On stability and bifurcation of solutions of an SEIR epidemic model with vertical transmission

Massad

Math Methods in App Sciences

et al. 2017

In this paper, a model for the spread of tuberculosis between buffaloes and lions is presented and analyzed. The most important system parameters are identified: vertical and horizontal disease transmission among the buffaloes and the influence of intraspecific competition between healthy and diseased buffaloes on the infected buffaloes population. Removal of diseased prey appears to be the most effective strategy to render the ecosystem disease free.

false(\frac{d}{d m} τ_{1} false(m false) false) |_{m = m^{*}}

. □…”

Section: Bifurcationsmentioning

confidence: 79%

A mathematical model for bovine tuberculosis among buffaloes and lions in the Kruger National Park

Massad

Math Methods in App Sciences

et al. 2017

Journal of Applied Mathematics

“…Proof. It is well known that, in order for Hopf bifurcation in four-dimensional systems to occur, the following conditions should be satisfied [21,22]:…”

Section: Journal Of Applied Mathematicsmentioning

confidence: 99%

“…An application of Sotomayor theorem [19,20] for local bifurcations is used to study the occurrence of local bifurcations near the equilibria. The Hopf bifurcation [21,22] conditions are derived. Finally, numerical simulations are used to confirm our obtained analytical results and specify the control set of parameters.…”

Section: Introductionmentioning

confidence: 99%

The Dynamics of Epidemic Model with Two Types of Infectious Diseases and Vertical Transmission

Naji

Hussien

2016

An epidemic model that describes the dynamics of the spread of infectious diseases is proposed. Two different types of infectious diseases that spread through both horizontal and vertical transmission in the host population are considered. The basic reproduction numberR0is determined. The local and the global stability of all possible equilibrium points are achieved. The local bifurcation analysis and Hopf bifurcation analysis for the four-dimensional epidemic model are studied. Numerical simulations are used to confirm our obtained analytical results.

Proceedings of the 2005 ACM Symposium on Applied Computing

“…The susceptibles, exposed, infectives, and removals (SEIR) model includes the class of exposed individuals who have been exposed to the disease, but are in the latent stage, and hence are not capable of infecting the susceptibles. A 4-dimensional SEIR epidemic model is considered and the criteria for stable equilibria has been established [6].…”

Section: Related Workmentioning

confidence: 99%

Temporal analysis of infectious diseases

Abbas

Mikler

Gatti

2005

A Bayesian network is developed to embed the probabilistic reasoning dependencies of the demographics on the incidence of infectious diseases. Influenza epidemics occur every year in both hemispheres during the winter. The Bayesian learning paradigm is used to create synthetic data sets that simulate an outbreak of influenza for a geographic area. The Bayesian prior and posterior probabilities can be altered to represent an outbreak for various demographics in different geographic regions. Epidemic curves are generated, via time series analysis of the data sets, for the temporal flow of influenza on different variants of the demographics. The analysis of the demographic-based epidemic curves facilitates in the identification of the risk levels among the different demographic sections. Spread vaccination lowers the impact of the epidemic, depending on the efficacy of the vaccine. Our model is equipped to analyze the effects of spread vaccination and design vaccination strategies, that optimize the use of public health resources, by identifying high-risk demographic groups. Our results show that application of the vaccine in the order of risk levels will further lower the epidemic impact as compared to uniform spread vaccination.