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Rapidly evolving viruses use antigenic drift as a key mechanism to evade host immunity and persist in real populations. While traditional models of antigenic drift and epidemic spread rely on low-dimensional antigenic spaces, genomic…
We use a multitype continuous time Markov branching process model to describe the dynamics of the spread of parasites of two types that can mutate into each other in a common host population. Instead of using a single virulence…
In this paper we study a diffusive age structured epidemic model with disease transmission between vector and host populations. The dynamics of the populations are described by reaction-diffusion equations, with infection age structure of…
Epidemiological models describe the spread of an infectious disease within a population. They capture microscopic details on how the disease is passed on among individuals in various different ways, while making predictions about the state…
We study the effect of the connectivity pattern of complex networks on the propagation dynamics of epidemics. The growth time scale of outbreaks is inversely proportional to the network degree fluctuations, signaling that epidemics spread…
Mathematical models of biological populations commonly use discrete structure classes to capture trait variation among individuals (e.g. age, size, phenotype, intracellular state). Upscaling these discrete models into continuum descriptions…
We introduce a kinetic model that couples the movement of a population of individuals with the dynamics of a pathogen in the same population. We consider that transmission occurs when a susceptible and an infectious individual are…
We propose a compartmental model for a disease with temporary immunity and secondary infections. From our assumptions on the parameters involved in the model, the system naturally evolves in three time scales. We characterize the equilibria…
The structure of heterogeneous networks and human mobility patterns profoundly influence the spreading of endemic diseases. In small-scale communities, individuals engage in social interactions within confined environments, such as homes…
Single virus epidemics over complete networks are widely explored in the literature as the fraction of infected nodes is, under appropriate microscopic modeling of the virus infection, a Markov process. With non-complete networks, this…
Despite the advanced stage of epidemic modeling, there is a major demand for methods to incorporate behavioral responses to the spread of a disease such as social distancing and adoption of prevention methods. Mobility plays an important…
We investigate an epidemiological model that incorporates waning of immunity at the individual level and boosting of the immune system upon re-exposure to the pathogen. When immunity is fully restored upon boosting, the system can be…
We present a continuous formulation of epidemic spreading on multilayer networks using a tensorial representation, extending the models of monoplex networks to this context. We derive analytical expressions for the epidemic threshold of the…
Internal feedbacks are commonly present in biological populations and can play a crucial role in the emergence of collective behavior. We consider a generalization of Fisher-KPP equation to describe the temporal evolution of the…
We study Eigen's model of quasi-species, characterized by sequences that replicate with a specified fitness and mutate independently at single sites. The evolution of the population vector in time is then closely related to that of quantum…
Recent years have seen a large amount of interest in epidemics on networks as a way of representing the complex structure of contacts capable of spreading infections through the modern human population. The configuration model is a popular…
We study the phase transition from the persistence phase to the extinction phase for the SIRS (susceptible/ infected/ refractory/ susceptible) model of diseases spreading on small world network. We show the effects of all the parameters…
This paper studies a discrete-time time-varying multi-layer networked SIWS (susceptible-infected-water-susceptible) model with multiple resources under both single-virus and competing multi-virus settings. Besides the human-to-human…
We present a systematic review of some basic results on the derivation of classical epidemiological models from simple agent-based dynamics. The evolution of large populations is coupled with the dynamics of the contact distribution,…
Coupling within-host infection dynamics with population-level transmission remains a major challenge in infectious disease modeling, especially for airborne pathogens with potential to spread indoor. The frequent emergence of such diseases…