New MAXCAP Related Problems: Formulation and Model Solutions: A class of competitive location problems

In this paper three related problems of the maximum capture (MAXCAP) model are proposed. These include the case where facilities provide a certain amount of service level for the customers, the possibility where customers do not allocate their demand completely to one facility but prorate their demand based on the service level, and finally we explore the situation where customers will not opt for sharing their demand irrespective of the service level if the next attractive facility is too far way which we express by a distance threshold. These models are put forward to mimic realistic situations related to customer behaviour when it comes to selecting a facility. Their respective mathematical formulations are put forward and tested on a case study and also over a range of larger data sets

Impact of routine vaccination against Haemophilus influenzae type b in The Gambia: 20 years after its introduction.

BACKGROUND: In 1997, The Gambia introduced three primary doses of Haemophilus influenzae type b (Hib) conjugate vaccine without a booster in its infant immunisation programme along with establishment of a population-based surveillance on Hib meningitis in the West Coast Region (WCR). This surveillance was stopped in 2002 with reported elimination of Hib disease. This was re-established in 2008 but stopped again in 2010. We aimed to re-establish the surveillance in WCR and to continue surveillance in Basse Health and Demographic Surveillance System (BHDSS) in the east of the country to assess any shifts in the epidemiology of Hib disease in The Gambia. METHODS: In WCR, population-based surveillance for Hib meningitis was re-established in children aged under-10 years from 24 December 2014 to 31 March 2017, using conventional microbiology and Real Time Polymerase Chain Reaction (RT-PCR). In BHDSS, population-based surveillance for Hib disease was conducted in children aged 2-59 months from 12 May 2008 to 31 December 2017 using conventional microbiology only. Hib carriage survey was carried out in pre-school and school children from July 2015 to November 2016. RESULTS: In WCR, five Hib meningitis cases were detected using conventional microbiology while another 14 were detected by RT-PCR. Of the 19 cases, two (11%) were too young to be protected by vaccination while seven (37%) were unvaccinated. Using conventional microbiology, the incidence of Hib meningitis per 100?000-child-year (CY) in children aged 1-59 months was 0.7 in 2015 (95% confidence interval (CI)?=?0.0-3.7) and 2.7 (95% CI?=?0.7-7.0) in 2016. In BHDSS, 25 Hib cases were reported. Nine (36%) were too young to be protected by vaccination and five (20%) were under-vaccinated for age. Disease incidence peaked in 2012-2013 at 15 per 100?000 CY and fell to 5-8 per 100?000 CY over the subsequent four years. The prevalence of Hib carriage was 0.12% in WCR and 0.38% in BHDSS. CONCLUSIONS: After 20 years of using three primary doses of Hib vaccine without a booster Hib transmission continues in The Gambia, albeit at low rates. Improved coverage and timeliness of vaccination are of high priority for Hib disease in settings like Gambia, and there are currently no clear indications of a need for a booster dose

Serogroup W135 meningococcal disease, The Gambia, 2012.

In 2012, an outbreak of Neisseria meningitidis serogroup W135 occurred in The Gambia. The attack rate was highest among young children. The associated risk factors were male sex, contact with meningitis patients, and difficult breathing. Enhanced surveillance facilitates early epidemic detection, and multiserogroup conjugate vaccine could reduce meningococcal epidemics in The Gambia

Staphylococcus aureus Bacteremia in Children of Rural Areas of The Gambia, 2008–2015

Staphylococcus aureus bacteremia is a substantial cause of childhood disease and death, but few studies have described its epidemiology in developing countries. Using a population-based surveillance system for pneumonia, sepsis, and meningitis, we estimated S. aureus bacteremia incidence and the case-fatality ratio in children <5 years of age in 2 regions in the eastern part of The Gambia during 2008–2015. Among 33,060 children with suspected pneumonia, sepsis, or meningitis, we performed blood culture for 27,851; of 1,130 patients with bacteremia, 198 (17.5%) were positive for S. aureus. S. aureus bacteremia incidence was 78 (95% CI 67–91) cases/100,000 person-years in children <5 years of age and 2,080 (95% CI 1,621–2,627) cases/100,000 person-years in neonates. Incidence did not change after introduction of the pneumococcal conjugate vaccine. The case-fatality ratio was 14.1% (95% CI 9.6%–19.8%). Interventions are needed to reduce the S. aureus bacteremia burden in The Gambia, particularly among neonates

Impact of the introduction of pneumococcal conjugate vaccination on pneumonia in The Gambia: population-based surveillance and case-control studies.

BACKGROUND: Pneumococcal conjugate vaccines (PCVs) are used in many low-income countries but their impact on the incidence of pneumonia is unclear. The Gambia introduced PCV7 in August, 2009, and PCV13 in May, 2011. We aimed to measure the impact of the introduction of these vaccines on pneumonia incidence. METHODS: We did population-based surveillance and case-control studies. The primary endpoint was WHO-defined radiological pneumonia with pulmonary consolidation. Population-based surveillance was for suspected pneumonia in children aged 2-59 months (minimum age 3 months in the case-control study) between May 12, 2008, and Dec 31, 2015. Surveillance for the impact study was limited to the Basse Health and Demographic Surveillance System (BHDSS), whereas surveillance for the case-control study included both the BHDSS and Fuladu West Health and Demographic Surveillance System. Nurses screened all outpatients and inpatients at all health facilities in the surveillance area using standardised criteria for referral to clinicians in Basse and Bansang. These clinicians recorded clinical findings and applied standardised criteria to identify patients with suspected pneumonia. We compared the incidence of pneumonia during the baseline period (May 12, 2008, to May 11, 2010) and the PCV13 period (Jan 1, 2014, to Dec 31, 2015). We also investigated the effectiveness of PCV13 using case-control methods between Sept 12, 2011, and Sept 31, 2014. Controls were aged 90 days or older, and were eligible to have received at least one dose of PCV13; cases had the same eligibility criteria with the addition of having WHO-defined radiological pneumonia. FINDINGS: We investigated 18 833 children with clinical pneumonia and identified 2156 cases of radiological pneumonia. Among children aged 2-11 months, the incidence of radiological pneumonia fell from 21·0 cases per 1000 person-years in the baseline period to 16·2 cases per 1000 person-years (23% decline, 95% CI 7-36) in 2014-15. In the 12-23 month age group, radiological pneumonia decreased from 15·3 to 10·9 cases per 1000 person-years (29% decline, 12-42). In children aged 2-4 years, incidence fell from 5·2 to 4·1 cases per 1000 person-years (22% decline, 1-39). Incidence of all clinical pneumonia increased by 4% (-1 to 8), but hospitalised cases declined by 8% (3-13). Pneumococcal pneumonia declined from 2·9 to 1·2 cases per 1000 person-years (58% decline, 22-77) in children aged 2-11 months and from 2·6 to 0·7 cases per 1000 person-years (75% decline, 47-88) in children aged 12-23 months. Hypoxic pneumonia fell from 13·1 to 5·7 cases per 1000 person-years (57% decline, 42-67) in children aged 2-11 months and from 6·8 to 1·9 cases per 1000 person-years (72% decline, 58-82) in children aged 12-23 months. In the case-control study, the best estimate of the effectiveness of three doses of PCV13 against radiological pneumonia was an adjusted odds ratio of 0·57 (0·30-1·08) in children aged 3-11 months and vaccine effectiveness increased with greater numbers of doses (p=0·026). The analysis in children aged 12 months and older was underpowered because there were few unvaccinated cases and controls. INTERPRETATION: The introduction of PCV in The Gambia was associated with a moderate impact on the incidence of radiological pneumonia, a small reduction in cases of hospitalised pneumonia, and substantial reductions of pneumococcal and hypoxic pneumonia in young children. Low-income countries that introduce PCV13 with reasonable coverage can expect modest reductions in hospitalised cases of pneumonia and a marked impact on the incidence of severe childhood pneumonia. FUNDING: GAVI's Pneumococcal vaccines Accelerated Development and Introduction Plan, Bill & Melinda Gates Foundation, and UK Medical Research Council

Effect of the introduction of pneumococcal conjugate vaccination on invasive pneumococcal disease in The Gambia: a population-based surveillance study.

BACKGROUND: Little information is available about the effect of pneumococcal conjugate vaccines (PCVs) in low-income countries. We measured the effect of these vaccines on invasive pneumococcal disease in The Gambia where the 7-valent vaccine (PCV7) was introduced in August, 2009, followed by the 13-valent vaccine (PCV13) in May, 2011. METHODS: We conducted population-based surveillance for invasive pneumococcal disease in individuals aged 2 months and older who were residents of the Basse Health and Demographic Surveillance System (BHDSS) in the Upper River Region, The Gambia, using standardised criteria to identify and investigate patients. Surveillance was done between May, 2008, and December, 2014. We compared the incidence of invasive pneumococcal disease between baseline (May 12, 2008-May 11, 2010) and after the introduction of PCV13 (Jan 1, 2013-Dec 31, 2014), adjusting for changes in case ascertainment over time. FINDINGS: We investigated 14 650 patients, in whom we identified 320 cases of invasive pneumococcal disease. Compared with baseline, after the introduction of the PCV programme, the incidence of invasive pneumococcal disease decreased by 55% (95% CI 30-71) in the 2-23 months age group, from 253 to 113 per 100 000 population. This decrease was due to an 82% (95% CI 64-91) reduction in serotypes covered by the PCV13 vaccine. In the 2-4 years age group, the incidence of invasive pneumococcal disease decreased by 56% (95% CI 25-75), from 113 to 49 cases per 100 000, with a 68% (95% CI 39-83) reduction in PCV13 serotypes. The incidence of non-PCV13 serotypes in children aged 2-59 months increased by 47% (-21 to 275) from 28 to 41 per 100 000, with a broad range of serotypes. The incidence of non-pneumococcal bacteraemia varied little over time. INTERPRETATION: The Gambian PCV programme reduced the incidence of invasive pneumococcal disease in children aged 2-59 months by around 55%. Further surveillance is needed to ascertain the maximum effect of the vaccine in the 2-4 years and older age groups, and to monitor serotype replacement. Low-income and middle-income countries that introduce PCV13 can expect substantial reductions in invasive pneumococcal disease. FUNDING: GAVI's Pneumococcal vaccines Accelerated Development and Introduction Plan (PneumoADIP), Bill & Melinda Gates Foundation, and the UK Medical Research Council

Impact of the introduction of pneumococcal conjugate vaccination on invasive pneumococcal disease and pneumonia in The Gambia: 10 years of population-based surveillance.

BACKGROUND: The Gambia introduced seven-valent pneumococcal conjugate vaccine (PCV7) in August 2009, followed by PCV13 in May, 2011, using a schedule of three primary doses without a booster dose or catch-up immunisation. We aimed to assess the long-term impact of PCV on disease incidence. METHODS: We did 10 years of population-based surveillance for invasive pneumococcal disease (IPD) and WHO defined radiological pneumonia with consolidation in rural Gambia. The surveillance population included all Basse Health and Demographic Surveillance System residents aged 2 months or older. Nurses screened all outpatients and inpatients at all health facilities using standardised criteria for referral. Clinicians then applied criteria for patient investigation. We defined IPD as a compatible illness with isolation of Streptococcus pneumoniae from a normally sterile site (cerebrospinal fluid, blood, or pleural fluid). We compared disease incidence between baseline (May 12, 2008-May 11, 2010) and post-vaccine years (2016-2017), in children aged 2 months to 14 years, adjusting for changes in case ascertainment over time. FINDINGS: We identified 22 728 patients for investigation and detected 342 cases of IPD and 2623 cases of radiological pneumonia. Among children aged 2-59 months, IPD incidence declined from 184 cases per 100 000 person-years to 38 cases per 100 000 person-years, an 80% reduction (95% CI 69-87). Non-pneumococcal bacteraemia incidence did not change significantly over time (incidence rate ratio 0·88; 95% CI, 0·64-1·21). We detected zero cases of vaccine-type IPD in the 2-11 month age group in 2016-17. Incidence of radiological pneumonia decreased by 33% (95% CI 24-40), from 10·5 to 7·0 per 1000 person-years in the 2-59 month age group, while pneumonia hospitalisations declined by 27% (95% CI 22-31). In the 5-14 year age group, IPD incidence declined by 69% (95% CI -28 to 91) and radiological pneumonia by 27% (95% CI -5 to 49). INTERPRETATION: Routine introduction of PCV13 substantially reduced the incidence of childhood IPD and pneumonia in rural Gambia, including elimination of vaccine-type IPD in infants. Other low-income countries can expect substantial impact from the introduction of PCV13 using a schedule of three primary doses. FUNDING: Gavi, The Vaccine Alliance; Bill & Melinda Gates Foundation; UK Medical Research Council; Pfizer Ltd

Customer Allocation in Maximum Capture Problems

The maximum capture (MAXCAP) model and its variants have been widely used to find the maximum capture that a firm can get as it enters a spatial market where there are already existing (competitor’s) facilities. While the model obtains the optimal demand capture, it however allows the customers to be assigned to the non-closest facility which may incur additional operating costs. A two stage method can be used that overcomes the drawback of the original model while requiring a negligible extra computational effort. To make the original model mathematically self contained and more concise two revised formulations of the problem RMAXCAP-1 and RMAXCAP-2 are proposed which assure that the customers patronize only their closest entering facilities. These models are tested on different sizes of datasets and their performances are compared

Pneumonia, meningitis, and septicaemia in adults and older children in rural Gambia: eight years of population-based surveillance.

BACKGROUND: Representative data describing serious infections in over five-year-old children and adults in Africa are limited. METHODS: We conducted population-based surveillance for pneumonia, meningitis, and septicaemia in a demographic surveillance area in The Gambia between May 12, 2008 and December 31, 2015. We used standardised criteria to identify, diagnose, and investigate patients aged ≥5 years using conventional microbiology and radiology. RESULTS: We enrolled 1638/1657 eligible patients and investigated 1618. Suspected pneumonia, septicaemia, or meningitis was diagnosed in 1392, 135, and 111 patients respectively. Bacterial pathogens from sterile sites were isolated from 105 (7·5%) patients with suspected pneumonia, 11 (8·1%) with suspected septicaemia, and 28 (25·2%) with suspected meningitis. Streptococcus pneumoniae (n = 84), Neisseria meningitidis (n = 16) and Staphylococcus aureus (n = 15) were the most common pathogens. Twenty-eight (1·7%) patients died in hospital and 40 (4·1%) died during the 4 months after discharge. Thirty post-discharge deaths occurred in patients aged ≥10 years with suspected pneumonia. The minimum annual incidence was 133 cases per 100,000 person-years for suspected pneumonia, 13 for meningitis, 11 for septicaemia, 14 for culture-positive disease, and 46 for radiological pneumonia. At least 2·7% of all deaths in the surveillance area were due to suspected pneumonia, meningitis or septicaemia. CONCLUSIONS: Pneumonia, meningitis and septicaemia in over five year-old children and adults in The Gambia are responsible for significant morbidity and mortality. Many deaths occur after hospital discharge and most cases are culture negative. Improvements in prevention, diagnosis, inpatient and follow up management are needed urgently

Childhood meningitis in rural Gambia: 10 years of population-based surveillance.

BACKGROUND: The introduction in many countries of conjugate vaccines against Haemophilus influenzae type b, Streptococcus pneumoniae, and Neisseria meningitidis has led to significant reductions in acute bacterial meningitis (ABM) in children. However, recent population-based data on ABM in sub-Saharan Africa are limited. METHODS: Population-based surveillance for meningitis was carried out in a rural area of The Gambia under demographic surveillance from 2008 to 2017, using standardised criteria for referral, diagnosis and investigation. We calculated incidence using population denominators. RESULTS: We diagnosed 1,666 patients with suspected meningitis and collected cerebrospinal fluid (n = 1,121) and/or blood (n = 1,070) from 1,427 (88%) of cases. We identified 169 cases of ABM, 209 cases of suspected non-bacterial meningitis (SNBM) and 1,049 cases of clinically suspected meningitis (CSM). The estimated average annual incidence of ABM was high at 145 per 100,000 population in the <2-month age group, 56 per 100,000 in the 2-23-month age group, but lower at 5 per 100,000 in the 5-14-year age group. The most common causes of ABM were Streptococcus pneumoniae (n = 44), Neisseria meningitidis (n = 42), and Gram-negative coliform bacteria (n = 26). Eighteen of 22 cases caused by pneumococcal serotypes included in PCV13 occurred prior to vaccine introduction and four afterwards. The overall case fatality ratio for ABM was 29% (49/169) and was highest in the <2-month age group 37% (10/27). The case fatality ratio was 8.6% (18/209) for suspected non-bacterial meningitis and 12.8% (134/1049) for clinically suspected meningitis cases. CONCLUSIONS: Gambian children continue to experience substantial morbidity and mortality associated with suspected meningitis, especially acute bacterial meningitis. Such severely ill children in sub-Saharan Africa require improved diagnostics and clinical care