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 20 for “"Disease-free equilibrium"”.
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Lyapunovfunctions in epidemiological modeling
… method” 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 …
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Mathematical modeling of an epidemic under vaccination in two interacting populations
… by S, who are uninfected but may contract the disease, infected individuals (I) who are infected and can spread the disease to the susceptible individuals and the class (R) of recovered individuals. If a susceptible individual becomes infected, it moves into the infected class. An infected …
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Mathematical models for Tuberculosis spread in humans
… the next generation method and conditions for disease elimination/persistence are determined. Numerical simulation results show that for the first model, R0 > 1; implying that the disease-free equilibrium is unstable. For the second model, however, R0 < 1; indicating that the disease-free …
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Centre Manifold Theory for some continuous and Discrete Epidemiological models
… host population. In this setting and for many diseases, the prediction of the likelihood of persistence or dying out of the disease within 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 …
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An SCIR Model of Meningococcal Meningitis
… of the 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 …
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Mathematical analysis of tuberculosis models with differential infectivity, general contact rates, migration and staged progression
… ratio 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 …
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A cholera model linking between-host, within-host and environmental disease dynamics
… Vibrio cholerae bacteria. The dynamics of the disease transmission are governed by human-human, environment-human, and within-human sub-dynamics. In this paper, a model is presented to incorporate all three of these dynamical components. The model is divided into three subgroups where the …
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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
… Vibrio cholerae bacteria. The dynamics of the disease transmission are governed by human-human, environment-human, and within-human sub-dynamics. Specifically, the within-host dynamics incorporate virus and immune cell interaction with the vibrios. One model is presented to incorporate all …
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Mathematical Models and Stability Analysis of Cholera Dynamics
… our attention 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 …
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Epidemiological model of the transmission and spread of Hepatitis B pandemic in Ghana
… or misconceptions and stigmatisation about the disease and worsened the disease prevalence in Ghana a Sub-Saharan African country. As a contribution, this study employed a SEIR deterministic compartmental model, which incorporates latent period and vertical transmission, to examine the …
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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
… infectiology and optimal control of dengue fever disease epidemics in Tanzania is formulated and analysed. The model describes the interaction between human and dengue fever mosquito populations with treatment. Susceptible human population is divided into two, namely, careful and careless …
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Structured deterministic models applied to malaria and other endemic diseases
… models. These models are used to study the disease dynamics of malaria or the joint disease dynamics of HIV and HSV-2. Each of the models includes multiple components containing individuals in various epidemiological classes for the purpose of addressing questions that are of interests to …
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Mathematical modeling and analysis of HIV/AIDS control measures
… that can minimize or prevent the spread of the disease in the population. In particular, we are interested in the effects of public-health education and of parental care.We consider existing models of public-health education in HIV/AIDS epidemi-ology, and provide some new insights on these. In …
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MODELING THE DYNAMICS OF INFECTIOUS DISEASES WITH Latency IN SPATIALLY HETEROGENEOUS Environments
Assuming that an infectious disease has a fixed latent period and latent individuals in the population may disperse in a spatially heterogeneous environment, we derive three new models of SIR type, which are more realistic than the existing related ones. The first one considers a 2-patch …
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Mathematical modeling of foot and mouth disease (FMD) in Cattle and Buffaloes using vaccination and culling: A Namibia perspective
Foot and mouth disease (FMD) is an acute, infectious viral disease for animals, and it is one of the most rapidly spreading diseases worldwide. Countries worldwide are putting efforts to curb the infection as it has devastating effects on agriculture and wildlife economies. Mathematical models have …
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Mathematical modelling of the HIV/AIDS epidemic and the effect of public health education
… education campaign. We study the existence of equilibrium points and their stability. Original contributions of this dissertation are the modifications on the model of Cai et al. [1], which enables us to use optimal control theory to identify optimal roll-out of strategies to control the …
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A discrete-time waning immunity model for the spread of an immune escape pathogen
… oscillations in infections about the endemic equilibrium. In Chapter 4, motivated by the surges in hospitalisations associated with the surges in Omicron infections in the community, we investigate whether surges in Omicron infections in a population can be suppressed by vaccination. We …
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Mathematical modelling to investigate the impact of awareness programs on the spread of HIV/AIDS amongst people who inject drugs (PWIDs)
… initiatives on the spread and containment of disease (Greenhalgh et al. 2015). In this thesis, we consider the effect of an awareness program on the dynamic behaviour of the spread of HIV/AIDS amongst PWIDs. The HIV/AIDS model can be modelled using the SIS and SIR models with time-varying …