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From pathogens and computer viruses to genes and memes, contagion models have found widespread utility across the natural and social sciences. Despite their success and breadth of adoption, the approach and structure of these models remain…
The waning of immunity after recovery or vaccination is a major factor accounting for the severity and prolonged duration of an array of epidemics, ranging from COVID-19 to diphtheria and pertussis. To study the effectiveness of different…
We show that disease transmission models in a spatially heterogeneous environment can have a large number of coexisting endemic equilibria. A general compartmental model is considered to describe the spread of an infectious disease in a…
Antibodies and humoral memory are key components of the adaptive immune system. We consider and computationally model mechanisms by which humoral memory present at baseline might instead increase infection load; we refer to this effect as…
The concept of cross diffusion is applied to some biological systems. The conditions for persistence and Turing instability in the presence of cross diffusion are derived. Many examples including: predator-prey, epidemics (with and without…
We introduce an interacting particle system that models the spread of an epidemic in terms of heterogeneous diffusive dynamics, rather than exogenous contact and transmission rates at the population level as in classical compartmental…
Complex contagion models that involve contagion along higher-order structures, such as simplicial complexes and hypergraphs, yield new classes of mean-field models. Interestingly, the differential equations arising from many such models…
A model for the transmission of dengue disease is presented. It consists of eight mutually-exclusive compartments representing the human and vector dynamics. It also includes a control parameter (insecticide) in order to fight the…
Traditional epidemic models consider that individual processes occur at constant rates. That is, an infected individual has a constant probability per unit time of recovering from infection after contagion. This assumption certainly fails…
We propose a compartmental model for vector-transmitted diseases, such as Malaria and Dengue, spreading over complex networks. Individuals are represented by independent random walkers and vectors by infected nodes. Both walkers and nodes…
Deterministic compartmental models have been used extensively in modeling epidemic propagation. These models are required to fit available data and numerical procedures are often implemented to this end. But not every model architecture is…
It is well known that behavioral changes in contact patterns may significantly affect the spread of an epidemic outbreak. Here we focus on simple endemic models for recurrent epidemics, by modelling the social contact rate as a function of…
The paper deals with the spread of two competing viruses over a network of population nodes, accounting for pairwise interactions and higher-order interactions (HOI) within and between the population nodes. We study the competitive…
Most previous studies of epidemic dynamics on complex networks suppose that the disease will eventually stabilize at either a disease-free state or an endemic one. In reality, however, some epidemics always exhibit sporadic and recurrent…
We study the tipping point collective dynamics of an adaptive susceptible-infected-susceptible (SIS) epidemiological network in a data-driven, machine learning-assisted manner. We identify a parameter-dependent effective stochastic…
To simplify mathematical models of disease spread, we often assume equal contact rates among hosts, but real-world scenarios differ. Network-based frameworks help capture these complexities and structural variations in actual systems. We…
OBJECTIVE: To propose a new approach to analyze the age-distribution of reported cases for vector-transmitted infections. METHODS: Using officially reported number of cases of dengue, Zika, chikungunya, malaria and leishmaniasis for…
Recent work in modeling the coupling between disease dynamics and dynamic social network geometry has led to the examination of how human interactions force a rewiring of connections in a population. Rewiring of the network may be…
We study epidemic arrival times in meta-population disease models through the lens of front propagation into unstable states. We demonstrate that several features of invasion fronts in the PDE context are also relevant to the network case.…
An adaptive network model using SIS epidemic propagation with link-type dependent link activation and deletion is considered. Bifurcation analysis of the pairwise ODE approximation and the network-based stochastic simulation is carried out,…