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Optimal Combination Therapy of Diseases with Evolutionary Dynamics

Akbari Sisi, Sanaz | 2022

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 54837 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Babazadeh, Maryam
  7. Abstract:
  8. This research studied optimal combination therapy of diseases with uncertain evolutionary dynamics. The problem of neutralizing HIV virus in the host’s body was modeled as a convex optimization problem whose objective function is minimizing disturbance effect while the disease dynamics is stable in the presence of polytopic uncertainty.In the first part of this thesis, according to the characteristics of positive systems, the convexity of H2 and H∞ in the presence of polytopic uncertainty was shown. To solve the minimization problem of disturbance effect, an algorithm based on minimizing a cutting plane was used. This algorithm, with solving the minimization problem iteratively in each step either finds a better approximation of the objective function or a better point to minimize the objective function. This algorithm can also be applied to a large scale system since it does not depend on the calculation of the objective function for all the vertices of the polytopic set. Therefore, the speed of the convergence and the simplicity of the calculation of this strategy are advantages over the strategies that need the calculation of the objective function for all vertices.In the second part of this thesis, the problem of minimizing the H2 norm was modeled as a standard and convex optimization problem. This optimization problem does not need adjusting hyper-parameters or iteratively solving the optimization problem. The optimal value of antibody can be obtained using off-the-shelf solvers. Also, with the help of positive systems and convex functions, it was shown that in the presence of uncertainty, the infinite-dimension optimization problem could be solved as a finite-dimension optimization problem. With the proposed optimization strategies, this question will be answered that for the combination therapy of HIV replication with uncertain evolutionary dynamics, how much of each antibody should be used to suppress all of the existing mutants
  9. Keywords:
  10. Convex Optimization ; Evolutionary Dynamics ; Combination Therapy ; Positive Systems ; HIV Infection

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