Mathematical model of the effects of government intervention and rehabilitation of prostitution

In the United States, prostitution is considered illegal in all but one state; Nevada allows some legal activities in exchange for substantial guidelines. In 2010, approximately 43,600 females were arrested for prostitution. Numerous intervention programs were established in order to obstruct the lifestyle of a prostitute (PRP, Project ROSE, etc.). There are many documentations and programs that share their forethought on prostitution; however, few target prostitution directly. To determine the dynamics of prostitution, this paper constructs a four-class compartmental model that focuses on the effectiveness of government intervention and rehabilitation of prostitutes mathematically. The basic reproductive number, [Formula: see text], helps to discover the threshold values for the dynamics of prostitution to become both prevalent or absent in society. This paper predominately observes government intervention to curtail a prostitution prevalent society. Various parameters and variables help to define and indicate the dynamics of prostitution to construct viable simulations. Successful prostitution interaction prevention deemed essential in prostitution prevention; however, government intervention corresponding with successful rehabilitation competitively challenges prostitution interaction prevention in reducing basic reproductive values.

Modelling and Optimal Control of Typhoid Fever Disease with Cost-Effective Strategies

We propose and analyze a compartmental nonlinear deterministic mathematical model for the typhoid fever outbreak and optimal control strategies in a community with varying population. The model is studied qualitatively using stability theory of differential equations and the basic reproductive number that represents the epidemic indicator is obtained from the largest eigenvalue of the next-generation matrix. Both local and global asymptotic stability conditions for disease-free and endemic equilibria are determined. The model exhibits a forward transcritical bifurcation and the sensitivity analysis is performed. The optimal control problem is designed by applying Pontryagin maximum principle with three control strategies, namely, the prevention strategy through sanitation, proper hygiene, and vaccination; the treatment strategy through application of appropriate medicine; and the screening of the carriers. The cost functional accounts for the cost involved in prevention, screening, and treatment together with the total number of the infected persons averted. Numerical results for the typhoid outbreak dynamics and its optimal control revealed that a combination of prevention and treatment is the best cost-effective strategy to eradicate the disease.

Exploring the Impact of Prostitution on HIV/AIDS Transmission

HIV/AIDS has been somehow linked to prostitution for decades now. A mathematical model is presented to assess the link between prostitution and HIV transmission. The epidemic thresholds known as the reproduction numbers and equilibria for the model are determined and stabilities analyzed. Analysis of the reproduction numbers suggests that HIV/AIDS control using antiretroviral therapy is more effective in the absence of prostitution. Numerical simulations further show high levels of HIV/AIDS when percentage of prostitutes in the community is high. Results from this study suggest that effectively controlling HIV/AIDS requires strategies that address both prostitution and HIV/AIDS transmission. Addressing HIV/AIDS through condom use and antiretroviral therapy may not be enough to stem HIV/AIDS in the community as some drug/alcohol misusing prostitutes may not be able to negotiate for safe sex while they are in drunken stupor. Furthermore, prostitutes are likely to get infected by different HIV strains some of which may be resistant to the antiretroviral therapy regimen in use.

MODELING THE SPREAD OF STREET KIDS IN ZIMBABWE

Child neglect and abuse has been linked with the growth in the number of street kids for some time. A mathematical model is used to explore the impact of peer influence and child abuse in the presence of removal of street kids from the streets into children's homes/foster homes and improvement in the welfare of adults. The threshold quantity known as the reproduction number and equilibria for the model are determined and analyzed. Results from this study suggest that removal of street kids from the streets into children's homes/foster homes and improving the welfare of adults have the potential to reduce the number of children living in the streets. Interestingly, our results illustrate that adult peer influence leading to child abuse of children makes the problem of street kids worse than any other factor. To effectively control the growth in the number of street kids require strategies that address both economic and social factors affecting children and their guardians. Addressing only an issue affecting one group like guardians through improvement of their welfare may not be enough to stem the growth in the number of street kids as some would be turning to the streets due to negative peer influence among children.