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Articles 1 - 9 of 9
Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
Modeling Covid-19 Spread And Effects Of Non-Pharmaceutical Interventions On A College Campus, Jakob Kotas, Priscilla Perey Ratonel
Modeling Covid-19 Spread And Effects Of Non-Pharmaceutical Interventions On A College Campus, Jakob Kotas, Priscilla Perey Ratonel
CODEE Journal
We consider an extension to the classical SIR compartmental model from mathematical epidemiology as applied to the spread of COVID-19 on a college campus. While the classical SIR model does not allow for recovered individuals to lose immunity, we alter the equations to allow for such (due to the rise of new variants), leading to a SIRS-type model. We study the system of ODEs analytically and through numerical simulation. Finally we discuss a quantitative approach for how college administrators can decide when to implement stricter non-pharmaceutical interventions (social distancing, mask mandates, quarantine, etc.) to eradicate the infection from the campus …
A Mathematical Modeling Approach To Investigate The Impacts Of Post-Infection Mortality And Partial Immunity On Disease Endemicity, Brendan M. Shrader
A Mathematical Modeling Approach To Investigate The Impacts Of Post-Infection Mortality And Partial Immunity On Disease Endemicity, Brendan M. Shrader
Honors Undergraduate Theses
A number of infectious diseases cause post-infection conditions or complications, such as COVID- 19, Q fever, and Polio. These conditions result in recovered individuals having a higher mortality rate than susceptibles, and this can impact disease dynamics. An existing mass-action model in the literature that incorporated post-infection mortality was shown to have limit cycles, or persistent oscillations, in the infected population. To better understand what causes these limit cycles, we develop and analyze a new epidemiological model with standard incidence. We show standard results, including the existence, uniqueness, and stability of the disease-free and endemic equilibria, and we rule out …
Using A Degree-Based Network Model To Understand And Control Traffic Jams In The Atlanta Metropolitan Area, Ian Salamone-Lent, Theresa Washington, Asma Azizi
Using A Degree-Based Network Model To Understand And Control Traffic Jams In The Atlanta Metropolitan Area, Ian Salamone-Lent, Theresa Washington, Asma Azizi
The Kennesaw Journal of Undergraduate Research
Traffic congestion is an enduring problem for major metropolitan areas, such as Atlanta, GA. Our goal is to understand the nature of traffic congestion patterns in the highway system of Cobb County in Atlanta, GA. We created a road network representative of the Cobb County highway system and then superimposed a degree-based SIR model to simulate traffic congestion on that network. The model’s parameters, propagation and dissipation rates, were estimated using empirical traffic data, which are vehicles’ speed time series and speed limit of each road in the network. We then conducted a local sensitivity analysis of the model’s key …
(Si10-057) Effect Of Time-Delay On An Sir Type Model For Infectious Diseases With Saturated Treatment, R. P. Gupta, Arun Kumar
(Si10-057) Effect Of Time-Delay On An Sir Type Model For Infectious Diseases With Saturated Treatment, R. P. Gupta, Arun Kumar
Applications and Applied Mathematics: An International Journal (AAM)
This study presents the complex dynamics of an SIR epidemic model incorporating a constant time-delay in incidence rate with saturated type of treatment rate. The system is studied to observe the effect of time lag in the asymptotic stability of endemic equilibrium states. We also establish global asymptotic stability of both disease-free and endemic equilibrium states by Lyapunov direct method with the help of suitable Lyapunov functionals. The existences of periodic solutions are ensured for the suitable choice of delay parameter. Finally, we perform numerical simulations supporting the analytical findings as well as to observe the effect of time-delay. The …
Analysis Of Sir Epidemic Models With Sociological Phenomenon, Robert F. Allen, Katherine C. Heller, Matthew A. Pons
Analysis Of Sir Epidemic Models With Sociological Phenomenon, Robert F. Allen, Katherine C. Heller, Matthew A. Pons
Spora: A Journal of Biomathematics
We propose two SIR models which incorporate sociological behavior of groups of individuals. It is these differences in behaviors which impose different infection rates on the individual susceptible populations, rather than biological differences. We compute the basic reproduction number for each model, as well as analyze the sensitivity of R0 to changes in sociological parameter values.
Flattening The Curve: The Effects Of Intervention Strategies During Covid-19, Kelly A. Reagan, Rachel J. Pryor, Gonzalo M. Bearman, David M. Chan
Flattening The Curve: The Effects Of Intervention Strategies During Covid-19, Kelly A. Reagan, Rachel J. Pryor, Gonzalo M. Bearman, David M. Chan
Spora: A Journal of Biomathematics
COVID-19 has plagued countries worldwide due to its infectious nature. Social distancing and the use of personal protective equipment (PPE) are two main strategies employed to prevent its spread. A SIR model with a time-dependent transmission rate is implemented to examine the effect of social distancing and PPE use in hospitals. These strategies’ effect on the size and timing of the peak number of infectious individuals are examined as well as the total number of individuals infected by the epidemic. The effect on the epidemic of when social distancing is relaxed is also examined. Overall, social distancing was shown to …
Modeling The Effects Of Passive Immunity In Birds For The Disease Dynamics Of West Nile Virus, Noelle West, Vinodh K. Chellamuthu
Modeling The Effects Of Passive Immunity In Birds For The Disease Dynamics Of West Nile Virus, Noelle West, Vinodh K. Chellamuthu
Spora: A Journal of Biomathematics
West Nile Virus (WNV) is a mosquito-borne virus that circulates among birds but also affects humans. Migrating birds carry these viruses from one place to another each year. WNV has spread rapidly across the continental United States resulting in numerous human infections and deaths. Several studies suggest that larval mosquito control measures should be taken as early as possible in a season to control the mosquito population size. Also, adult mosquito control measures are necessary to prevent the transmission of WNV from mosquitoes to birds and humans. To better understand the effective strategy for controlling affected larvae mosquito population, we …
A Survey Of Mathematical Models Of Dengue Fever, Iurii Bakach
A Survey Of Mathematical Models Of Dengue Fever, Iurii Bakach
College of Graduate Studies: Theses & Dissertations
In this paper, we compare and contrast five models of Dengue fever. We evaluate each model using different scenarios and identify the strenghts and wecknesses of each of the model
Eradicating Malaria: Improving A Multiple-Timestep Optimization Model Of Malarial Intervention Policy, Taryn M. Ohashi
Eradicating Malaria: Improving A Multiple-Timestep Optimization Model Of Malarial Intervention Policy, Taryn M. Ohashi
Scripps Senior Theses
Malaria is a preventable and treatable blood-borne disease whose complications can be fatal. Although many interventions exist in order to reduce the impacts of malaria, the optimal method of distributing these interventions in a geographical area with limited resources must be determined. This thesis refines a model that uses an integer linear program and a compartmental model of epidemiology called an SIR model of ordinary differential equations. The objective of the model is to find an intervention strategy over multiple time steps and multiple geographic regions that minimizes the number of days people spend infected with malaria. In this paper, …