Related papers: A stochastic household model for vector-borne dise…
This paper considers a stochastic SIR (susceptible$\to$infective$\to$removed) epidemic model in which individuals may make infectious contacts in two ways, both within `households' (which for ease of exposition are assumed to have equal…
The ongoing Zika virus (ZIKV) epidemic poses a major global public health emergency. It is known that ZIKV is spread by \textit{Aedes} mosquitoes, recent studies show that ZIKV can also be transmitted via sexual contact and cases of…
Ross-Macdonald models are the building blocks of most vector-borne disease models. Even for the same disease, different authors use different model formulations, but a study of the dynamical consequences of assuming different hypotheses is…
This paper is concerned with a stochastic model for the spread of an SEIR (susceptible -> exposed (=latent) -> infective -> removed) epidemic with a contact tracing scheme, in which removed individuals may name some of their infectious…
A stochastic epidemic model accounting for the effect of contact-tracing on the spread of an infectious disease is studied. Precisely, individuals identified as infected may contribute to detecting other infectious individuals by providing…
In this paper we propose a Stochastic model for studying a spatial cholera epidemic spreading where communities (Humans and Bacteria) are spatially distributed on a one-dimensional lattice and the bacteria are transported along a network…
We develop a stochastic two-patch epidemic model with nonlinear recidivism to investigate infectious disease dynamics in heterogeneous populations. Extending a deterministic framework, we introduce stochasticity to account for random…
An age structured mathematical model with time dependent parameters is developed to investigate the dynamics of dengue transmission. Its properties are thoroughly analyzed in the first part of this work, as for example its disease free…
Dengue is a vector-borne disease transmitted by the mosquito Aedes aegypti. It has been observed that its incidence is strongly influenced by temperature and other abiotic factors like rainfall and humidity. In this work we compare the…
Horizontal gene transfer consists in exchanging genetic materials between microorganisms during their lives. This is a major mechanism of bacterial evolution and is believed to be of main importance in antibiotics resistance. We consider a…
Mycobacterium tuberculosis infection can involve all immune system components and can result in different disease outcomes. The antibiotic TB drugs require strict adherence to prevent both disease relapse and mutation of drug- and…
Epidemic models currently play a central role in our attempts to understand and control infectious diseases. Here, we derive a model for the diffusion limit of stochastic susceptible-infectious-removed (SIR) epidemic dynamics on a…
Mosquitoes are vectors of viral diseases with epidemic potential in many regions of the world, and in absence of vaccines or therapies, their control is the main alternative. Chemical control through insecticides has been one of the…
This paper focuses on and analyzes realistic SIR models that take stochasticity into account. The proposed systems are applicable to most incidence rates that are used in the literature including the bilinear incidence rate, the…
We study the relation between different social behaviors and the onset of epidemics in a model for the dynamics of sexual transmitted diseases. The model considers the society as a system of individual sexuated agents that can be organized…
To better describe the spread of a disease, we extend a discrete time stochastic SIR-type epidemic model of Tuckwell and Williams. We assume the dependence on time of the number of daily encounters and include a parameter to represent a…
Stochastic epidemic models can estimate infection and removal rates, and derived quantities such as the basic reproductive number ($R_0$), when both infection and removal times are observed. In practice, however, removal times are often…
Consider stochastic models for the spread of an infection in a structured community, where this structured community is itself described by a random network model. Some common network models and transmission models are defined and large…
A mathematical model of Zika virus transmission incorporating human movement between rural areas and nearby forests is presented to investigate the role of human movement in the spread of Zika virus infections in human and mosquito…
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…