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Transmission topology control is a tool used by system operators in the role of a control action taken into account as a preventive or corrective action relative to a specific outage or set of outages. However, their inclusion in most…
We introduce a general system of ordinary differential equations that includes some classical and recent models for the epidemic spread in a closed population without vital dynamic in a finite time horizon. The model is vectorial, in the…
We present a local spread model of disease transmission on a regular network and compare different control options ranging from treating the whole population to local control in a well-defined neighborhood of an infectious individual.…
In this paper, we explore the solvability and the optimal control problem for a compartmental model based on reaction-diffusion partial differential equations describing a transmissible disease. The nonlinear model takes into account the…
Optimal curing strategy of suppressing competing epidemics spreading over complex networks is a critical issue. In this paper, we first establish a framework to capture the coupling between two epidemics, and then analyze the system's…
This study presents a mathematical model for optimal vaccination strategies in interconnected metropolitan areas, considering commuting patterns. It is a compartmental model with a vaccination rate for each city, acting as a control…
In this paper, we consider a stochastic recursive optimal control problem under model uncertainty. In this framework, the cost function is described by solutions of a family of backward stochastic differential equations. With the help of…
We analyze a class of general nonlinear epidemic models with age and space structure, including a nonlocal infection term depending on age and space. After establishing the well-posedness of the state partial differential equation, we…
Cell heterogeneity plays an important role in patient responses to drug treatments. In many cancers, it is associated with poor treatment outcomes. Many modern drug combination therapies aim to exploit cell heterogeneity, but determining…
We formulate an optimal control problem to determine the lockdown policy to curb an epidemic where other control measures are not available yet. We present a unified framework to model the epidemic and economy that allows us to study the…
We present and compare two different optimal control approaches applied to SEIR models in epidemiology, which allow us to obtain some policies for controlling the spread of an epidemic. The first approach uses Dynamic Programming to…
A model with six mutually-exclusive compartments related to dengue is studied. Three vector control tools are considered: insecticides (larvicide and adulticide) and mechanical control. The basic reproduction number associated to the model…
Understanding how to effectively control an epidemic spreading on a network is a problem of paramount importance for the scientific community. The ongoing COVID-19 pandemic has highlighted the need for policies that mitigate the spread,…
In this paper, we address an optimal distributed control problem for a non-local model of phase-field type, describing the evolution of tumour cells in presence of a nutrient. The model couples a non-local and viscous Cahn-Hilliard equation…
This paper investigates a behavioral-feedback SIR model in which the infection rate adapts dynamically based on the fractions of susceptible and infected individuals. We introduce an invariant of motion and we characterize the peak of…
In this study initially, we propose an age structured model and calculate the equilibrium points and basic reproduction number. Later we propose an optimal control problem to understand the roles of treatment in controlling the epidemic.…
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.…
Efficient testing and vaccination protocols are critical aspects of epidemic management. To study the optimal allocation of limited testing and vaccination resources in a heterogeneous contact network of interacting susceptible, recovered,…
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 the context of epidemiology, policies for disease control are often devised through a mixture of intuition and brute-force, whereby the set of logically conceivable policies is narrowed down to a small family described by a few…