Related papers: Type reproduction number for epidemic models on he…
Vaccination and outbreak monitoring are essential tools for preventing and minimizing outbreaks of infectious diseases. Targeted strategies, where the individuals most important for monitoring or preventing outbreaks are selected for…
In the first part of this paper, we review old and new results about the influence of host population heterogeneity on (various characteristics of) epidemic outbreaks. In the second part we highlight a modelling issue that so far has…
In this paper, we propose two novel immunization strategies, i.e., combined immunization and duplex immunization, for SIS model in directed scale-free networks, and obtain the epidemic thresholds for them with linear and nonlinear…
In this paper we first introduce the general stochastic epidemic model for the spread of infectious diseases. Then we give methods for inferring model parameters such as the basic reproduction number $R_0$ and vaccination coverage $v_c$…
We consider the simple epidemiological SIS model for a general heterogeneous population introduced by Lajmanovich and Yorke (1976) in finite dimension, and its infinite dimensional generalization we introduced in previous works. In this…
It is widely known that the spread of the HIV virus was slower than exponential in several populations, even at the very beginning of the epidemic. We show that this implies a significant reduction in the effective reproductive rate of the…
We consider the effect of inducement to vaccinate during the spread of an infectious disease on complex networks. Suppose that public resources are finite and that only a small proportion of individuals can be vaccinated freely (complete…
We consider an infectious disease spreading along the edges of a network which may have significant clustering. The individuals in the population have heterogeneous infectiousness and/or susceptibility. We define the out-transmissibility of…
We performed a thorough sensitivity analysis of the herd immunity threshold for discrete-time SIR compartmental models with a static network structure. We find unexpectedly that these models violate classical intuition which holds that the…
In this study, we present an immuno-epidemic model to understand mitigation options during an epidemic break. The model incorporates comorbidity and multiple-vaccine doses through a system of coupled integro-differential equations to…
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…
The success of a vaccination program is crucially dependent on its adoption by a critical fraction of the population, as the resulting herd immunity prevents future outbreaks of an epidemic. However, the effectiveness of a campaign can…
The epidemic threshold is probably the most studied quantity in the modelling of epidemics on networks. For a large class of networks and dynamics the epidemic threshold is well studied and understood. However, it is less so for clustered…
We study the SIR model of epidemics on positively correlated heterogeneous networks with population variability, and explore the dependence of the final outbreak size on the network heterogeneity strength and basic reproduction number $R_0$…
An approach to estimate the influence of the treatment-type controls on the basic reproduction number, R 0 , is proposed and elaborated. The presented approach allows one to estimate the effect of a given treatment strategy or to compare a…
The dynamics of contact networks and epidemics of infectious diseases often occur on comparable time scales. Ignoring one of these time scales may provide an incomplete understanding of the population dynamics of the infection process. We…
Using the continuous-time susceptible-infected-susceptible (SIS) model on networks, we investigate the problem of inferring the class of the underlying network when epidemic data is only available at population-level (i.e. the number of…
Heterogeneity is an important property of any population experiencing a disease. Here we apply general methods of the theory of heterogeneous populations to the simplest mathematical models in epidemiology. In particular, an SIR…
The spread of sexually transmitted diseases (e.g. Chlamydia, Syphilis, Gonorrhea, HIV) across populations is a major concern for scientists and health agencies. In this context, both data collection on sexual contact networks and the…
Many infectious diseases can lead to re-infection. We examined the relationship between the prevalence of repeat infection and the basic reproductive number (R0). First we solved a generic, deterministic compartmental model of re-infection…