In this study, criminal gang membership is treated as an infection that spreads through a community by interactions among gang members and the population. A mathematical model consisting of a system of coupled, nonlinear ordinary differential equations is used to describe this spread and to suggest control mechanisms to minimize this infection. The analysis shows the existence of three equilibrium states -two of which contain no gang members. When parameters such as recruitment, conviction and recidivism rates and longer jail sentences are varied, the greatest reduction occurs by changing the parameters in combination. A bifurcation analysis shows transcritical bifurcations and no hopf bifurcations.

Abstract.A free-boundary model is used to describe frontal polymerization. Autoacceleration effects, such as the gel effect, are accounted for in the formulation. Weakly nonlinear analysis is applied to investigate pulsating instabilities in two dimensions. The analysis produces a pair of Landau equations that describe the evolution of the linearly unstable modes. Autoacceleration influences the linear stability of the system as well as the onset and stability of spinning and standing modes.

Social media plays an important role in alerting and educating the public during disease outbreaks. By increasing awareness of the disease and its prevention, it can lead to a modification of behaviour which then affects contact/incidence rates. Social media data may also be used when formulating, developing and parameterising models. As mobile technology continues to evolve and proliferate, social media is expected to occupy an increasingly prominent role in the field of infectious disease modelling to improve their predictive power. This article presents a review of existing models incorporating media in general and highlights opportunities for social media to enhance traditional compartmental models so as to make the best use of this resource in controlling the spread of disease.

No abstract