Dengue Fever: A Continuous Threat

Dengue fever is a vector borne disease and is caused by DEN Virus. This virus has four different serotypes. The vectors are two mosquitoes known as Aedesaegypti (the yellow fever mosquito) and Aedesalbopictus(the Asian tiger mosquito).  First case of dengue fever was reported back in 1994 in Karachi. A complete outbreak of this epidemic shook the whole nation in 2012. Uptill now, Lahore a city full of culture, witnessed about 16,580 confirmed cases and 257 deaths. About 5000 confirmed cases with 60 deaths were reported from the rest of the provinces. Under guidelines of WHO, Government has made efforts to combat this epidemic. Although the overall efforts have minimized the outbreak on controllable levels but dengue fever is a continuous threat. Since no permanent cure is available, the transmission of DEN virus is controlled indirectly. So the prime focus is to control mosquito population and decrease the possible hot spots i.e. Mosquito breeding sites in human habitations. Every year, the country witnesses monsoon season which brings vast areas full of clear standing waters providing breeding sites for mosquitoes which ultimately leads to increased number of patients suffering from dengue fever. Efforts have been made to fight against dengue including formation of dengue wards in hospitals, vector surveillance, community education, reactive vector control etc. A study has shown prevalence of four mosquito genera in Pakistan including Aedes, Culex, Armigeresand Anopheles. All of the above mentioned genera are associated with disease transmissions as they are the vectors of different viruses and parasites. It is the need of hour to do a collaborative effort stressing the community mobilization and management in war against dengue.

Bayesian Analysis of Mixture Distributions

In this thesis, we consider type-I mixtures of the members of a subclass of one parameter exponential family. This subclass includes Exponential, Rayleigh, Pareto, a Burr type XII and Power function distributions. Except the Exponential, mixtures of distributions of this subclass get either no or least attention in literature so far. The elegant closed form expressions for the Bayes estimators of the parameters of each of these mixtures are presented along with their variances assuming uninformative and informative priors. The proposed informative Bayes estimators emerge advantageous in terms of their least standard errors. An extensive simulation study is conducted for each of these mixtures to highlight the properties and comparison of the proposed Bayes estimators in terms of sample sizes, censoring rates, mixing proportions and different combinations of the parameters of the component densities. A type-IV sample consisting of ordinary type-I, right censored observations is considered. Bayesian analysis of the real life mixture data sets is conducted as an application of each mixture and some interesting observations and comparisons have been observed. The systems of non-linear equations to evaluate the classical maximum likelihood estimates, the components of the information matrices, complete sample expressions, the posterior predictive distributions and the equations for the evaluation of the Bayesian predictive intervals are derived for each of these mixtures as relevant algebra. The predictive intervals are evaluated in case of the Rayleigh mixture only for a number of combinations of the hyperparameters to look for a trend among the hyperparameters that may lead towards an efficient estimation.