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Dynamic models have been successfully used in producing estimates of HIV epidemics at the national level due to their epidemiological nature and their ability to estimate prevalence, incidence, and mortality rates simultaneously. Recently,…
The relationship between epidemiology, mathematical modeling and computational tools allows to build and test theories on the development and battling of a disease. This PhD thesis is motivated by the study of epidemiological models applied…
We study the optimal control problem of a free boundary PDE model describing the growth of multilayered tumor tissue in vitro. We seek the optimal amount of tumor growth inhibitor that simultaneously minimizes the thickness of the tumor…
Mitigation measures are essential for controlling the spread of infectious diseases during pandemics and epidemics, but they impose considerable societal, individual, and economic costs. We developed a general optimization framework to…
In multi-objective black-box optimization, the goal is typically to find solutions that optimize a set of $T$ black-box objective functions, $f_1, \ldots f_T$, simultaneously. Traditional approaches often seek a single Pareto-optimal set…
Several mathematical models in SARS-CoV-2 have shown how target-cell model can help to understand the spread of the virus in the host and how potential candidates of antiviral treatments can help to control the virus. Concepts as…
A treatment regime is a deterministic function that dictates personalized treatment based on patients' individual prognostic information. There is a fast-growing interest in finding optimal treatment regimes to maximize expected long-term…
In this paper, we study a distributed optimal control problem for a diffuse interface model for tumor growth. The model consists of a Cahn-Hilliard type equation for the phase field variable coupled to a reaction diffusion equation for the…
Effective epidemic control is crucial for mitigating the spread of infectious diseases, particularly when pharmaceutical interventions such as vaccines or treatments are limited. Non-pharmaceutical strategies, including mobility…
Understanding treatment heterogeneity is essential to the development of precision medicine, which seeks to tailor medical treatments to subgroups of patients with similar characteristics. One of the challenges to achieve this goal is that…
We analyze equilibrium behavior and optimal policy within a Susceptible-Infected-Recovered epidemic model augmented with potentially undiagnosed agents who infer their health status and a social planner with imperfect enforcement of social…
We consider an optimal control problem for a diffuse interface model of tumor growth. The state equations couples a Cahn-Hilliard equation and a reaction-diffusion equation, which models the growth of a tumor in the presence of a nutrient…
Severe infectious diseases such as the novel coronavirus (COVID-19) pose a huge threat to public health. Stringent control measures, such as school closures and stay-at-home orders, while having significant effects, also bring huge economic…
Autonomous systems have witnessed a rapid increase in their capabilities, but it remains a challenge for them to perform tasks both effectively and safely. The fact that performance and safety can sometimes be competing objectives renders…
The consensus control with optimal cost remains major challenging although consensus control problems have been well studied in recent years. In this paper, we study the consensus control of multi-agent system associated with a given cost…
The spread of an epidemic is often modeled by an SIR random process on a social network graph. The MinINF problem for optimal social distancing involves minimizing the expected number of infections, when we are allowed to break at most $B$…
Decision-makers frequently must choose a single action from a finite set of alternatives -- for example, physicians selecting a treatment, investors choosing a portfolio risk level, or judges determining sentences. To improve outcomes,…
In this work we introduce a differential equation model with time-delay that describes the three-stage dynamics and the two time scales observed in HIV infection. Assuming that the virus has high mutation and rapid reproduction rates that…
This study aims to determine an optimal control strategy for vaccine scheduling in COVID-19 pandemic treatment by converting widely acknowledged infectious disease model named SEIR into an optimal control problem. The problem is augmented…
During decades, mathematical models have been used to predict the behavior of physical and biologic systems, and to define strategies aiming the minimization of the effects regarding different types of diseases. In the present days, the…