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In this paper we introduce the optimal control of a kinetic model describing agents who migrate on a graph and interact within its nodes exchanging a physical quantity. As a prototype model, we consider the spread of an infectious disease…
We present a mathematical analysis of the early detection of Ebola virus. The propagation of the virus is analysed by using a Susceptible, Infected, Recovered (SIR) model. In order to provide useful predictions about the potential…
A model based on a thermodynamic approach is proposed for predicting the dynamics of communicable epidemics in a city, when the epidemic is governed by controlling efforts of multiple scales so that an entropy is associated with the system.…
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…
The incidence of Dengue epidemiologic disease has grown in recent decades. In this paper an application of optimal control in Dengue epidemics is presented. The mathematical model includes the dynamic of Dengue mosquito, the affected…
We study the problem of a policymaker who aims at taming the spread of an epidemic while minimizing its associated social costs. The main feature of our model lies in the fact that the disease's transmission rate is a diffusive stochastic…
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…
In this paper, we propose a new model for the dynamics of COVID-19 infections. Our approach consists of seven phenotypes: the susceptible humans, exposed humans, infectious humans, the recovered humans, the quarantine population, the…
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 a social planner's optimal control problem for a partially observable stochastic epidemic model. The control measures include social distancing, testing, and vaccination. Using a diffusion approximation for the…
This paper combines a canonical epidemiology model of disease dynamics with government policy of lockdown and testing, and agents' decision to social distance in order to avoid getting infected. The model is calibrated with data on deaths…
An analytical expression for the optimal control of an Ebola problem is obtained. The analytical solution is found as a first-order approximation to the Pontryagin Maximum Principle via the Euler-Lagrange equation. An implementation of the…
A model for the transmission of dengue disease is presented. It consists of eight mutually-exclusive compartments representing the human and vector dynamics. It also includes a control parameter (adulticide spray) in order to combat the…
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…
In this paper we propose and study a spatial diffusion model for the control of anthracnose disease in a bounded domain. The model is a generalization of the one previously developed in [14]. We use the model to simulate two different types…
Testing is a crucial control mechanism in the beginning phase of an epidemic when the vaccines are not yet available. It enables the public health authority to detect and isolate the infected cases from the population, thereby limiting the…
We consider the SEIRS compartment epidemiology model suitable for predicting the evolution of the COVID-19 pandemy in the extreme limiting case of no acquired immunity. The disease-free and endemic fixed points are found and their stability…
The process of contagiousness spread modelling is well-known in epidemiology. However, the application of spread modelling to banking market is quite recent. In this work, we present a system of ordinary differential equations, simulating…
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.…
The adoption of containment measures to reduce the amplitude of the epidemic peak is a key aspect in tackling the rapid spread of an epidemic. Classical compartmental models must be modified and studied to correctly describe the effects of…