Related papers: An eradication time problem for the SIR model
We introduce a multi-layer networked compartmental $SIRS-V_o$ model that captures opinion dynamics, disease spread, risk perception, and self-interest vaccine-uptake behavior in an epidemic process. We characterize the target vaccination…
The COVID-19 pandemic has posed a policy making crisis where efforts to slow down or end the pandemic conflict with economic priorities. This paper provides mathematical analysis of optimal disease control policies with idealized…
We analyse the infection-age-dependent SIR model from a numerical point of view. First, we present an algorithm for calculating the solution the infection-age-structured SIR model without demography of the background host. Second, we…
We study a discrete Susceptible-Infected-Recovered (SIR) model for the spread of infectious disease on a homogeneous tree and the limit behavior of the model in the case when the tree vertex degree tends to infinity. We obtain the…
Compartmental models are popular in the mathematics of epidemiology for their simplicity and wide range of applications. Although they are typically solved as initial value problems for a system of ordinary differential equations, the…
We present an exact analytical solution to a one-dimensional model of the Susceptible-Infected-Recovered (SIR) epidemic type, with infection rates dependent on nearest-neighbor occupations. We use a quantum mechanical approach, transforming…
In previous articles, we formalized the problem of optimal allocation strategies for a (perfect) vaccine in an infinite-dimensional metapopulation model. The aim of the current paper is to illustrate this theoretical framework with multiple…
How to allocate vaccines over heterogeneous individuals is one of the important policy decisions in pandemic times. This paper develops a procedure to estimate an individualized vaccine allocation policy under limited supply, exploiting…
The outbreak of mutant strains and vaccination behaviors have been the focus of recent epidemiological research, but most existing epidemic models failed to simultaneously capture viral mutation and consider the complexity and behavioral…
Exact solution of the Susceptible-Infectious-Recovered (SIR) epidemic model is derived, and various properties of solution are obtained directly from the exact solution. It is shown that there exists an exact solution of an initial value…
Since the recent introduction of several viable vaccines for SARS-CoV-2, vaccination uptake has become the key factor that will determine our success in containing the COVID-19 pandemic. We argue that game theory and social network models…
In this work, to support decision making of immunisation strategies, we propose the inclusion of two vaccination doses in the SEIR model considering a stochastic cellular automaton. We analyse three different scenarios of vaccination: $i)…
In this paper, we have studied epidemiological models for Ebola infection using nonlinear ordinary differential equations and optimal control theory. We considered optimal control analysis of SIR and SEIR models for the deadly Ebola…
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…
The stochastic SIRS model is a continuous-time Markov chain modelling the spread of infectious diseases with temporary immunity, in a homogeneously-mixing population of fixed size $N$. We study the scaling behaviour of the extinction time…
This study presents a family of stochastic models for the dynamics of influenza in a closed human population. We consider treatment for the disease in the form of vaccination, and incorporate the periods of effectiveness of the vaccine and…
We investigate an epidemic model based on Bailey's continuous differential system. In the continuous time domain, we extend the classical model to time-dependent coefficients and present an alternative solution method to Gleissner's…
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.…
This work introduces a novel epidemiological model that simultaneously considers multiple viral strains, reinfections due to waning immunity response over time and an optimal control formulation. This enables us to derive optimal mitigation…
The aim of this paper is to provide a rigorous mathematical analysis of an optimal control problem with SIR dynamics. The main feature of our study is the presence of state constraints (related to intensive care units ICU capacity) and…