My research partner Mallessa Yeboah and I have spent this summer analyzing an extension of a modified SIWR model created by Dr. Ghosh-Dastidar and Lenhart, with the hopes of getting a better understanding of this recent cholera outbreak in Haiti.
Weekly Log
Week 1:
Orientation
The preliminary presentation outlining the type of research that will be done for the remaining of the program was presented.
Week 2:
My mentor had me focus on acquiring all the necessary background information needed to thoroughly understand and study the research. During this week I began to make concrete connections about the relevance of my project to the real world. I did reading and problems related to epidemiology. The topics that were introduced were:
Endemic and Disease-Free Equilibria
Stability Analysis/Linearization technique
Basic Reproductive Number
Week 3:
I began practicing the linearization technique on simpler practice SIR models. I was having trouble finding both the disease-free and endemic equilibria points of the two models. I sought the aid of another researcher.
I was finally able to fully evaluate the equilibria of the sample models from last week. I was able to create and evaluate the Jacobian matrices for both.I did find the eigenvalues for the disease-free equilibrium of one. I attempted to evaluate the eigenvalues for stability.
Week 4:
I attempted to find the basic reproductive number of the SIWVR using a model created by Nielan as medium. I later found out that I used the wrong approach. With further research I learned about the next generation method for more complex epidemiology models.
The rule of the infectivity parameter over the infectious period parameter giving the basic reproductive number is only valued for simple models.
Week 5:
During this week I worked with another sample SIR model but this one was much similar to the one that we are working on with my mentor. I was able to fully evaluate the equilibria and analyze the stability of this new sample model.
After working on the sample I began to evaluate the SIWVR model with fresh eyes.
Week 6:
This week the final presentation for the projects were presented. At this point I was able to attempt calculating the basic reproductive number using the next generation method, found the disease-free equilibrium,and evaluated the endemic equilibrium that I collaborated on with my mentor.
Week 7:
This week the emphasis was placed on the basic reproductive number of the SIWVR model. The matrices were very long and took much effort to evaluate.
Week 8:
My focus this week was to complete the research report discussing my results.
I worked on a continuation of finding the basic reproductive number for the SIWVR model. Using the next generation method I was able to find the F matrix, and the V inverse matrix. Finding the dominant eigenvalues of the matrix would give me the reproductive number but I was unable to evaluate it.
Week 9:
I finished the final edits to the research paper.
Continued working on finding the eigenvalues of the next generation matrix.