Mathematical modeling of infectious diseases

Ahmed, Iftikhar

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https://hdl.handle.net/2142/108229 Copy

Description

Title

Mathematical modeling of infectious diseases

Author(s)

Ahmed, Iftikhar

Issue Date

2020-04-09

Director of Research (if dissertation) or Advisor (if thesis)

Rapti, Zoi

Doctoral Committee Chair(s)

DeVille, Lee

Committee Member(s)

• Zharnitsky, Vadim
• Caceres, Carla

Department of Study

Mathematics

Discipline

Mathematics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Epidemic Models
• Wolbachia
• Optimal Control
• Daphnia
• Dynamical Systems
• Partial Differential Equations

Abstract

In this dissertation, we studied mathematical models of infectious diseases that consist of ordinary differential equations (ODEs) and partial differential equations (PDEs). An ODE model is formulated to describe the dynamics of wild mosquitoes when Wolbachia-infected female and male mosquitoes are introduced in the wild as a biological control, where we assume imperfect maternal transmission of Wolbachia to offspring and incomplete cytoplasmic incompatibility. In order to reduce the population of wild mosquitoes with minimal release of Wolbachia-infected mosquitoes in the wild, we develop an optimal control model. The optimal controls are found by using the Pontryagin's Maximum Principle. We also formulated an ODE optimal control model to describe the dynamics of dengue-infected humans when Wolbachia-infected mosquitoes are introduced in the wild along with efforts on educational campaigns to motivate individuals for using personal protection in order to reduce humans-mosquitoes. In this optimal control model, we also determined the most cost-effectiveness control strategy among different control interventions to reduce dengue infections in humans. In the host (Daphnia)- parasite (fungal spores) system, we study the disease dynamics of Daphnia in a water column where both algae and spores sink and diffuse. We formulated the Daphnia-spores-algae model using advection-diffusion partial differential equations (PDEs). We studied the effects of algal carrying capacity, sinking rates of algae and spores, and the water column maximum depth on the disease dynamics of Daphnia.

Graduation Semester

2020-05

Type of Resource

Thesis

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http://hdl.handle.net/2142/108229

Copyright and License Information

Copyright 2020 Iftikhar Ahmed

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