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In this article we consider a microscopic model for host-vector disease transmission based on configuration space analysis. Using Vlasov scaling we obtain the corresponding mesoscopic (kinetic) equations, describing the density of…
Due to its ability to summarise 'real-time' epidemic behaviour, the time-dependent reproduction number, Rt, is a useful metric for tracking pathogen transmission and quantifying the effects of interventions during infectious disease…
Gut microbial composition has been linked to multiple health outcomes. Yet, temporal analysis of this composition had been limited to deterministic models. In this paper, we introduce a probabilistic model for the dynamics of intestinal…
We use a stochastic Markovian dynamics approach to describe the spreading of vector-transmitted diseases, like dengue, and the threshold of the disease. The coexistence space is composed by two structures representing the human and mosquito…
In order to explore the impact of periodically evolving domain on the transmission of disease, we study a SIS reaction-diffusion model with logistic term on a periodically evolving domain. The basic reproduction number ${\mathcal{R}}_0$ is…
In this paper we study invasion probabilities and invasion times of cooperative parasites spreading in spatially structured host populations. The spatial structure of the host population is given by a random geometric graph on $[0,1]^n$,…
This paper studies a distributed continuous-time bi-virus model in which two competing viruses spread over a network consisting of multiple groups of individuals. Limiting behaviors of the network are characterized by analyzing the…
I study the spreading of infectious diseases on heterogeneous populations. I represent the population structure by a contact-graph where vertices represent agents and edges represent disease transmission channels among them. The population…
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.…
We study an epidemic model for a constant population by taking into account four compartments of the individuals characterizing their states of health. Each individual is in one of the compartments susceptible (S); incubated - infected yet…
Human mobility, contact patterns, and their interplay are key aspects of our social behavior that shape the spread of infectious diseases across different regions. In the light of new evidence and data sets about these two elements,…
For many infectious diseases, a small-world network on an underlying regular lattice is a suitable simplified model for the contact structure of the host population. It is well known that the contact network, described in this setting by a…
Interactions among multiple infectious agents are increasingly recognized as a fundamental issue in the understanding of key questions in public health, regarding pathogen emergence, maintenance, and evolution. The full description of…
We investigate the long-time dynamics of a SIR epidemic model in the case of a population of pathogens infecting a homogeneous host population. The pathogen population is structured by a genotypic variable. When the initial mass of the…
The spreading of epidemics is very much determined by the structure of the contact network, which may be impacted by the mobility dynamics of the individuals themselves. In confined scenarios where a small, closed population spends most of…
An epidemiological model which incorporates synergistic effects that allow the infectivity and/or susceptibility of hosts to be dependent on the number of infected neighbours is proposed. Constructive synergy induces an exploitative…
This work is devoted to studying the dynamics of a structured population that is subject to the combined effects of environmental stochasticity, competition for resources, spatio-temporal heterogeneity and dispersal. The population is…
Bacteria and their viruses ("bacteriophages") coexist in natural environments forming complex infection networks. Recent empirical findings suggest that phage-bacteria infection networks often possess a nested structure such that there is a…
Traditional disease transmission models assume that the infectious period is exponentially distributed with a recovery rate fixed in time and across individuals. This assumption provides analytical and computational advantages, however it…
Motivated by observations in sequence data of herpesviruses, we introduce a multi-locus model for the joint evolution of different genotypes in a virus population that is distributed across a population of hosts. In the model, virus…