Related papers: Renewal equations for vector-borne diseases
The basic reproduction number ($R_0$) is an epidemiological metric that represents the average number of new infections caused by a single infectious individual in a completely susceptible population. The methodology for calculating this…
Age-dependent dynamics is an important characteristic of many infectious diseases. Age-group epidemic models describe the infection dynamics in different age-groups by allowing to set distinct parameter values for each. However, such models…
We study two simple mathematical models of the epidemic. At first, we study the repetitive infection spreading in a simplified SIRS model including the effect of the decay of the acquired immune. The model is an intermediate model of the…
The reproduction number of deterministic models is an essential quantity to predict whether an epidemic will spread or die out. Thresholds for disease extinction contribute crucial knowledge on disease control, elimination, and mitigation…
There are economic and physical limitations when applying prevention and control strategies for urban vector borne diseases. Consequently, there are increasing concerns and interest in designing efficient strategies and regulations that…
A very large class of ODE epidemic models (2.2) discussed in this paper enjoys the property of admitting also an integral renewal formulation, with respect to an "age of infection kernel" a(t) which has a matrix exponential form (3.2). We…
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…
Traditional disease transmission models assume that the infectious period is exponentially distributed with a recovery rate fixed in time and across individuals. This assumption provides analytical and computational advantages, however it…
A multi-patch and multi-group modeling framework describing the dynamics of a class of diseases driven by the interactions between vectors and hosts structured by groups is formulated. Hosts' dispersal is modeled in terms of patch-residence…
The issue of state estimation is considered for an SIR-SI epidemiological model describing a vector-borne disease such as dengue fever, subject to seasonal variations. Assuming continuous measurement of the incidence rate (that is the…
In this paper we describe the dynamics of a vector-borne relapsing disease, such as tick-borne relapsing fever, using the methods of compartmental models. After some motivation, model description, and a brief overview of the theory of…
Waning immunity and reinfection are critical features of many infectious diseases, but epidemiological models often fail to capture the intricate interaction between an individual's history of immunity and their current infection status;…
The versatility of renewal theory is owed to its abstract formulation. Renewals can be interpreted as steps of a random walk, switching events in two-state models, domain crossings of a random motion, etc. We here discuss a renewal process…
It is possible to model vector-borne infection using the classical Ross-Macdonald model. This attempt, however fails in several respects. First, using measured (or estimated) parameters, the model predicts a much greater number of cases…
We propose an integral model describing an epidemic of an infectious disease. The model is behavioural in the sense that the constitutive law for the force of infection includes a distributed delay, called "information index", that…
A great issue of discussion of an infectious disease is its basic reproduction number R0, which provides an estimation of the contagiousness of the disease. When R0 > 1, the disease spread will potentially lead to an outbreak, such that of…
The reconstruction of phylogenetic trees based on viral genetic sequence data sequentially sampled from an epidemic provides estimates of the past transmission dynamics, by fitting epidemiological models to these trees. To our knowledge,…
A model describing the dynamics related to the spreading of non-lethal infectious diseases in a fixed-size population is proposed. The model consists of a non-linear delay-differential equation describing the time evolution of the increment…
The emergence or adaptation of pathogens may lead to epidemics, highlighting the need for a thorough understanding of pathogen evolution. The tradeoff hypothesis suggests that virulence evolves to reach an optimal transmission intensity…
The basic reproductive number -- $R_0$ -- is one of the most common and most commonly misapplied numbers in public health. Although often used to compare outbreaks and forecast pandemic risk, this single number belies the complexity that…