The dynamics of poverty and crime

Poverty and crime are two maladies that plague metropolitan areas. The economic theory of crime[1]demonstrates a direct correlation between poverty and crime. The model considered in this study seeks to examine the dynamics of the poverty-crime system through stability analysis of a system of ordinary differential equations in order to identify cost-effective strategies to combat crime in metropolises.

Epidemics on networks: Reducing disease transmission using health emergency declarations and peer communication

Understanding individual decisions in a world where communications and information move instantly via cell phones and the internet,contributes to the development and implementation of policies aimed at stopping or ameliorating the spread of diseases.In this manuscript,the role of official social network perturbations generated by public health officials to slow down or stop a disease outbreak are studied over distinct classes of static social networks.The dynamics are stochastic in nature with individuals(nodes)being assigned fixed levels of education or wealth.Nodes may change their epidemiological status from susceptible,to infected and to recovered.Most importantly,it is assumed that when the prevalence reaches a pre-determined threshold level,P*,information,called awareness in our framework,starts to spread,a process triggered by public health authorities.Information is assumed to spread over the same static network and whether or not one becomes a temporary informer,is a function of his/her level of education or wealth and epidemiological status.Stochastic simulations show that threshold selection Pand the value of the average basic reproduction number impact the final epidemic size differentially.For the ErdÖos-Rényi and Small-world networks,an optimal choice for Pthat minimize the final epidemic size can be identified under some conditions while for Scalefree networks this is not case.

Some models for epidemics of vector-transmitted diseases

Vector-transmitted diseases such as dengue fever and chikungunya have been spreading rapidly in many parts of the world.The Zika virus has been known since 1947 and invaded South America in 2013.It can be transmitted not only by(mosquito)vectors but also directly through sexual contact.Zika has developed into a serious global health problem because,while most cases are asymptomatic or very light,babies born to Zika-infected mothers may develop microcephaly and other very serious birth defects.We formulate and analyze two epidemic models for vector-transmitted diseases,one appropriate for dengue and chikungunya fever outbreaks and one that includes direct transmission appropriate for Zika virus outbreaks.This is especially important because the Zika virus is the first example of a disease that can be spread both indirectly through a vector and directly(through sexual contact).In both cases,we obtain expressions for the basic reproduction number and show how to use the initial exponential growth rate to estimate the basic reproduction number.However,for the model that includes direct transmission some additional data would be needed to identify the fraction of cases transmitted directly.Data for the 2015 Zika virus outbreak in Barranquilla,Colombia has been used to fit parameters to the model developed here and to estimate the basic reproduction number.

Role of short-term dispersal on the dynamics of Zika virus in an extreme idealized environment

In November 2015,El Salvador reported their first case of Zika virus(ZIKV)infection,an event followed by an explosive outbreak that generated over 6000 suspected cases in a period of two months.National agencies began implementing control measures that included vector control and recommending an increased use of repellents.Further,in response to the alarming and growing number of microcephaly cases in Brazil,the importance of avoiding pregnancies for two years was stressed.In this paper,we explore the role of mobility within communities characterized by extreme poverty,crime and violence.Specifically,the role of short term mobility between two idealized interconnected highly distinct communities is explored in the context of ZIKV outbreaks.We make use of a Lagrangian modeling approach within a two-patch setting in order to highlight the possible effects that short-term mobility,within highly distinct environments,may have on the dynamics of ZIKV outbreak when the overall goal is to reduce the number of cases not just in the most affluent areas but everywhere.Outcomes depend on existing mobility patterns,levels of disease risk,and the ability of federal or state public health services to invest in resource limited areas,particularly in those where violence is systemic.The results of simulations in highly polarized and simplified scenarios are used to assess the role of mobility.It quickly became evident that matching observed patterns of ZIKV outbreaks could not be captured without incorporating increasing levels of heterogeneity.The number of distinct patches and variations on patch connectivity structure required to match ZIKV patterns could not be met within the highly aggregated model that is used in the simulations.