| Abstract: |
| Time delays are intrinsic to many infectious disease processes, arising from biological latency, intracellular dynamics, and delays in immune response or transmission. In this talk, we introduce time-delayed mathematical models formulated as systems of delayed differential equations and related optimal control problems, applied to two case studies: HIV in-host dynamics and the population-level transmission of brucellosis.
For HIV, we develop both compartmental and in-host models incorporating biologically motivated delays associated with viral replication and immune cell activation. An optimal control problem is formulated to assess combined antiretroviral therapy and immunotherapy. The problem includes state constraints on effector immune cells, and we derive the necessary optimality conditions using Pontryagin`s Maximum Principle for delayed systems. Numerical simulations highlight the impact of delays on treatment strategies and the trade-offs between therapeutic effectiveness and treatment side effects.
In parallel, we examine a delayed epidemiological model for brucellosis transmission in livestock and humans, featuring multiple latent-period delays.
Taken together, these studies illustrate how delayed models and optimal control provide powerful tools for understanding infection mechanisms and for designing effective intervention strategies. |
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