Related papers: Renewal equations for vector-borne diseases
The time-dependent reproduction number Rt can be used to track pathogen transmission and to assess the efficacy of interventions. This quantity can be estimated by fitting renewal equation models to time series of infectious disease case…
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…
The time-varying reproduction number ($R_t$) gives an indication of the trajectory of an infectious disease outbreak. Commonly used frameworks for inferring $R_t$ from epidemiological time series include those based on compartmental models…
In the face of an infectious disease, a key epidemiological measure is the basic reproduction number, which quantifies the average secondary infections caused by a single case in a susceptible population. In practice, the effective…
Transmission rates are key in understanding the spread of infectious diseases. Using the framework of compartmental models, we introduce a simple method that enables us to reconstruct time series of transmission rates directly from…
During an infectious disease outbreak, public health decision-makers require real-time monitoring of disease transmission to respond quickly and intelligently. In these settings, a key measure of transmission is the instantaneous…
Renewal processes are a popular approach used in modelling infectious disease outbreaks. In a renewal process, previous infections give rise to future infections. However, while this formulation seems sensible, its application to infectious…
Vector-borne diseases with reservoir cycles are complex to understand because new infections come from contacts of the vector with humans and different reservoirs. In this scenario, the basic reproductive number $\mathcal{R}^h_0$ of the…
When an infectious disease strikes a population, the number of newly reported cases is often the only available information that one can obtain during early stages of the outbreak. An important goal of early outbreak analysis is to obtain a…
The time-varying reproduction number $R(t)$ measures the number of new infections per infectious individual and is closely correlated with the time series of infection incidence by definition. The timings of actual infections are rarely…
The effective reproduction number, R(t), is a central point in the study of infectious diseases. It establishes in an explicit way the extent of an epidemic spread process in a population. The current estimation methods for the time…
We present a unified framework ensuring well posedness and providing stability estimates to a class of Initial Boundary Value Problems for renewal equations comprising a variety of biological or epidemiological models. This versatility is…
We construct an epidemic model for the transmission of dengue fever with an early-life stage in the vector dynamics and age-structure within hosts. The early-life stage of the vector is modeled via a general function that supports multiple…
A wide range of infectious diseases are both vertically and horizontally transmitted. Such diseases are spatially transmitted via multiple species in heterogeneous environments, typically described by complex meta-population models. The…
Mathematical models of infectious diseases, which are in principle analytically tractable, use two general approaches. The first approach, generally known as compartmental modeling, addresses the time evolution of disease propagation at the…
We study a renewal problem within a periodic environment, departing from the classical renewal theory by relaxing the assumption of independent and identically distributed inter-arrival times. Instead, the conditional distribution of the…
In most models of the spread of disease over contact networks it is assumed that the probabilities per unit time of disease transmission and recovery from disease are constant, implying exponential distributions of the time intervals for…
Infectious disease outbreaks recapitulate biology: they emerge from the multi-level interaction of hosts, pathogens, and their shared environment. As a result, predicting when, where, and how far diseases will spread requires a complex…
We introduce an epidemic model with varying infectivity and general exposed and infectious periods, where the infectivity of each individual is a random function of the elapsed time since infection, those function being i.i.d. for the…
The illness-death model for chronic conditions is combined with a renewal equation for the number of newborns taking into account possibly different fertility rates in the healthy and diseased parts of the population. The resulting boundary…