Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 26 for “"Free equilibrium"”.
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Lyapunovfunctions in epidemiological modeling
… is used to analyse the stability of the disease-free equilibrium. Moreover, a matrix-theoretic method is critically examined for its capability and overall functionality in the construction and development of an appropriate Lyapunov function for the stability analysis of the nonlinear dynamical …
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Mathematical modeling of an epidemic under vaccination in two interacting populations
… Then we present the stability analysis of equilibrium points and the effect of vaccination. Our primary finding is that the behaviour of the disease free equilibrium depend on the vaccination rates of the combined population. We show that the disease free equilibrium is locally …
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Mathematical models for Tuberculosis spread in humans
… first model, R0 > 1; implying that the disease-free equilibrium is unstable. For the second model, however, R0 < 1; indicating that the disease-free equilibrium is a stable steady state and that in case of an outbreak, the disease will not spread. Simulation results also shows that increasing …
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Centre Manifold Theory for some continuous and Discrete Epidemiological models
… the population reads as follows: the disease-free equilibrium is locally asymptotically stable (LAS) when R0 < 1, it is unstable when R0 > 1 and at least one endemic equilibrium (EE) which is LAS is born in this case. In other words, at R0 = 1, a forward bifurcation occurs. However, some …
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An SCIR Model of Meningococcal Meningitis
… model shows the local stability of the disease free equilibrium, the existence of an endemic equilibrium and computation of the reproduction number, ℜ0 . Using a MATLAB program we simulate a time course of the model using parameters gathered from the World Health Organization. The numerical …
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Mathematical analysis of tuberculosis models with differential infectivity, general contact rates, migration and staged progression
… is less than unity in the models, the disease-free equilibrium is globally asymptotically stable and when the basic reproduction ratio is greater than unity, a unique endemic equilibrium exists and happens to be globally asymptotically stable under certain conditions. Direct and indirect …
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On Equilibria and Feasibility of Ecological Polynomial Dynamical Systems
… in ecological models based on the number of free-equilibrium points that can emerge in a system (i.e., equilibria that can be feasible or unfeasible as a function of model parameters). We characterize complexity by the number of free-equilibrium points generated by a model, which is a …
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Modeling the dynamics of user adoption and abandonment for a single product
… and derive the threshold quantity ℛ0. The user-free equilibrium is always present, and its stability is analyzed under the condition ℛ0 < 1. Moreover, a user-prevailing equilibrium does not exist when ℛ0 ≤ 1, but at least one user-prevailing equilibrium is guaranteed when ℛ0 > 1. We further …
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A cholera model linking between-host, within-host and environmental disease dynamics
… the existence and uniqueness of a DFE (Disease Free Equilibrium) by calculation of the Basic Reproduction number R_0, when applicable, and the existence and uniqueness of a positive EE (Endemic Equilibrium) solution. We also discuss the conditions needed to achieve local and global stability in …
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Tuberkuliozės matematinis modelis su netiesine gydymo funkcija /
… be poor. The local and global stability of the equilibrium points determine the dynamics of the proposed models. Conditions for the global stability of the disease free equilibrium are given. It plays an important role in determining if an infection can be eradicated. The basic reproduction …
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Multi-scale and multi-group modeling techniques applied to Cholera and COVID-19
… The existence and uniqueness of a DFE (Disease Free Equilibrium) are discussed in light of the number R0, when applicable, as well as the existence and uniqueness of a positive EE (Endemic Equilibrium). The conditions needed to achieve local and global stability in each system are reviewed, and …
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Mathematical Models and Stability Analysis of Cholera Dynamics
… on the stability analysis at the disease-free equilibrium which determines the short-term epidemic behavior, and the endemic equilibrium which determines the long-term disease dynamics. Particularly, we incorporate the Volterra-Lyapunov matrix theory into Lyapunov functions to facilitate …
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Epidemiological model of the transmission and spread of Hepatitis B pandemic in Ghana
… di_erential equations (ODEs). The model has two equilibrium states namely, the disease-free equilibrium Q0 and the endemic equilibrium Q*. Stability analysis indicated that the model has an epidemiological threshold parameter R0 which is defined as the expected proportion of secondary infections …
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Mathematical epidemiological models with finite time extinction : the case of African swine fever virus in wildlife areas
In Mathematical Epidemiology disease free states are commonly represented as equilibria of dynamical systems which model the respective epidemiological processes. However, in cases when the equilibrium is zero and is related to extinction (of the population), due to the uniqueness property of a …
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Modelling Infectiology and Optimal Control of Dengue Fever Disease Epidemics in Tanzania
… susceptible. The model presents two disease-free and two endemic equilibrium points. The results show that the disease-free equilibrium point is locally and globally asymptotically stable if the reproduction number is less than unity. Endemic equilibrium point is locally and globally …
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Structured deterministic models applied to malaria and other endemic diseases
… to determine the local stability of the disease free equilibrium. Global stability of the disease free equilibrium is shown analytically under certain assumptions and conditions for the existence of endemic equilibria are identified. Numerical results suggest that the incorporation of two …
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Mathematical modeling and analysis of HIV/AIDS control measures
… that in the absence of infected youths, disease-free equilibrium is achievable and is asymptotically stable. Further, we use optimal control methods to determine the necessary conditions for the optimality of intervention, and for disease eradication or control. Using Pontryagin’s Maximum …
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Calculation of temperature - oxygen fugacity tables for H₂-CO₂ gas mixtures at one atmosphere total pressure, and an investigation of the zoisite-clinozoisite transition
… experiments at 6500 bars constrain the iron-free equilibrium clinozoisite zoisite to lie below 407°C. Electron microprobe and single crystal x-ray diffraction studies of epitactically related zoisite-clinozoisite crystals grown from seeded mixtures of anorthite, calcite, hematite and silica …
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Magnetospheres of neutron stars accreting from disks
… also assume that the magnetic field is in force-free equilibrium. The validity of these simplifying assumptions for astrophysical systems is discussed in some detail. The boundary conditions on the magnetic field at the disk have been chosen to mimic the expected electrodynamic interaction …
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MODELING THE DYNAMICS OF INFECTIOUS DISEASES WITH Latency IN SPATIALLY HETEROGENEOUS Environments
… number Ro is obtained. It is shown that disease free equilibrium is globally asymptotically stable if Ro < 1, and unstable if Ro > 1. In the latter case, there is at least one interior equilibrium and the disease is uniformly persistent. For n = 2, two special cases are considered to obtain more …
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