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Epidemic disease spreading is conventionally often modelled and analyzed by means of rate and diffusion equations, following the paradigms of well-controlled chemical reactions and diffusive dynamics in a test tube. Yet, serious worries…

The SIR model is a three-compartment model of the time development of an epidemic. After normalizing the dependent variables, the model is a system of two non-linear differential equations for the susceptible proportion $S$ and the infected…

The time-varying reproduction number ($R_t$) gives an indication of the trajectory of an infectious disease outbreak. Commonly used frameworks for inferring $R_t$ from epidemiological time series include those based on compartmental models…

Controlling and understanding epidemic outbreaks has recently drawn great interest in a large spectrum of research communities. Vaccination is one of the most well-established and effective strategies in order to contain an epidemic. In the…

In general insurance companies, a correct estimation of liabilities plays a key role due to its impact on management and investing decisions. Since the Financial Crisis of 2007-2008 and the strengthening of regulation, the focus is not only…

Epidemiological forecasting from surveillance data is a hard problem and hybridizing mechanistic compartmental models with neural models is a natural direction. The mechanistic structure helps keep trajectories epidemiologically plausible,…

The ongoing COVID-19 pandemic is challenging every part of society. From a scientific point of view the first major task is to predict the dynamics of the pandemic, allowing governments to allocate proper resources and measures to fight it,…

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…

When an unprecedented infectious disease with high mortality and transmissibility emerges, immediate usage of vaccines or medicines is hardly available. Thus, many health authorities rely on non-pharmaceutical interventions through…

We develop a multi-patch and multi-group model that captures the dynamics of an infectious disease when the host is structured into an arbitrary number of groups and interacts into an arbitrary number of patches where the infection takes…

We study the spreading of an infection within an SIS epidemiological model on a network. Susceptible agents are given the opportunity of breaking their links with infected agents. Broken links are either permanently removed or reconnected…

Age-dependent dynamics is an important characteristic of many infectious diseases. Age-group epidemic models describe the infection dynamics in different age-groups by allowing to set distinct parameter values for each. However, such models…

This paper introduces a microscopic approach to model epidemics, which can explicitly consider the consequences of individual's decisions on the spread of the disease. We first formulate a microscopic multi-agent epidemic model where every…

The time-dependent reproduction number Rt can be used to track pathogen transmission and to assess the efficacy of interventions. This quantity can be estimated by fitting renewal equation models to time series of infectious disease case…

One of the most fascinating phenomena observed in reaction-diffusion systems is the emergence of segregated solutions, i.e. population densities with disjoint supports. We analyse such a reaction cross-diffusion system. In order to prove…

Meta-analytic methods may be used to combine evidence from different sources of information. Quite commonly, the normal-normal hierarchical model (NNHM) including a random-effect to account for between-study heterogeneity is utilized for…

Mathematical modeling of disease spreading plays a crucial role in understanding, controlling and preventing epidemic outbreaks. In a microscopic description of the propagation of a disease over the complex network of human contacts, the…

Individual contributions to the spread of an epidemic vary widely due to an individual's location in a social network and their intrinsic ability to spread or contract diseases. While the effect of heterogeneous population structure and…

This work presents a model combining the simplest communicable and non-communicable disease models. The latter is, by far, the leading cause of sickness and death in the World, and introduces basal heterogeneity in populations where…

In the absence of drugs and vaccines, policymakers use non-pharmaceutical interventions such as social distancing to decrease rates of disease-causing contact, with the aim of reducing or delaying the epidemic peak. These measures carry…