Current Search: Tuncer, Necibe (x)
View All Items
- Title
- Dynamics of low and high pathogenic avian influenza in wild and domestic bird populations.
- Creator
- Tuncer, Necibe, Torres, Juan, Martcheva, Maia, Barfield, Michael, Holt, Robert D.
- Date Issued
- 2016-01-14
- PURL
- http://purl.flvc.org/fau/fd/FAUIR000194
- Format
- Citation
- Title
- Identifiability Analysis of the H1N1 Influenza and COVID-19 Viruses.
- Creator
- Sreejithkumar, Vivek, Tuncer, Necibe, Harriet L. Wilkes Honors College, Florida Atlantic University
- Abstract/Description
-
Mathematics is useful in modeling biological phenomena, such as the spread of infectious diseases in a population. This research applies mathematical modeling to investigate the spread of H1N1 influenza in the U.S. and COVID-19 in Florida. The model parameters represent epidemiological characteristics of the disease and validating the model with data allows for the estimation of model parameter values. The identifiability of the model, or the reliability of parameter estimates, is determined...
Show moreMathematics is useful in modeling biological phenomena, such as the spread of infectious diseases in a population. This research applies mathematical modeling to investigate the spread of H1N1 influenza in the U.S. and COVID-19 in Florida. The model parameters represent epidemiological characteristics of the disease and validating the model with data allows for the estimation of model parameter values. The identifiability of the model, or the reliability of parameter estimates, is determined with Monte Carlo simulations. This research demonstrated successful curve-fitting of H1N1 influenza and COVID-19 data to a mathematical model and generating identifiable parameter estimations. Furthermore, this research quantified the effectiveness of social distancing in preventing COVID-19 spread and demonstrated that social distancing prevented about 185,000 weekly COVID-19 incidences and about 8,500 weekly deaths. Using mathematical modeling, epidemiologists and public health officials can possibly direct the implementation of disease control measures such as vaccines, treatments, mask-wearing, and social distancing.
Show less - Date Issued
- 2022
- PURL
- http://purl.flvc.org/fau/fd/FAUHT00218
- Format
- Document (PDF)
- Title
- INFECTION AGE STRUCTURED VECTOR BORNE DISEASE MODEL WITH DIRECT TRANSMISSION.
- Creator
- Giri, Sunil, Tuncer, Necibe, Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
- Abstract/Description
-
Mathematical modeling is a powerful tool to study and analyze the disease dynamics prevalent in the community. This thesis studies the dynamics of two time since infection structured vector borne models with direct transmission. We have included disease induced death rate in the first model to form the second model. The aim of this thesis is to analyze whether these two models have same or different disease dynamics. An explicit expression for the reproduction number denoted by R0 is derived....
Show moreMathematical modeling is a powerful tool to study and analyze the disease dynamics prevalent in the community. This thesis studies the dynamics of two time since infection structured vector borne models with direct transmission. We have included disease induced death rate in the first model to form the second model. The aim of this thesis is to analyze whether these two models have same or different disease dynamics. An explicit expression for the reproduction number denoted by R0 is derived. Dynamical analysis reveals the forward bifurcation in the first model. That is when the threshold value R0 < 1, disease free-equilibrium is stable locally implying that if there is small perturbation of the system, then after some time, the system will return to the disease free equilibrium. When R0 > 1 the unique endemic equilibrium is locally asymptotically stable. For the second model, analysis of the existence and stability of equilibria reveals the existence of backward bifurcation i.e. where the disease free equilibrium coexists with the endemic equilibrium when the reproduction number R02 is less than unity. This aspect shows that in order to control vector borne disease, it is not sufficient to have reproduction number less than unity although necessary. Thus, the infection can persist in the population even if the reproduction number is less than unity. Numerical simulation is presented to see the bifurcation behaviour in the model. By taking the reproduction number as the bifurcation parameter, we find the system undergoes backward bifurcation at R02 = 1. Thus, the model has backward bifurcation and have two positive endemic equilibrium when R02 < 1 and unique positive endemic equilibrium whenever R02 > 1. Stability analysis shows that disease free equilibrium is locally asymptotically stable when R02 < 1 and unstable when R02 > 1. When R02 < 1, lower endemic equilibrium in backward bifurcation is locally unstable.
Show less - Date Issued
- 2020
- PURL
- http://purl.flvc.org/fau/fd/FA00013552
- Subject Headings
- Vector Borne Diseases, Mathematical models, Simulations, Dynamics--Mathematical models
- Format
- Document (PDF)
- Title
- IDENTIFIABILITY ANALYSIS AND OPTIMAL CONTROL OF INFECTIOUS DISEASES EPIDEMICS AND PARAMETERIZATION METHOD FOR (UN)STABLE MANIFOLDS OF IMPLICITLY DEFINED DYNAMICAL SYSTEMS.
- Creator
- Neupane Timsina, Archana, Tuncer, Necibe, Mireles James, Jason D., Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
- Abstract/Description
-
This dissertation is a study about applied dynamical systems on two concentrations. First, on the basis of the growing association between opioid addiction and HIV infection, a compartmental model is developed to study dynamics and optimal control of two epidemics; opioid addiction and HIV infection. We show that the disease-free-equilibrium is locally asymptotically stable when the basic reproduction number R0 = max(Ru0; Rv0) 1 and it is locally asymptotically stable when the invasion...
Show moreThis dissertation is a study about applied dynamical systems on two concentrations. First, on the basis of the growing association between opioid addiction and HIV infection, a compartmental model is developed to study dynamics and optimal control of two epidemics; opioid addiction and HIV infection. We show that the disease-free-equilibrium is locally asymptotically stable when the basic reproduction number R0 = max(Ru0; Rv0) < 1; here Rv0 is the reproduction number of the HIV infection, and Ru0 is the reproduction number of the opioid addiction. The addiction-only boundary equilibrium exists when Ru0 > 1 and it is locally asymptotically stable when the invasion number of the opioid addiction is Ruinv < 1: Similarly, HIV-only boundary equilibrium exists when Rv0 > 1 and it is locally asymptotically stable when the invasion number of the HIV infection is Rvinv < 1. We study structural identifiability of the parameters, estimate parameters employing yearly reported data from Central for Disease Control and Prevention (CDC), and study practical identifiability of estimated parameters. We observe the basic reproduction number R0 using the parameters. Next, we introduce four distinct controls in the model for the sake of control approach, including treatment for addictions, health care education about not sharing syringes, highly active anti-retroviral therapy (HAART), and rehab treatment for opiate addicts who are HIV infected. US population using CDC data, first applying a single control in the model and observing the results, we better understand the influence of individual control. After completing each of the four applications, we apply them together at the same time in the model and compare the outcomes using different control bounds and state variable weights. We conclude the results by presenting several graphs.
Show less - Date Issued
- 2022
- PURL
- http://purl.flvc.org/fau/fd/FA00013970
- Subject Headings
- Dynamical systems, Infectious diseases, Parameter estimation
- Format
- Document (PDF)