Half‐Cauchy and Power Cauchy Distributions: Ordinary Differential Equations

In this chapter, homogenous ordinary differential equations (ODES) of different orders were obtained for the probability density function, quantile function, survival function inverse survival function, hazard function and reversed hazard functions of half‐Cauchy and power Cauchy distributions. This is possible since the aforementioned probability functions are differentiable. Differentiation and modified product rule were used to obtain the required ordinary differential equations, whose solutions are the respective probability functions. The different conditions necessary for the existence of the ODEs were obtained and it is almost in consistent with the support that defined the various probability functions considered. The parameters that defined each distribution greatly affect the nature of the ODEs obtained. This method provides new ways of classifying and approximating other probability distributions apart from half‐Cauchy and power Cauchy distributions considered in this chapter. In addition, the result of the quantile function can be compared with quantile approximation using the quantile mechanics

Parasitoid Increases Survival of Its Pupae by Inducing Hosts to Fight Predators

Many true parasites and parasitoids modify the behaviour of their host, and these changes are thought to be to the benefit of the parasites. However, field tests of this hypothesis are scarce, and it is often unclear whether the host or the parasite profits from the behavioural changes, or even if parasitism is a cause or consequence of the behaviour. We show that braconid parasitoids (Glyptapanteles sp.) induce their caterpillar host (Thyrinteina leucocerae) to behave as a bodyguard of the parasitoid pupae. After parasitoid larvae exit from the host to pupate, the host stops feeding, remains close to the pupae, knocks off predators with violent head-swings, and dies before reaching adulthood. Unparasitized caterpillars do not show these behaviours. In the field, the presence of bodyguard hosts resulted in a two-fold reduction in mortality of parasitoid pupae. Hence, the behaviour appears to be parasitoid-induced and confers benefits exclusively to the parasitoid

Surveillance of dengue fever virus: A review of epidemiological models and early warning systems

Dengue fever is one of the world’s most important vector-borne diseases. The transmission area of this disease continues to expand due to many factors including urban sprawl, increased travel and global warming. Current preventative techniques are primarily based on controlling mosquito vectors as other prophylactic measures, such as a tetravalent vaccine are unlikely to be available in the foreseeable future. However, the continually increasing dengue incidence suggests that this strategy alone is not sufficient. Epidemiological models attempt to predict future outbreaks using information on the risk factors of the disease. Through a systematic literature review, this paper aims at analyzing the different modeling methods and their outputs in terms of accurately predicting disease outbreaks. We found that many previous studies have not sufficiently accounted for the spatio-temporal features of the disease in the modeling process. Yet with advances in technology, the ability to incorporate such information as well as the socio-environmental aspect allowed for its use as an early warning system, albeit limited geographically to a local scale

Panic Disorder Induced by a “Herbal” Product Containing Sibutramine: Case Series with Review of Literature

Sibutramine is a serotonin and noradrenaline reuptake inhibitor which has been used for weight loss in obese patients. There are slimming products on the market claiming to be 'natural' which nevertheless contain sibutramine. In this report, we present three cases where panic attacks were associated with the use of a product and persisted even long after its discontinuation