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Optimal control theory in epidemiology has been used to establish the most effective intervention strategies for managing and mitigating the spread of infectious diseases while considering constraints and costs. Using Pontryagin's Maximum…

In the framework of homogeneous susceptible-infected-recovered (SIR) models, we use a control theory approach to identify optimal pandemic mitigation strategies. We derive rather general conditions for reaching herd immunity while…

Optimal intervention design is formulated as a hybrid optimal control problem for multiphase homogeneous epidemiological systems. The system extends a foundational compartmental model through intermediate phases that incorporate…

We study the problem of optimal control of the stochastic SIR model. Models of this type are used in mathematical epidemiology to capture the time evolution of highly infectious diseases such as COVID-19. Our approach relies on…

Modelling epidemics via classical population-based models suffers from shortcomings that so-called individual-based models are able to overcome, as they are able to take heterogeneity features into account, such as super-spreaders, and…

The spread of COVID-19 has been thwarted in most countries through non-pharmaceutical interventions. In particular, the most effective measures in this direction have been the stay-at-home and closure strategies of businesses and schools.…

We apply optimal control theory to a tuberculosis model given by a system of ordinary differential equations. Optimal control strategies are proposed to minimize the cost of interventions, considering reinfection and post-exposure…

In this paper, we consider an optimal distributed control problem for a reaction-diffusion-based SIR epidemic model with human behavioral effects. We develop a model wherein non-pharmaceutical intervention methods are implemented, but a…

HIV pre-exposure prophylaxis (PrEP) drastically reduces the risk of HIV infection if taken as prescribed, providing almost perfect protection even during unprotected sexual intercourse. Although this has been transformative in reducing new…

In this study, we present an epidemic-controlled SIRD model with two types of control strategies: mask wear and screening. The aim of this study is to minimize the number of deceased keeping a minimal cost of mask advertising and screening.…

A central challenge in Human Immunodeficiency Virus (HIV) public health policy lies in determining whether to universally expand treatment access, despite the risk of sub-optimal adherence and consequent drug resistance, or to adopt a more…

We propose a versatile model with a flexible choice of control for an early-pandemic outbreak prevention when vaccine/drug is not yet available. At that stage, control is often limited to non-medical interventions like social distancing and…

Optimizing the impact on the economy of control strategies aiming at containing the spread of COVID-19 is a critical challenge. We use daily new case counts of COVID-19 patients reported by local health administrations from different…

A delayed model describing the dynamics of HIV (Human Immunodeficiency Virus) with CTL (Cytotoxic T Lymphocytes) immune response is investigated. The model includes four nonlinear differential equations describing the evolution of…

We analyze the optimal control of disease prevention and treatment in a basic SIS model. We develop a simple macroeconomic setup in which the social planner determines how to optimally intervene, through income taxation, in order to…

A deterministic mathematical model is formulated and analyzed to study the transmission dynamics of Nipah virus both qualitatively and numerically. Existence and stability of equilibria were investigated and the model was rigorously…

We propose and study a new mathematical model of the human immunodeficiency virus (HIV). The main novelty is to consider that the antibody growth depends not only on the virus and on the antibodies concentration but also on the uninfected…

We consider a behavioral-feedback SIR epidemic model, in which the infection rate depends in feedback on the fractions of susceptible and infected agents, respectively. The considered model allows one to account for endogenous adaptation…

In this paper, we consider the problem of controlling a diffusion process pertaining to an opioid epidemic dynamical model with random perturbation so as to prevent it from leaving a given bounded open domain. Here, we assume that the…

We present a control framework for stochastic compartmental models in epidemiology. In this framework, rather than directly controlling the stochastic system, we perform optimal control of an associated Fokker-Planck equation, with the goal…