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Analysis of a Mathematical Model Describing the Geographical Spread of Dengue Disease

Gazori, Fereshteh | 2023

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 56269 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Hesaaraki, Mahmoud
  7. Abstract:
  8. Dengue is one of the most important infectious diseases in the world. This disease is a viral infection that is transmitted to humans through the bite of a mosquito called Aedes aegypti. For this reason, geographical regions infected with this type of mosquito are at risk of Dengue outbreak. In this thesis, we first present a mathematical model describing the geographical spread of Dengue disease, which includes the movement of both the human population and the winged mosquito population. This model is derived from a mixed system of partial and ordinary differential equations. Our proposed model has the ability to consider the possibility of asymptomatic infection, so that the presence of this is an effective factor in the spread of the disease. Also, the possibility of superinfection of asymptomatic individuals can be investigated in this model. We show the global existence of a unique non-negative solution to this model. Then, using numerical simulations and sensitivity analysis of model parameters (related to the contact rate and mortality rate of winged mosquitoes), we establish strategies to control Dengue disease. By using numerical simulations, it can also be concluded that local control of Dengue transmission can be done at a lower cost. In the next step, aiming to analyze the transmission speed of Dengue disease, we seek to simplify the proposed model by applying assumptions. Additionally, due to the interest of investigating the local spread of Dengue, we ignore the movement of humans. By obtaining the basic reproduction number denoted by〖 R〗_0, the stability condition of the equilibrium points of this model is investigated. If R_0>1, the disease-free equilibrium is unstable and a unique endemic equilibrium is locally asymptotically stable. In this case, by calculating the minimum speed of the model's traveling waves, if they exist, we determine the local spread of the infection during a short period of the epidemic. Finally, we verify the existence of traveling wave solutions by presenting some numerical simulations
  9. Keywords:
  10. Dengue Disease ; Global Existence ; Basic Reproduction Number ; Stability Analysis ; Traveling Wave ; Nonlinear Diffusion-Advection System