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The immune system is a real-time example of an evolving system that navigates the essentially infinite complexity of protein sequence space. How this system responds to disease and vaccination is discussed. Of particular focus is the case…

The paper describes and compares three approaches to modeling an epidemic spread. The first approach is a well-known system of SIR ordinary differential equations. The second is a mean-field model, in which an isolation strategy for each…

Estimating vaccination uptake is an integral part of ensuring public health. It was recently shown that vaccination uptake can be estimated automatically from web data, instead of slowly collected clinical records or population surveys. All…

Network-based intervention strategies can be effective and cost-efficient approaches to curtailing harmful contagions in myriad settings. As studied, these strategies are often impractical to implement, as they typically assume complete…

Background: Despite the consensus that vaccines play an important role in combating the global spread of infectious diseases, vaccine inequity is still rampant with deep-seated mentality of self-priority. This study aims to evaluate the…

We consider optimal control problems involving nonlinear ordinary differential equations with uncertain inputs. Using the sample average approximation, we obtain optimal control problems with ensembles of deterministic dynamical systems.…

In contemporary society, social networks accelerate decision dynamics causing a rapid switch of opinions in a number of fields, including the prevention of infectious diseases by means of vaccines. This means that opinion dynamics can…

We consider the effect of inducement to vaccinate during the spread of an infectious disease on complex networks. Suppose that public resources are finite and that only a small proportion of individuals can be vaccinated freely (complete…

This paper investigates optimal vaccination strategies in a metapopulation epidemic model. We consider a linear cost to better capture operational considerations, such as the total number of vaccines or hospitalizations, in contrast to the…

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…

Epidemiological models increasingly rely on self-reported behavioral data such as vaccination status, mask usage, and social distancing adherence to forecast disease transmission and assess the impact of non-pharmaceutical interventions…

We analyze infection spreading processes in a system where only a fraction $p$ of individuals can be affected by disease, while remaining $1-p$ individuals are immune. Such a picture can emerge as a natural consequence of previously…

The approach of N. Gay for estimating the coverage of a multivalent vaccine from antibody prevalence data in certain age cohorts is improved by using computer aided elimination theory of variables. Hereby, Gay's usage of numerical…

Motivated by massive outbreaks of COVID-19 that occurred even in populations with high vaccine uptake, we propose a novel multi-population temporal network model for the spread of recurrent epidemic diseases. We study the effect of human…

We study the continuous absorbing-state phase transition in the one-dimensional diffusive epidemic process via mean-field theory and Monte Carlo simulation. In this model, particles of two species (A and B) hop on a lattice and undergo…

Heterogeneity of population is a key factor in modeling the transmission of disease among the population and has huge impact on the outcome of the transmission. In order to investigate the decision making process in the heterogeneous mixing…

The current survey paper concerns stochastic mathematical models for the spread of infectious diseases. It starts with the simplest setting of a homogeneous population in which a transmittable disease spreads during a short outbreak.…

The propagation of model epidemics on a small-world network under the action of immunization is studied. Although the connectivity in this kind of networks is rather uniform, a vaccination strategy focused on the best connected individuals…

Seasonal influenza is a significant public health concern in the United States and globally. While influenza vaccines are the single most effective intervention to reduce influenza morbidity and mortality, there is considerable debate…

Vaccination is an effective way to prevent and control the occurrence and epidemic of infectious diseases. However, many factors influence whether the residents decide to get vaccinated or not, such as the efficacy and side effects while…