Loading...

An Analysis of a Mathematical Model Describing the Geographic Spread of Dengue Disease

Hashemifar, Alireza | 2019

1526 Viewed
  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 52485 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Hesaraki, Mahmoud
  7. Abstract:
  8. We consider a system of nonlinear partial differential equations corresponding to a generalization of a mathematical model for geographical spreading of dengue disease. the mosquito population is divided into subpopulations: winged form (mature female mosquitoes) and aquatic form (comprising eggs, larvae and pupae); the human population is divided into the subpopulations:susceptible, infected and removed (or immune). On the other hand we allow higher spatial dimensions and also parameters depending on space and time. is last generalization is done to cope with possible abiotic effects as variations in temperature, humidity, wind velocity, carrier capacities, and so on; thus, the results hold for more realistic situations. Moreover, we also consider the effects of additional control terms. We perform a rigorous mathematical analysis and present a result on existence and uniqueness of solutions of the problem; furthermore, we obtain estimates of the solution in terms of certain norms of the given parameters of the problem. is kind of result is important for the analysis of optimal control problems with the given dynamics; to exemplify their utility, we also briefly describe how they can be used to show the existence of optimal controls that minimize a given optimality criteria
  9. Keywords:
  10. Nonlinear Systems ; Existence Results ; Optimal Control ; Dengue Disease

 Digital Object List