# Estimating Population Size of Fake Drug Syndicates: A Capture-Recapture Approach by Sampling Coverage Methods

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Published on International Journal of Biology, Physics & Matematics
ISSN: 2721-3757, Volume 2, Issue 1, page 1 – 10
Publication Date: 7 February 2019

U.A Osisiogu & E.E. Chinwuba
Department of Mathematics & Computer Science
Professor of Mathematics & Statistics Lecturer
Ebonyi State University
Abakaliki, Nigeria

Abstract
National Agency for Food and Drug Administration Control (NAFDAC), the agency responsible for checkmating illicit and counterfeit drugs in Nigeria has raised alarm over the years the menace caused by fake, adulterated and substandard drugs in the Nigeria health sector. The Agency reported that counterfeit drugs have claimed the life of many Nigerians, especially children and old people, and we believe this is only part of the story. The syndicates of these drugs are also integral part of the problem. However, less effort was focused on the population size of these syndicates. This study, therefore, uses capture-recapture (CR) method to estimate the size of this hiding population. Information on fake drug syndicates was extracted from NAFDAC press releases and NAFDAC news coverage, in 2015. Based on the information, sampling coverage approach of CR methods was used to estimate the population size of this difficult-to-reach population. Overall, we identified 542 cases of which 440 were from Onitsha zone, 270 were from at least two other zonal offices of Lagos and Kano and 136 were common to all the three zonal offices. 336 of them were falsified cases while 206 were at least on expired, unregistered and banned drugs. The sample coverage estimate for these data is C ̂ = 88.6 per cent with average overlapped cases D= 496.667, so that an estimate without possible dependence is 561. The data were further analyzed within each stratum to crosscheck validity, and we found that the sum of the four estimators is N ̂=559 which is very close to our earlier results

Keywords: Fake Drug, Capture-Recapture, Sampling Coverage, Hidden Population.

1. Introduction
The circulation of fake, adulterated and substandard drugs in Nigerian market, for many years now, has become a very big health concern not alone to the National Agency for Food and Drug Administration and Control (NAFDAC)—an agency responsible for checkmating illicit and counterfeit drugs in Nigeria, but to Nigerian populace as a whole. The health problem associated with the consumption of fake and counterfeit drugs cannot be over emphasized. Administering counterfeit drugs to patients can lead to drug resistance by parasites, bacteria or virus that courses illness, abuse or even death. NAFDAC was worried because for the past three decades the menace caused by counterfeit drugs has claimed the life of many Nigerians, especially children and old people. Often referred as the “Paracetamol syrup disaster of 1990”, about 109 children residing in two cities in Nigeria (Ibadan and Jos) were killed after ingesting paracetamol-based cough syrup produced with toxic diethylene glycol solvent instead of propylene glycol (NAFDAC,2013).
Documented cases of counterfeit drugs published by the Nigerian Law Intellectual Property Watch (NLIPW, 2013) resulting in deaths of many Nigerians in recent years are overwhelming. The report stated that in 1995 and 1996, fake meningitis vaccines obtained from the Onitsha drug market killed thousands of children in the northern parts of Nigeria. Unfortunately, such fake vaccines did not stop in Nigeria ……..

1.1 Background
The National Agency for Food and Drug Administration and Control (NAFDAC) is a Nigerian government agency responsible for regulating and controlling the manufacture, importation, exportation, advertisement, distribution, sale and use of food, drugs, cosmetics, medical devices, chemicals and pre-packed water (Chinwendu, 2008). The Agency was created following the 1988 World Health Assembly resolution requesting countries all over the world to help combat the global health threat posed by counterfeit pharmaceutical, and amidst growing concerns about the growing problem of fake and poorly regulated drugs in Nigeria.
(Chinwendu, 2008) noted that around 70% of drugs in Nigeria are imported, and India is a major drug exporter to Nigeria. He stated that some Nigerian drug importers connived with some Indian manufacturers to produce fake and substandard drugs at cheaper rate with less active ingredients; adding that these drugs are imported into Nigeria, sold to the wholesalers and retailers who may or may not know if the drugs are fakes or not. WHO survey on fake drugs according to (Nigerian Tribune Newspaper 2007, September edition), reported that prevalence rate of fake drug at Onitsha market alone stands at 30% as against 10% in other parts of the country. Crude method (aggregated cases divided by the total population) was used to estimate the prevalence ……….