Related papers: Basic Vaccination Control Techniques for a General…
The non-population conserving SIR (SIR-NC) model to describe the spread of infections in a community is proposed and studied. Unlike the standard SIR model, SIR-NC does not assume population conservation. Although similar in form to the…
In the face of serious infectious diseases, governments endeavour to implement containment measures such as public vaccination at a macroscopic level. Meanwhile, individuals tend to protect themselves by avoiding contacts with infections at…
Real-time vaccination following an outbreak can effectively mitigate the damage caused by an infectious disease. However, in many cases, available resources are insufficient to vaccinate the entire at-risk population, logistics result in…
Taking precautions before or during the start of a virus outbreak can heavily reduce the number of infected. The question which individuals should be immunized in order to mitigate the impact of the virus on the rest of population has…
The Susceptible-Infected-Recovered (SIR) model is the cornerstone of epidemiological models. However, this specification depends on two parameters only, which implies a lack of flexibility and the difficulty to replicate the volatile…
We study the interaction between epidemic spreading and a vaccination process. We assume that, similar to the disease spreading, also the vaccination process occurs through direct contact, i.e., it follows the standard…
Ebola virus is one of the most virulent pathogens for humans. We present a mathematical description of different Susceptible-Exposed-Infectious-Recovered (SEIR) models. By using mathematical modeling and analysis, the latest major outbreak…
The success of an infectious disease to invade a population is strongly controlled by the population's specific connectivity structure. Here a network model is presented as an aid in understanding the role of social behavior and…
We study the minimum eradication time problem for controlled Susceptible-Infected-Recovered (SIR) epidemic models that incorporate vaccination control and time-varying infected and recovery rates. Unlike the SIR model with constant rates,…
We present a detailed set-based analysis of the well-known SIR and SEIR epidemic models subjected to hard caps on the proportion of infective individuals, and bounds on the allowable intervention strategies, such as social distancing,…
Vaccinations are an important tool in the prevention of disease. Vaccinations are generally voluntary for each member of a population and vaccination decisions are influenced by individual risk perceptions and contact structures within…
In this paper, we consider an adaptive optimal control problem for an SIR/V epidemic model with human behavioral effects.We develop a model where effective management of infectious diseases are monitored by the means of non pharmaceutical…
Recent Covid-19 pandemic has demonstrated the need of efficient epidemic outbreak management. We study the optimal control problem of minimizing the fraction of infected population by applying vaccination and treatment control strategies,…
This work is concerned with epidemiological models defined on networks, which highlight the prominent role of the social contact network of a given population in the spread of infectious diseases. In particular, we address the modelling and…
We consider the simple epidemiological SIS model for a general heterogeneous population introduced by Lajmanovich and Yorke (1976) in finite dimension, and its infinite dimensional generalization we introduced in previous works. In this…
Containing an epidemic at its origin is the most desirable mitigation. Epidemics have often originated in rural areas, with rural communities among the first affected. Disease dynamics in rural regions have received limited attention, and…
We present a data-driven optimal control approach which integrates the reported partial data with the epidemic dynamics for COVID-19. We use a basic Susceptible-Exposed-Infectious-Recovered (SEIR) model, the model parameters are…
We formulate a generalized susceptible exposed infectious recovered (SEIR) model on a graph, describing the population dynamics of an open crowded place with an arbitrary topology. As a sample calculation, we discuss three simple cases,…
The SIR model is the cornerstone model for mathematical epidemiology, explaining key epidemic features such as the second-order transition between disease-free and epidemic states, the initial exponential growth of outbreaks or the…
Heterogeneity is an important property of any population experiencing a disease. Here we apply general methods of the theory of heterogeneous populations to the simplest mathematical models in epidemiology. In particular, an SIR…