335 research outputs found
On the backward bifurcation of a vaccination model with nonlinear incidence
A compartmental epidemic model, introduced by Gumel and Moghadas [1], is considered. The model incorporates a nonlinear incidence rate and an imperfect preventive vaccine given to susceptible individuals. A bifurcation analysis is performed by applying the bifurcation method introduced in [2], which is based on the use of the center manifold theory. Conditions ensuring the occurrence of backward bifurcation are derived. The obtained results are numerically validated and then discussed from both the mathematical and the epidemiological perspective
Population heterogeneity in vaccine coverage impacts epidemic thresholds and bifurcation dynamics
Population heterogeneity, especially in individuals' contact networks, plays
an important role in transmission dynamics of infectious diseases. For
vaccine-preventable diseases, outstanding issues like vaccine hesitancy and
availability of vaccines further lead to nonuniform coverage among groups, not
to mention the efficacy of vaccines and the mixing pattern varying from one
group to another. As the ongoing COVID-19 pandemic transitions to endemicity,
it is of interest and significance to understand the impact of aforementioned
population heterogeneity on the emergence and persistence of epidemics. Here we
analyze epidemic thresholds and characterize bifurcation dynamics by accounting
for heterogeneity caused by group-dependent characteristics, including
vaccination rate and efficacy as well as disease transmissibility. Our analysis
shows that increases in the difference in vaccination coverage among groups can
render multiple equilibria of disease burden to exist even if the overall basic
reproductive ratio is below one (also known as backward bifurcation). The
presence of other heterogeneity factors such as differences in vaccine
efficacy, transmission, mixing pattern, and group size can each exhibit subtle
impacts on bifurcation. We find that heterogeneity in vaccine efficacy can
undermine the condition for backward bifurcations whereas homophily tends to
aggravate disease endemicity. Our results have practical implications for
improving public health efforts by addressing the role of population
heterogeneity in the spread and control of diseases.Comment: 14 pages, 8 figure
Analysis of a Vaccination Model for Carrier Dependent Infectious Diseases with Environmental Effects
We have proposed and analyzed a nonlinear mathematical model for the spread of carrier dependent infectious diseases in a population with variable size structure including the role of vaccination. It is assumed that the susceptibles become infected by direct contact with infectives and/or by the carrier population present in the environment. The density of carrier population is assumed to be governed by a generalized logistic model and is dependent on environmental and human factors which are conducive to the growth of carrier population. The model is analyzed using stability theory of differential equations and numerical simulation. We have found a threshold condition, in terms of vaccine induced reproduction number R(φ) which is, if less than one, the disease dies out in the absence of carriers provided the vaccine efficacy is high enough, and otherwise the infection is maintained in the population. The model also exhibits backward bifurcation at R(φ) = 1. It is also shown that the spread of an infectious disease increases as the carrier population density increases. In addition, the constant immigration of susceptibles makes the disease more endemic
- …