Related papers: Herd immunity under individual variation and reinf…
In this note we estimate herd immunity levels for the Covid-19 epidemic using a standard SEIR system that models the disease dynamics in homogeneous populations. The results obtained are indicative of values between 80% and 90% for…
Herd immunity is a critical concept in epidemiology, describing a threshold at which a sufficient proportion of a population is immune, either through infection or vaccination, thereby preventing sustained transmission of a pathogen. In the…
The Susceptible-Infected-Recovered (SIR) model is the cornerstone of epidemiological models. However, this specification depends on two parameters only, which implies a lack of flexibility and the difficulty to replicate the volatile…
Population heterogeneity is a key factor in epidemic dynamics, influencing both transmission and final epidemic size. While heterogeneity is often modelled through age structure, spatial location, or contact patterns, differences in host…
We study the influence of the rate of the attainment of herd immunity (HI), in the absence of an approved vaccine, on the vulnerable population. We essentially ask the question: how hard the evolution towards the desired herd immunity could…
SIRS epidemic models assume that individual immunity (from infection and vaccination) wanes in one big leap, from complete immunity to complete susceptibility. For many diseases immunity on the contrary wanes gradually, something that's…
Human behavior plays a critical role in shaping epidemic trajectories. During health crises, people respond in diverse ways in terms of self-protection and adherence to recommended measures, largely reflecting differences in how individuals…
COVID-19 pandemic has been raging all around the world for almost a year now, as of November 1, 2020. In this paper, we try to analyze the variation of the COVID-19 pandemic in different countries in the light of some modifications to the…
Recently, [8] has proposed that heterogeneity of infectiousness (and susceptibility) across individuals in infectious diseases, plays a major role in affecting the Herd Immunity Threshold (HIT). Such heterogeneity has been observed in…
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…
We model and calculate the fraction of infected population necessary to reach herd immunity, taking into account the heterogeneity in infectiousness and susceptibility, as well as the correlation between those two parameters. We show that…
We consider the SEIRS compartment epidemiology model suitable for predicting the evolution of the COVID-19 pandemy in the extreme limiting case of no acquired immunity. The disease-free and endemic fixed points are found and their stability…
Susceptibility governs the dynamics of contagion. The classical SIR model is one of the simplest compartmental models of contagion spread, assuming a single shared susceptibility level. However, variation in susceptibility over a population…
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…
We study variants of the SEIR model for interpreting some qualitative features of the statistics of the Covid-19 epidemic in France. Standard SEIR models distinguish essentially two regimes: either the disease is controlled and the number…
Individual contributions to the spread of an epidemic vary widely due to an individual's location in a social network and their intrinsic ability to spread or contract diseases. While the effect of heterogeneous population structure and…
We formulate a general SEIR epidemic model in a heterogenous population characterized by some trait in a discrete or continuous subset of a space R d. The incubation and recovery rates governing the evolution of each homogenous…
How to prevent the spread of human diseases is a great challenge for the scientific community and so far there are many studies in which immunization strategies have been developed. However, these kind of strategies usually do not consider…
In this paper, we propose a modified susceptible-infected-recovered (SIR) model, in which each node is assigned with an identical capability of active contacts, $A$, at each time step. In contrast to the previous studies, we find that on…
We study a susceptible-vaccinated--infected--recovered (SVIR) epidemic-spreading model with diversity of infection rate of the individuals. By means of analytical arguments as well as extensive computer simulations, we demonstrate that the…