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Morphogenesis is the biological process by which form and structure is created during embryonic development. How are pigment cells determined and distributed through the skin when a mammal develops? How does this process determine the types of patterns in animal coat patterns, such as zebra stripes and cheetah spots? We can investigate this process through the following system of partial differential equations, known as the reaction-diffusion equations: \begin{aligned}u_t &= \Delta u + \gamma\left[a-u-\frac{\rho u v}{1+u+Ku^2}\right],\\v_t &= d\Delta v + \gamma\left[\alpha(b-v)-\frac{\rho u v}{1+u+Ku^2}\right].\end{aligned}
The standard SIR model is used to study how an infectious disease is spread through a healthy population. The model has many shortcomings. We study differences in the populations in a systematic manner through the following model: \begin{aligned}S' &= -\beta S^xI^y\\I' &= \beta S^xI^y - \alpha S^mI^n\\R' &= \alpha S^mI^n\end{aligned}
 Name Project Title Year A. Prudhom Multiplication Operators Between $\mathcal{L}^{(p)}$ Spaces on a Tree 2012-2013 T. Xiong The Contagiousness of Rumors 2012 C. Jens Surviving an Outbreak of Zombiism 2010-2011