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Motility-induced phase separation (MIPS) is a paradigmatic non-equilibrium transition in active matter, determined by the P\'eclet number and packing fraction. We investigate the single-phase and phase-separated regimes of MIPS using a…
Rapidly mutating pathogens may be able to persist in the population and reach an endemic equilibrium by escaping hosts' acquired immunity. For such diseases, multiple biological, environmental and population-level mechanisms determine the…
Almost all viruses, regardless of their genomic material, produce defective viral genomes (DVG) as an unavoidable byproduct of their error-prone replication. Defective interfering (DI) elements are a subgroup of DVGs that have been shown to…
This paper studies large deviations of a ``fully coupled" finite state mean-field interacting particle system in a fast varying environment. The empirical measure of the particles evolves in the slow time scale and the random environment…
The steady state properties of the mean density population of infected cells in a viral spread is simulated by a general forest fire like cellular automaton model with two distinct populations of cells ( permissive and resistant ones) and…
Infectious diseases are caused by pathogenic microorganisms and can spread through different ways. Mathematical models and computational simulation have been used extensively to investigate the transmission and spread of infectious…
We consider a countable system of interacting (possibly non-Markovian) stochastic differential equations driven by independent Brownian motions and indexed by the vertices of a locally finite graph $G = (V,E)$. The drift of the process at…
The flux of visitors through popular places undoubtedly influences viral spreading -- from H1N1 and Zika viruses spreading through physical spaces such as airports, to rumors and ideas spreading though online spaces such as chatrooms and…
The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one of the mechanisms…
Empirical studies suggest that contact patterns follow heterogeneous inter-event times, meaning that intervals of high activity are followed by periods of inactivity. Combined with birth and death of individuals, these temporal constraints…
Defective interfering particles arise spontaneously during a viral infection as mutants lacking essential parts of the viral genome. Their ability to replicate in the presence of the wild-type (WT) virus (at the expense of viable viral…
Recent work on information survival in sensor and human P2P networks, try to study the datum preservation or the virus spreading in a network under the dynamical system approach. Some interesting solutions propose to use non-linear…
Interactions in time-varying complex systems are often very heterogeneous at the topological level (who interacts with whom) and at the temporal level (when interactions occur and how often). While it is known that temporal heterogeneities…
Different pathogens spreading in the same host population often generate complex co-circulation dynamics because of the many possible interactions between the pathogens and the host immune system, the host life cycle, and the space…
Infectious disease models can be of great use for understanding the underlying mechanisms that influence the spread of diseases and predicting future disease progression. Modeling has been increasingly used to evaluate the potential impact…
We have designed a computational model of a virus spread near the outbreak threshold. Using computer simulation we studied the Susceptible - Infected - Recovered (SIR) process where in consequence of a force of habit that is manifested by…
Dengue virus transmission models commonly assume an exponential distribution for the mosquito extrinsic incubation period (EIP), potentially oversimplifying biological variability. We developed a stochastic mechanistic dengue transmission…
Using a stochastic Susceptible-Infected-Removed (SIR) meta-population model of disease transmission, we present analytical calculations and numerical simulations dissecting the interplay between stochasticity and the division of a…
We study an interacting particle system whose dynamics depends on an interacting random environment. As the number of particles grows large, the transition rate of the particles slows down (perhaps because they share a common resource of…
We study an abstract model for the co-evolution between mutating viruses and the adaptive immune system. In sequence space, these two populations are localized around transiently dominant strains. Delocalization or error thresholds exhibit…