Applied Mathematics Commons^™

Modeling An Infection Outbreak With Quarantine: The Sibkr Model, Mikenna Dew, Amanda Langosch, Theadora Baker-Wallerstein

Rose-Hulman Undergraduate Mathematics Journal

Influenza is a respiratory infection that places a substantial burden in the world population each year. In this project, we study and interpret a data set from a flu outbreak in a British boarding school in 1978 with mathematical modeling. First, we propose a generalization of the SIR model based on the quarantine measure in place and establish the long-time behavior of the model. By analyzing the model mathematically, we determine the analytic formulas of the basic reproduction number, the long-time limit of solutions, and the maximum number of infection population. Moreover, we estimate the parameters of the model based …

(R2032) Modeling The Effect Of Sanitation Effort On The Spread Of Carrier-Dependent Infectious Diseases Due To Environmental Degradation, Ram Naresh, Sandhya Rani Verma, J. B. Shukla, Manju Agarwal

Applications and Applied Mathematics: An International Journal (AAM)

In this present study, an SIS model is proposed and analyzed to study the effect of sanitation effort in controlling the spread of carrier-dependent infectious disease in a human habitat due to environmental degradation. The dynamics of the model consist of six dependent variables, the susceptible population density, infective population density, carrier population density, cumulative density of environmental degradation and the density of sanitation effort applied on carrier population and degraded environment. In the modeling process, the carrier population density and sanitation effort are modeled logistically and the degradation of the environment is assumed to be directly proportional to the …

On Efficacy And Effectiveness Of Vaccines: A Mathematical Approach Based On Conditional Probability With Applications To The Covid-19 Context, Flavius Guias

Spora: A Journal of Biomathematics

This paper presents a mathematically formalized approach which points out the relation between efficacy and effectiveness of vaccines. The first term denotes the relative degree of protection in clinical trials or under ideal conditions, while the latter is based on observed real-life data. We define the efficacy by a similar formula to the effectiveness, but the probabilities involved in the relative risk are conditional with respect to the exposure to the virus. If exposure and vaccination status are independent, the two quantities are equal. Otherwise, the observed value of the effectiveness is a biased one, as it could be seen …

(R1468) Global Analysis Of An Seirs Model For Covid-19 Capturing Saturated Incidence With Treatment Response, David A. Oluyori, Helen O. Adebayo, Ángel G.C. Pérez

Applications and Applied Mathematics: An International Journal (AAM)

In this work, a new SEIRS model with saturated incidence rate and piecewise linear treatment response is proposed to describe the dynamics of COVID-19. It is assumed that the treatment response is proportional to the number of infected people as long as the incidence cases are within the capacity of the healthcare system, after which the value becomes constant, when the number of confirmed cases exceeds the carrying capacity of the available medical facilities. Thus, the basic reproduction number of the model is obtained. It is proved that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number …

(R1412) Stability And Bifurcation Of A Cholera Epidemic Model With Saturated Recovery Rate, Huda Abdul-Satar, Raid K. Naji

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a Cholera epidemic model is proposed and studied analytically as well as numerically. It is assumed that the disease is transmitted by contact with Vibrio cholerae and infected person according to dose-response function. However, the saturated treatment function is used to describe the recovery process. Moreover, the vaccine against the disease is assumed to be utterly ineffective. The existence, uniqueness and boundedness of the solution of the proposed model are discussed. All possible equilibrium points and the basic reproduction number are determined. The local stability and persistence conditions are established. Lyapunov method and the second additive compound …

Mathematical Modeling, Analysis, And Simulation Of The Covid-19 Pandemic With Behavioral Patterns And Group Mixing, Comfort Ohajunwa, Padmanabhan Seshaiyer

Spora: A Journal of Biomathematics

Due to the rise of COVID-19 cases, many mathematical models have been developed to study the disease dynamics of the virus. However, despite its role in the spread of COVID-19, many SEIR models neglect to account for human behavior. In this project, we develop a novel mathematical modeling framework for studying the impact of mixing patterns and social behavior on the spread of COVID-19. Specifically, we consider two groups, one exhibiting normal behavior who do not reduce their contacts and another exhibiting altered behavior who reduce their contacts by practicing non-pharmaceutical interventions such as social distancing and self-isolation. The dynamics …

Long-Term Dynamics Of The Kidney Disease Epidemic Among Hiv-Infected Individuals, Heather Gudaz, Henry A. Ogu, Elissa J. Schwartz

Spora: A Journal of Biomathematics

One of many risks facing HIV+ individuals is the development of kidney dysfunction and end stage kidney disease (ESKD). A differential equation-based mathematical model was developed to assess the impact of antiretroviral therapy on the progression to kidney disease and on reducing mortality due to kidney failure. Analytical and numerical predictions of long-term HIV+ ESKD prevalence show that therapy can lead to either extremely low levels of disease prevalence or increased prevalence, depending on drug efficacy levels and mechanisms of action. Maintenance of HIV+ ESKD prevalence below one individual is possible with sufficient efficacy (e.g., 99%) against the progression from …

Sars-Cov-2 Pandemic Analytical Overview With Machine Learning Predictability, Anthony Tanaydin, Jingchen Liang, Daniel W. Engels

SMU Data Science Review

Understanding diagnostic tests and examining important features of novel coronavirus (COVID-19) infection are essential steps for controlling the current pandemic of 2020. In this paper, we study the relationship between clinical diagnosis and analytical features of patient blood panels from the US, Mexico, and Brazil. Our analysis confirms that among adults, the risk of severe illness from COVID-19 increases with pre-existing conditions such as diabetes and immunosuppression. Although more than eight months into pandemic, more data have become available to indicate that more young adults were getting infected. In addition, we expand on the definition of COVID-19 test and discuss …

Projecting The Covid-19 Weekly Deaths And Hospitalizations For Jefferson County, Kentucky, Seyed Karimi, Natalie Dupre, W. Paul Mckinney, Bert B. Little, Naiya Patel, Sarah Moyer

The University of Louisville Journal of Respiratory Infections

Introduction: The trends in the numbers of active hospitalizations and fatalities caused by the COVID-19 in Jefferson County, Kentucky, were projected over the period May 7 to August 20, 2020.

Methods: The projections provided in this report are from a susceptible-exposed-infectious-recovered (SEIR) model. The model was calibrated using the COVID-19 transmission dynamics parameters from relevant literature and clinical dynamics parameters from the county’s data. The model was used to measure the impact of public health policy interventions designed to contain the infection. The policy was modeled by its intervention day and impact on the transmission of the virus such that …

Modeling And Analysis Of The Spread Of Japanese Encephalitis With Environmental Effects, Ram Naresh, Surabhi Pandey

Applications and Applied Mathematics: An International Journal (AAM)

A nonlinear mathematical model for the spread of Japanese Encephalitis, caused by infected mosquito feeding on susceptible human population incorporating demographic and environmental factors is proposed and analyzed. In the modeling process, it is assumed that the growth rates of reservoir animal population and vector mosquito population are enhanced due to environmental discharges caused by human population related factors. The model is analyzed by stability theory of differential equations and computer simulation. Both the disease-free and the endemic equilibria are found and their stability is investigated. It is found that whenever the disease-free equilibrium is locally asymptotically stable, the endemic …

Global Stability Results Of An Sis Age-Structured Epidemic Model With Vertical Transmission, M. El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

An SIS age-structured epidemic model for a vertically as well as horizontally transmitted disease is investigated when the fertility, mortality and cure rates depend on age and the force of infection of proportionate mixing assumption type. We determine the steady states and prove the global stability for the endemic equilibriums.

Stability Analysis For An Seir Age-Structured Epidemic Model Under Vaccination, M. El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

An SEIR age-structured epidemic model is investigated when susceptible and immune individuals are vaccinated indiscriminately and the force of infection of proportionate mixing type. We determine the steady states and obtain an explicitly computable threshold condition, and then study the stability of the steady states.

Global Stability Results And Well Posedness Of An Si Age-Structured Epidemic Model With Vertical Transmission, M. El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

An SI age-structured epidemic model for a vertically as well as horizontally transmitted disease is investigated when the fertility and mortality rates depend on age and the force of infection of proportionate mixing assumption type. We prove the well posedness of the model as well as the global stability for endemic equilibriums.

Analysis Of An Sirs Age-Structured Epidemic Model With Vaccination And Vertical Transmission Of Disease, Mohammed El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

An SIRS age-structured epidemic model for a vertically as well as horizontally transmitted disease under vaccination is investigated when the fertility, mortality and removal rates depend on age and the force of infection of proportionate mixing assumption type, and vaccination wanes over time. We prove the existence and uniqueness of solution to the model equations, and show that solutions of the model equations depend continuously on the initial age-distributions. Furthermore, we determine the steady states and obtain an explicitly computable threshold condition, in terms of the demographic and epidemiological parameters of the model; we then study the stability of the …