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We develop a minimalist compartmental model to study the impact of mobility restrictions in Italy during the Covid-19 outbreak. We show that an early lockdown shifts the epidemic in time, while that beyond a critical value of the lockdown…

Infectious or contagious diseases can be transmitted from one person to another through social contact networks. In today's interconnected global society, such contagion processes can cause global public health hazards, as exemplified by…

Inferring how an epidemic will progress and what actions to take when presented with limited information is of critical importance for epidemiologists and health professionals. In real world settings, epidemiology data can be scarce or…

Metapopulation models are commonly used in ecology, evolution, and epidemiology. These models usually entail homogeneity assumptions within patches and study networks of migration between patches to generate insights into conservation of…

Major advances in public health have resulted from disease prevention. However, prevention of a new infectious disease by vaccination or pharmaceuticals is made difficult by the slow process of vaccine and drug development. We propose an…

A stochastic epidemic model is defined in which each individual belongs to a household, a secondary grouping (typically school or workplace) and also the community as a whole. Moreover, infectious contacts take place in these three settings…

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 contact structure between hosts has a critical influence on disease spread. However, most networkbased models used in epidemiology tend to ignore heterogeneity in the weighting of contacts. This assumption is known to be at odds with…

In a prior study, a novel deterministic compartmental model known as the SEIHRK model was introduced, shedding light on the pivotal role of test kits as an intervention strategy for mitigating epidemics. Particularly in heterogeneous…

Many real networks exhibit a layered structure in which links in each layer reflect the function of nodes on different environments. These multiple types of links are usually represented by a multiplex network in which each layer has a…

Contagious processes, such as spread of infectious diseases, social behaviors, or computer viruses, affect biological, social, and technological systems. Epidemic models for large populations and finite populations on networks have been…

We study the diffusion of epidemics on networks that are partitioned into local communities. The gross structure of hierarchical networks of this kind can be described by a quotient graph. The rationale of this approach is that individuals…

In this paper, we develop a method to estimate the infection-rate of a disease, over a region, as a field that varies in space and time. To do so, we use time-series of case-counts of symptomatic patients as observed in the areal units that…

Compartmental models have long served as important tools in mathematical epidemiology, with their usefulness highlighted by the recent COVID-19 pandemic. However, most of the classical models fail to account for certain features of this…

Most spreading processes require spatial proximity between agents. The stationary state of spreading dynamics in a population of mobile agents thus depends on the interplay between the time and length scales involved in the epidemic process…

We introduce a methodology to guarantee safety against the spread of infectious diseases by viewing epidemiological models as control systems and by considering human interventions (such as quarantining or social distancing) as control…

Throughout the course of an epidemic, the rate at which disease spreads varies with behavioral changes, the emergence of new disease variants, and the introduction of mitigation policies. Estimating such changes in transmission rates can…

We study how the interplay between the memory immune response and pathogen mutation affects epidemic dynamics in two related models. The first explicitly models pathogen mutation and individual memory immune responses, with contacted…

We propose a model for epidemic spreading on a finite complex network with a restriction to at most one contamination per time step. Because of a highly discrete character of the process, the analysis cannot use the continous approximation,…

We introduce and analyze coupled, multi-strain epidemic models designed to simulate the emergence and dissemination of mutant (e.g. drug-resistant) pathogen strains. In particular, we investigate the mathematical and biological properties…