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Articles 1 - 5 of 5
Full-Text Articles in Applied Mathematics
Hepatitis B And D: A Forecast On Actions Needed To Reduce Incidence And Achieve Elimination, Scott Greenhalgh, Andrew Klug
Hepatitis B And D: A Forecast On Actions Needed To Reduce Incidence And Achieve Elimination, Scott Greenhalgh, Andrew Klug
Spora: A Journal of Biomathematics
Viral hepatitis negatively affects the health of millions, with the worst health outcomes associated with the hepatitis D virus (HDV). Fortunately, HDV is rare and requires prior infection with the hepatitis B virus (HBV) before it can establish infection and transmit. Here, we develop a mathematical model of HBV and HDV transmission in Sub-Saharan Africa to investigate the effects of hepatitis B vaccination on both HBV and HDV. Our findings illustrate a hepatitis B vaccination rate above 0.006 year-1 reduces hepatitis D by over 90%, and a vaccination rate above 0.0221 year-1 reduces hepatitis B by over 90%, …
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 …
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.
Effective Dose Fractionation Schemes Of Radiotherapy For Prostate Cancer, Jose Alvarez, Kathleen M. Storey, Pavitra Kannan, Heyrim Cho
Effective Dose Fractionation Schemes Of Radiotherapy For Prostate Cancer, Jose Alvarez, Kathleen M. Storey, Pavitra Kannan, Heyrim Cho
Spora: A Journal of Biomathematics
Radiation therapy remains as one of the main cancer treatment modalities. Typical regimens for radiotherapy comprise a constant dose administered on weekdays, and no radiation on weekends. In this paper, we examine adaptive dosages of radiation treatment strategies for heterogeneous tumors using a dynamical system model that consist of radiation-resistant and parental populations with unique interactive properties, namely, PC3 and DU145 prostate cancer cell lines. We show that stronger doses of radiation given in longer time intervals, while keeping the overall dosage the same, are effective in PC3 cell lines, but not in DU145 cell lines. In addition, we tested …
An Axiomatic And Contextual Review Of The Armitage And Doll Model Of Carcinogenesis, W. Zane Billings, Justin Clifton, Josh Hiller, Tommy Meek, Andrew Penland, Wesley Rogers, Gabriella Smokovich, Andrew Velasquez-Berroteran, Eleni Zamagias
An Axiomatic And Contextual Review Of The Armitage And Doll Model Of Carcinogenesis, W. Zane Billings, Justin Clifton, Josh Hiller, Tommy Meek, Andrew Penland, Wesley Rogers, Gabriella Smokovich, Andrew Velasquez-Berroteran, Eleni Zamagias
Spora: A Journal of Biomathematics
In 1954, Armitage and Doll published one of the most influential papers in the history of mathematical epidemiology. However, when one examines the literature one finds that there are in fact at least three distinct mathematical models attributed to the 1954 paper. In this study, we examine this important paper and the mathematical derivation of their model. We find, very surprisingly, that no stochastic process can account for all the assumptions of the model and that many of the models in the literature use a consistent subset of the assumptions used in Armitage and Doll's paper.