A general class of spreading processes with non-Markovian dynamics

In this paper we propose a general class of models for spreading processes we call the $SI^*V^*$ model. Unlike many works that consider a fixed number of compartmental states, we allow an arbitrary number of states on arbitrary graphs with heterogeneous parameters for all nodes and edges. As a result, this generalizes an extremely large number of models studied in the literature including the MSEIV, MSEIR, MSEIS, SEIV, SEIR, SEIS, SIV, SIRS, SIR, and SIS models. Furthermore, we show how the $SI^*V^*$ model allows us to model non-Poisson spreading processes letting us capture much more complicated dynamics than existing works such as information spreading through social networks or the delayed incubation period of a disease like Ebola. This is in contrast to the overwhelming majority of works in the literature that only consider spreading processes that can be captured by a Markov process. After developing the stochastic model, we analyze its deterministic mean-field approximation and provide conditions for when the disease-free equilibrium is stable. Simulations illustrate our results

A multilayer temporal network model for STD spreading accounting for permanent and casual partners

Sexually transmitted diseases (STD) modeling has used contact networks to study the spreading of pathogens. Recent findings have stressed the increasing role of casual partners, often enabled by online dating applications. We study the Susceptible-Infected-Susceptible (SIS) epidemic model -appropriate for STDs- over a two-layer network aimed to account for the effect of casual partners in the spreading of STDs. In this novel model, individuals have a set of steady partnerships (links in layer 1). At certain rates, every individual can switch between active and inactive states and, while active, it establishes casual partnerships with some probability with active neighbors in layer 2 (whose links can be thought as potential casual partnerships). Individuals that are not engaged in casual partnerships are classified as inactive, and the transitions between active and inactive states are independent of their infectious state. We use mean-field equations as well as stochastic simulations to derive the epidemic threshold, which decreases substantially with the addition of the second layer. Interestingly, for a given expected number of casual partnerships, which depends on the probabilities of being active, this threshold turns out to depend on the duration of casual partnerships: the longer they are, the lower the threshold

Assessing Dengue Risk Globally Using Non-Markovian Models

Dengue is a vector-borne disease transmitted by Aedes mosquitoes. The worldwide spread of these mosquitoes and the increasing disease burden have emphasized the need for a spatio-temporal risk map capable of assessing dengue outbreak conditions and quantifying the outbreak risk. Given that the life cycle of Aedes mosquitoes is strongly influenced by habitat temperature, numerous studies have utilized temperature-dependent development rates of these mosquitoes to construct virus transmission and outbreak risk models. In this study, we advance existing research by developing a mechanistic model for the mosquito life cycle that accurately accounts for the non-Markovian nature of the process. By fitting the model to data on human dengue cases, we estimate several model parameters, allowing the development of a global spatiotemporal dengue risk map. This risk model employs temperature and precipitation data to assess the environmental suitability for dengue outbreaks in a given area. Furthermore, we demonstrate how to reduce the model to the corresponding differential equations, enabling us to utilize existing methods for analyzing the system and fitting the model to observations. This approach can be further applied to similar non-Markovian processes that are currently described with less accurate Markovian models