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Full-Text Articles in Physical Sciences and Mathematics
(R1522) Modelling The Influence Of Desertic Aerosols On The Transmission Dynamics Of Neisseria Meningitidis Serogroup A, Francis Signing, Berge Tsanou, Samuel Bowong
(R1522) Modelling The Influence Of Desertic Aerosols On The Transmission Dynamics Of Neisseria Meningitidis Serogroup A, Francis Signing, Berge Tsanou, Samuel Bowong
Applications and Applied Mathematics: An International Journal (AAM)
This paper assesses the role of desert aerosols and vaccine on the transmission dynamics of Neisseria Meningitis serogroup A (NmA). It is biologically well-documented that the inhalation of aerosol dust and its presence in the nasal cavity weakens the nasopharyngeal mucosa by damaging the mucosal barrier and inhibiting the mucosal immune defenses of susceptible and vaccinated individuals. We address the latter by proposing and analyzing a mathematical model for the dynamics of NmA that specifically accounts for the fast progression of susceptible and vaccinated individuals to the invasive stage of the disease. We compute the basic reproduction number and use …
Mathematical Models Of Covid-19, Kate Faria
Mathematical Models Of Covid-19, Kate Faria
Honors Program Theses and Projects
For more than a year, the COVID-19 pandemic has been a major public health issue, affecting the lives of most people around the world. With both people’s health and the economy at great risks, governments rushed to control the spread of the virus. Containment measures were heavily enforced worldwide until a vaccine was developed and distributed. Although researchers today know more about the characteristics of the virus, a lot of work still needs to be done in order to completely remove the disease from the population. However, this is true for most of the infectious diseases in existence, including Influenza, …
An Examination Of Mathematical Models For Infectious Disease, David M. Jenkins
An Examination Of Mathematical Models For Infectious Disease, David M. Jenkins
Williams Honors College, Honors Research Projects
Starting with the original 1926 formulation of the SIR (Susceptible-Infected-Removed) model for infectious diseases, mathematical epidemiology continued to grow. Many extensions such as the SEIR, MSIR, and MSEIR models were developed using SIR as a basis to model diseases in a variety of circumstances. By taking the original SIR model, and reducing the system of three first-order equations to a single first-order equation, analysis shows that the model predicts two possible situations. This analysis is followed by discussion of an alternative use of the SIR model which allows for one to track the amount of sustainable genetic variation in a …
Putting The X In Biology: A Review Of The Mathematics Of Life, John Adam
Putting The X In Biology: A Review Of The Mathematics Of Life, John Adam
Mathematics & Statistics Faculty Publications
(First Paragraph) Charles Darwin's 1859 work On the Origin of the Species contained no equations. But that does not mean mathematics has no role to play in the science of life; in fact, the field of biomathematics is burgeoning and has been for several decades. Ian Stewart's new book does an admirable job of unfolding the mathematics undergirding so much of the research being carried out today in the many fields that comprise the subject of biology. Stewart sets the context by noting five great revolutions that have changed the way scientists think about life. These five revolutions are: (i) …
Classroom Manipulative To Engage Students In Mathematical Modeling Of Disease Spread: 1 + 1 = Achoo!, H. Gaff, M. Lyons, G. Watson
Classroom Manipulative To Engage Students In Mathematical Modeling Of Disease Spread: 1 + 1 = Achoo!, H. Gaff, M. Lyons, G. Watson
Biological Sciences Faculty Publications
Infectious diseases ranging from the common cold to cholera affect our society physically, emotionally, ecologically, and economically. Yet despite their importance and impact, there remains a lack of effective teaching materials for epidemiology and disease ecology in K-12, undergraduate, and graduate curricula [2]. To address this deficit, we've developed a classroom lesson with three instructional goals: (1) Familiarize students on basic concepts of infectious disease ecology; (2) Introduce students to a classic compartmental model and its applications in epidemiology; (3) Demonstrate the application and importance of mathematical modeling as a tool in biology. The instructional strategy uses a game-based mathematical …
Activator-Inhibitor Control Of Tissue Growth, John A. Adam
Activator-Inhibitor Control Of Tissue Growth, John A. Adam
Mathematics & Statistics Faculty Publications
This note develops a simple model for the competition between activator and inhibitor control mechanisms in one-dimensional tissue growth. The pedagogic usefulness of such a model is that it is easily accessible to undergraduate applied mathematicians and is suggestive of behavior known to occur in more realistic biological systems (e.g., some types of cancer). The limitations of the model are obvious and can provide a basis for discussion of the applicability of complementary levels of description in mathematical modeling.