Stability Analysis Of Mathematical Model Research Articles

Stability Analysis of Mathematical Model of Hepatitis B Dynamics with Vaccination, Treatment and Post Exposure Prophylaxis

Stability Analysis of Mathematical Model of Hepatitis B Dynamics with Vaccination, Treatment and Post Exposure Prophylaxis

Stability Analysis of Mathematical Model of Spread of Covid19 SEIRS Type with Constant Birth Rate

The Covid19 case dated 11 November 2021 recorded that the human population died from Covid19 (143,595 people) with confirmed cases (4,249,323 cases) and active cases (9,537 cases). Based on these data, it can be concluded that COVID-19 is an acute and deadly disease. In addition to deaths, due to Covid-19, namely the increase in divorce cases, decreased income in the economy and tourism. In this study, the author made a mathematical modeling of Covid19 type as an effort to prevent the spread of Covid19. In the modeling there are human populations susceptible to Covid19 , human populations have been vaccinated , human populations have not been vaccinated , human populations are exposed , human populations are infected with Covid19 , and human populations recovered from Covid19 . The research objectives are 1) to build a mathematical model of Covid19, 2) to determine the fixed point and basic reproduction numbers, and 3) to analyze the stability of the fixed point. This type of research includes applied science research. The research procedure is 1) observing real phenomena, 2) searching literature, 3) determining variables, parameters, and assumptions in mathematical modeling, 4) building a mathematical model of Covid19, 5) analyzing the Covid19 mathematical model in the form of fixed points, basic reproduction numbers, and fixed point stability. The results of the analysis 1) the mathematical model type has a fixed point without disease and an endemic fixed point, 2) a fixed point without disease is stable for the condition , and the endemic fixed point is stable for the condition .

Stability analysis of mathematical model for spread of pest in tea plant by RKM-4 and ABM-2

Tea is an aromatic beverage, obtained from the leaves of the tree Camellia sinensis. It is one of the popular beverages. Presently it is the matter of great concern to control pest by using reduced amount of chemical fertilizer. Beneficial insects that eat dangerous insects and mites are known as predators. But both pest and predators cause huge loss in Tea production. So, in this article we have studied the tritrophic model which consists of tea plant, pest and predator. We have studied stability of positive fixed points and boundary (boundedness). For positive equilibrium point, the global stability properties are also examined. The dynamical behaviour of the system has been shown analytically as well as numerically by computer simulation. Two step Adams–Bashforth and Runge–Kutta method of fourth order has been employed in the solution and simulation of the system of non-linear ordinary differential equation of tritrophic model. The imperative feature of our proposed model is that it suggests some measures theoretically which is useful in implementing biological control strategy.

Stability analysis of mathematical model for the dynamics of diabetes mellitus and its complications in a population

This study present a mathematical model for the dynamics of diabetess and its complications in a population. The population under study was compartmentalized into healthy, susceptible, diabetic without complications, diabetic with complication and diabetic with complications undergoing treatment. The model is a system of linear ordinary differential equations. The stability of the model was investigated using Bellman and Coke method and the system was found to be stable.

Stability Analysis of Mathematical Model on HIV Infection with the Effects of Antiretroviral therapy

HIV is a retrovirus, a virus which has enzymes and can convert genetic material from RNA to DNA. Antiretroviral therapies are the treatment to make the activity of the virus slow. The purpose of this article is to develop a mathematical model of HIV infection by reviewing antiretroviral therapy, analyze the equilibrium point, and determine the effectiveness of antiretroviral therapy. There are two equilibrium points in this HIV infection model, namely infection-free equilibrium and infected equilibrium. Numerical simulations are carried out based on selected parameters showed that infection free equilibrium is reached when the effectiveness of antiretroviral therapy is 0,4 for RT inhibitor and 0,3 for Protease Inhibitor. This means that antiretroviral therapy may change infected conditions to infection free conditions.

Stability analysis of mathematical model (sirb) in the spread of cholera with vaccination and disinfection

Cholera is a disease as a kind of acute diarrhea caused by bacteria V. Cholerae. The spread of cholera can be modeled in the form of nonlinear differential equation systems with 4 variables SIRB. This paper aims to research to analyze the local stability of the equilibrium point of the dynamical population in the spread of cholera by the Routh-Hurwitz stability criterion and bifurcation method. Next Generation Matrix (NGM) method is used to get the basic reproductive numbers ( ℜ0 ) to find the local stability at the equilibrium point of the. The disease-free equilibrium point is locally asymptotically stable if ℜ0 < 1, while the endemic equilibrium point is locally asymptotically stable if ℜ0 > 1 the results of numerical simulations obtained ℜ0 = 0 0.87 indicated that the disease-free equilibrium point is locally asymptotically stable. In endemic condition ( ℜ0 > 1 ) show that increasing the rate of vaccination and disinfection can reduce the population of susceptible, infected and bacteria of V. Cholerae.

Stability analysis of mathematical model of competition in a chain of chemostats in series with delay

We study a nonlinear system of differential delay equations describing a model of a chain of two chemostats, where one contains two microbial species in competition for a single limiting nutrient and receives an external input of the less advantaged competitor, which is cultivated in an external chemostat. We obtain sufficient conditions ensuring coexistence of all the species in competition which consist in upper delay bounds.

Stability Analysis of Mathematical Model including Pathogen-Specific Immune System Response with Fractional-Order Differential Equations.

In this study, the mathematical model examined the dynamics between pathogen and specific immune system cells (memory T cells) for diseases such as chronic infection and cancer in which nonspecific immune system cells are inadequate to destroy the pathogen and has been suggested by using a system of the fractional-order differential equation with multi-orders. Qualitative analysis of the proposed model reveals the equilibrium points giving important ideas about the proliferation of the pathogen and memory T cells. According to the results of this analysis, the possible scenarios are as follows: the absence of both pathogen and memory T cells, only the existence of pathogen, and the existence of both pathogen and memory T cells. The qualitative analysis of the proposed model has expressed the persistent situations of the disease where the memory T cells either do not be able to respond to the pathogen or continue to exist with the disease-causing pathogen in the host. Results of this analysis are supported by numerical simulations. In the simulations, the time-dependent size of the tumor population under the pressure of the memory T cells was tried to be estimated.

Stability Analysis of Mathematical Model of Virus Therapy for Cancer

Stability Analysis of Mathematical Model of Virus Therapy for Cancer