IMS Student Papers
http://hdl.handle.net/11071/3938
Sat, 20 Jan 2018 14:54:40 GMT2018-01-20T14:54:40ZMathematical modeling for Human Immunodeficiency Virus (HIV) transmission using generating function approach
http://hdl.handle.net/11071/3642
Mathematical modeling for Human Immunodeficiency Virus (HIV) transmission using generating function approach
This study is concerned with the mathematical modeling for human immunodeficiency
virus (HIV) transmission epidemics. The mathematical models are
specified by stochastic differential equations that are solved by use of Generating
Functions (GF). Models based on Mother to child transmission (MTCT) (age
group 0-5 years), Heterosexual transmission (age group 15 and more years) and
combined case (incorporating all groups and the two modes of transmission) were
developed and the expectations and variances of Susceptible (S) persons, Infected
(I) persons and AIDS cases were found. The S1(t) Susceptible model produces
a constant expectation and increasing variance. It was shown that Mother to
Child transimission and Heterosexual models are special cases of the Combined
model.
http://hdl.handle.net/11071/3642Mathematical model for pneumonia dynamics among children
http://hdl.handle.net/11071/3615
Mathematical model for pneumonia dynamics among children
The 2012 Southern Africa mathematical sciences association Conference (SAMSA 2012)26th -29th Nov 2012; There are major advances which have been made to understand the epidemiology of infectious diseases. However, more than 2 million children in the developing countries still die from pneumonia each year.
The eorts to promptly detect, eectively treat and control the spread of pneumonia is possible if its dynamics is understood. In this paper,we develop a mathematical model for pneumonia among children underve years of age. The model is analyzed using the theory of ordinary dierential equations and dynamical systems. We derive the basic reproduction number, R0, analyze the stability of equilibrium points and bifurcation analysis. The results of the analysis shows that there exist a locally stable disease free equilibrium point, Ef when R0 < 1 and a unique endemic equilibrium, Ee when R0 > 1.The analysis also shows that there is a possibility of a forward bifurcation.
http://hdl.handle.net/11071/3615Surprising applications and possible extensions of Dellsarte's method
http://hdl.handle.net/11071/3591
Surprising applications and possible extensions of Dellsarte's method
This is a short informal survey on some surprising applications of Delsarte's method, written for anyone being interested. I try to keep it as short and as informative as possible
Paper presented at Strathmore International Math Research Conference on July 23 - 27, 2012; This is a short informal survey on some surprising
applications of Delsarte's method, written for anyone being interested.
I try to keep it as short and as informative as possible
http://hdl.handle.net/11071/3591On the distribution of multiplicities in integer partitions
http://hdl.handle.net/11071/3583
On the distribution of multiplicities in integer partitions
Paper presented at Strathmore International Math Research Conference on July 23 - 27, 2012; We study the distribution of the number of parts of given
multiplicity (or equivalently ascents of given size) in integer partitions.
In this paper we give methods to compute asymptotic formulas for the
expected value and variance of the number of parts of multiplicity d (d
is a positive integer) in a random partition of a large integer n and also
prove that the limiting distribution is asymptotically normal for fixed
d. However, if we let d increase with n, we get a phase transition for d
around n1=4. Our methods can also be applied to so called -partitions
where the parts are members of a sequence of integers .
http://hdl.handle.net/11071/3583