all. It is shown, using Lyapunov function and LaSalle's Invariance Principle, that the virus-free equilibrium of the model is globally-asymptotically stable whenever a certain biological threshold, known as the reproduction number, is l
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Lutendo, Nemaranzhe. "A mathematical modeling of optimal vaccination strategies in epidemiology." Thesis, 2010. http://etd.uwc.ac.za/index.php?module=etd&action=viewtitle&id=gen8Srv25Nme4_1862_1363774585.

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<p>We review a number of compartmental models in epidemiology which leads to a nonlinear system of ordinary differential equations. We focus an SIR, SEIR and SIS epidemic models with and without vaccination. A threshold parameter R0 is identified which governs the spread of diseases, and this parameter is known as the basic reproductive number. The models have at least two equilibria, an endemic equilibrium and the disease-free equilibrium. We demonstrate that the disease will die out, if the basic reproductive number R0 &lt<br>1. This is the case of a disease-free&nbsp<br>state, with no infec
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Melesse, Dessalegn Yizengaw. "Mathematical Analysis of an SEIRS Model with Multiple Latent and Infectious Stages in Periodic and Non-periodic Environments." 2010. http://hdl.handle.net/1993/4086.

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The thesis focuses on the qualitative analysis of a general class of SEIRS models in periodic and non-periodic environments. The classical SEIRS model, with standard incidence function, is, first of all, extended to incorporate multiple infectious stages. Using Lyapunov function theory and LaSalle's Invariance Principle, the disease-free equilibrium (DFE) of the resulting SEI<sup>n</sup>RS model is shown to be globally-asymptotically stable whenever the associated reproduction number is less than unity. Furthermore, this model has a unique endemic equilibrium point (EEP), which is shown (using
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Book chapters on the topic "Disease-free equilibrium"

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Iyare, Egberanmwen Barry, Daniel Okuonghae, and Francis E. U. Osagiede. "Global Stability Conditions of the Disease-Free Equilibrium for a Lymphatic Filariasis Model." In Trends in Mathematics. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-25261-8_16.

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Wu, Chunqing, and Yanxin Zhang. "Stability Analysis for the Disease Free Equilibrium of a Discrete Malaria Model with Two Delays." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-31576-3_44.

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Luscombe, D. K., M. Tucker, C. J. Pepper, P. J. Nicholls, M. Sandler, and H. J. Smith. "Enzyme Inhibitors as Drugs: From Design to the Clinic." In Pre-Equilibrium Nuclear Reactions. Oxford University PressOxford, 1992. http://dx.doi.org/10.1093/oso/9780198517344.003.0001.

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Abstract Characterization of the biochemical pathways involved in many of the physiological activities which take place within the cell, and their relevance to disease processes, has resulted in the development of a number of clinically useful drugs which owe their effectiveness to the ability to inhibit a specific enzyme. This particular approach to the development of new therapeutic agents has gathered momentum over the past decade, not least because it offers a means of increasing the selectivity of a substance for a particular target site. It should be stressed that, once an enzyme system
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Regassa Cheneke, Kumama. "Forward Bifurcation and Stability Analysis." In Bifurcation Theory and Applications [Working Title]. IntechOpen, 2023. http://dx.doi.org/10.5772/intechopen.112600.

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Bifurcation is an indispensable tool to describe the behavior of the system at steady states. Recently, the forward bifurcation showed the existence of both local and global stability of equilibrium points obtained from epidemiological models. It is known that the computing process to show the global stability of endemic equilibrium is tricky. But, in this chapter, we incorporate the principles that support the simplification of computation and give the exact existence of global stability of endemic equilibrium point. The most important issue is the application of forward bifurcation diagram o
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Patel, Zalak Ashvinkumar, and Nita H. Shah. "Vertical Transmission of Syphilis With Control Treatment." In Research Anthology on Advancements in Women's Health and Reproductive Rights. IGI Global, 2022. http://dx.doi.org/10.4018/978-1-6684-6299-7.ch010.

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Syphilis is a sexually transmitted disease having different signs and symptoms with four main stages, namely primary, secondary, latent, and tertiary. Congenital (vertical) transmission of syphilis from infected mother to fetus or neonatal is still a cause of high perinatal morbidity and mortality. A model of transmission of syphilis with three different ways of transmission, namely vertical, heterosexual, and homosexual, is formulated as a system of nonlinear ordinary differential equations. Treatment is also incorporated at various stages of infection. Total male and female population is div
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Patel, Zalak Ashvinkumar, and Nita H. Shah. "Vertical Transmission of Syphilis With Control Treatment." In Mathematical Models of Infectious Diseases and Social Issues. IGI Global, 2020. http://dx.doi.org/10.4018/978-1-7998-3741-1.ch011.

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Syphilis is a sexually transmitted disease having different signs and symptoms with four main stages, namely primary, secondary, latent, and tertiary. Congenital (vertical) transmission of syphilis from infected mother to fetus or neonatal is still a cause of high perinatal morbidity and mortality. A model of transmission of syphilis with three different ways of transmission, namely vertical, heterosexual, and homosexual, is formulated as a system of nonlinear ordinary differential equations. Treatment is also incorporated at various stages of infection. Total male and female population is div
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VARSHNEY, KRISHNA GOPAL, and YOGENDRA KUMAR DWIVEDI. "A MATHEMATICAL INVESTIGATION OF SBIRS MODEL FOR MANAGING TYPHOID AND CHOLERA CO-INFECTION." In Recent Advances in Applied Science & Technology towards Sustainable Environment. NOBLE SCIENCE PRESS, 2024. https://doi.org/10.52458/9788197112492.nsp.2024.eb.ch-09.

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Typhoid and cholera transmission dynamics were studied by employing a mathematical model with optimal control strategies. Using a deterministic compartmental model, the impact of different forms of regulation was assessed and contrasted. Using the next-generation matrix, we can calculate the fitness of the virus, which serves as a measure of the epidemic's severity. Both a disease-free stable state, in which no populations are infected with typhoid and cholera, and an endemic condition, in which a co-infected population exists and is capable of transmitting the disease, are demonstrated to exi
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"Extended Compartmental Model." In Controlling Epidemics With Mathematical and Machine Learning Models. IGI Global, 2022. http://dx.doi.org/10.4018/978-1-7998-8343-2.ch005.

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In this chapter, a new compartmental model that extends the classical SIR model by incorporating various infectious stages of the COVID-19 epidemic in Sultanate of Oman for a period of 145 days is presented. This incorporates the various stages of infection such as mildly infected, moderately infected, hospitalized, and critically infected. The transmission stage of the disease is categorized as pre-symptomatic transmission, asymptomatic transmission, and symptomatic transmission. The various transmission as well as transition parameters are estimated during the period from June 4th – October
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Archunan, Govindaraju, and Renganathan Senthil. "CANCER THERAPEUTIC TARGETS: AN OVERVIEW OF DIFFERENT TYPES OF PROTEASES." In Futuristic Trends in Biotechnology Volume 3 Book 20. Iterative International Publishers, Selfypage Developers Pvt Ltd, 2024. http://dx.doi.org/10.58532/v3bjbt20p4ch2.

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In healthy cells, proteases play an important part in the execution of biological processes. Proteases and associated anti-proteases coexist in equilibrium in biological systems, and disruption of this balance results in a variety of illnesses, including cancer. Serine, cysteine, aspartate, threonine, and matrix metalloproteases are five different types of proteases that contribute to the progression of a tumor from its early stages through growth, metastasis, and eventually invasion into a new place. The term "cancer degradome" refers to a group of peptides' roles in the course of the disease
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Fraústo da Silva, J. J. R., and R. J. P. Williams. "Sodium, Potassium, and Chlorine: Osmotic Control, Electrolytic Equilibria, and Currents." In The Biological Chemistry of the Elements. Oxford University PressOxford, 2001. http://dx.doi.org/10.1093/oso/9780198508472.003.0009.

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Abstract There are large amounts of sodium, potassium, and chloride ions in sea waters but not very much in fresh waters, yet life abounds in both media and to a very good approximation it holds the internal free ion concentrations of these elements constant, not only in cells but also in the circulating fluids of higher organisms (Table 8.1). Even small deviations from normal levels in man are recognized as symptoms of malfunction or disease. (Common salt is not to be despised within organisms.)
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Conference papers on the topic "Disease-free equilibrium"

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Pinto, Carla M. A., and J. A. Tenreiro Machado. "Fractional Model for Malaria Disease." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12946.

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In this paper we study a fractional order model for malaria transmission. It is considered the integer order model proposed by Chitnis et al [1] and we generalize it up to become a fractional model. The new model is simulated for distinct values of the fractional order. Are considered two initial conditions and a set of parameter values satisfying a value of the reproduction number, R0, less than one, for the integer model. In this case, there is co-existence of a stable disease free equilibrium and an endemic equilibrium. The results are in agreement with the integer order model and reveal th
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Turnea, Marius, Mariana Rotariu, Andrei Gheorghita, Fuior Robert, and Iustina Condurache. "AN EDUCATIONAL APPROACH FOR MATHEMATICAL MODELS OF COVID-19 PROPAGATION: ODE AND NEURAL NETWOKS." In eLSE 2021. ADL Romania, 2021. http://dx.doi.org/10.12753/2066-026x-21-179.

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A special type of coronavirus responsible for respiratory illness was first discovered in Wuhan, China in December 2019 and shortly is spreading in the world. Even few vaccines have been developed, actually their effects are not completely studies during few years over a large population, and it is possible that this pandemic to be seasonal in the future, in a similar manner like the flu. An educational tool will be useful for students and research to learn the model of spreading the disease, especially for biomedical engineering students that have knowledge both about the infectious diseases
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