Graduate Students Seminar

Speaker 1: Dejene Chala

Title

Multivariate meta analysis of time to event data

Abstract

Medical study usually involves multiple effects that were collected from the same study subject and these effect sizes tends to correlate. The conventional meta analysis method ignores these correlation structures that can results in misleading estimates. The multivariate methods of meta analysis incorporate the correlation among the estimates. This study uses both the Multivariate and univariate methods of meta analysis to estimate the effect sizes, test for the publication bias and between studies heterogeneity and compare the two methods.The result has indicated that the univariate methods higher value of estimate with smaller standard error. Both the univariate and multivariate method has shown that there was no problem of publication bias. The multivariate methods has shown that there was problem of between studies heterogeneity, while the univariate method has found that there was no problem of heterogeneity except for θ4. This discrepancy between the result might be due to ignoring the correlation among the effects in the univariate methods of meta analysis.

Speaker 2: Ehsan Shakeri

Title

PDE Modeling of Epidemics

Abstract

Our approach extends the traditional SIR compartment model to a Partial Differential Equation (PDE) framework, allowing for both spatial and temporal variations in the dynamics of epidemics. Specifically, we consider the susceptible (S), infected (I), and recovered (R) populations as functions of both time and space. In our model, diffusion is introduced as a key factor affecting the spread of the infected individuals, while external influences, such as incoming tourists or travelers, are represented by a forcing term, denoted as f(x,t). To numerically solve the model, we employ the finite element method to obtain a semi-discrete equation. The temporal evolution is discretized using the backward Euler method. At each time step, we tackle a system of nonlinear equations, which we solve efficiently using Newton's method. We provide an algorithm, complete with pseudocode, that unifies these numerical techniques.  Furthermore, we analyze the sparsity pattern and eigenvalues of the Jacobian matrix, and explore some well-known direct and iterative methods to determine the most efficient approach for solving the linear system in our context.