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Table of Contents
Year : 2015  |  Volume : 14  |  Issue : 2  |  Page : 89-96  

Development of a time-trend model for analyzing and predicting case-pattern of Lassa fever epidemics in Liberia, 2013-2017

1 Department of Veterinary Public Health and Preventive Medicine, Centre for Control and Prevention of Zoonoses, Faculty of Veterinary Medicine, Ibadan, Oyo State, Nigeria
2 Department of Epidemiology and Medical Statistics, Faculty of Public Health, College of Medicine, Ibadan, Oyo State, Nigeria
3 Department of Statistics, Faculty of Science, University of Ibadan, Ibadan, Oyo State, Nigeria

Date of Web Publication19-Feb-2015

Correspondence Address:
Babasola O Olugasa
Centre for Control and Prevention of Zoonoses, Department of Veterinary Public Health and Preventive Medicine, 101 Faculty of Veterinary Medicine, University of Ibadan, Ibadan, Oyo State
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Source of Support: Support for improving postgraduate programmes for surveillance of human-animal diseases in West Africa was provided by John D. and Catherine T. MacArthur Foundation (Grant No. 97944) to the University of Ibadan, Nigeria. Ethics approval for the study was granted by the Liberian Institute for Biomedical Research (EC/LIBR/014/039). Facilitation of in-country study was provided by Cuttington University, Suakoko Liberia, Conflict of Interest: None

DOI: 10.4103/1596-3519.149892

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Objective: The objective was to develop a case-pattern model for Lassa fever (LF) among humans and derive predictors of time-trend point distribution of LF cases in Liberia in view of the prevailing under-reporting and public health challenge posed by the disease in the country.
Materials and Methods: A retrospective 5 years data of LF distribution countrywide among humans were used to train a time-trend model of the disease in Liberia. A time-trend quadratic model was selected due to its goodness-of-fit (R2 = 0.89, and P < 0.05) and best performance compared to linear and exponential models. Parameter predictors were run on least square method to predict LF cases for a prospective 5 years period, covering 2013-2017.
Results: The two-stage predictive model of LF case-pattern between 2013 and 2017 was characterized by a prospective decline within the South-coast County of Grand Bassa over the forecast period and an upward case-trend within the Northern County of Nimba. Case specific exponential increase was predicted for the first 2 years (2013-2014) with a geometric increase over the next 3 years (2015-2017) in Nimba County.
Conclusion: This paper describes a translational application of the space-time distribution pattern of LF epidemics, 2008-2012 reported in Liberia, on which a predictive model was developed. We proposed a computationally feasible two-stage space-time permutation approach to estimate the time-trend parameters and conduct predictive inference on LF in Liberia.

   Abstract in French 

L'objectif ιtait de mettre au point un cas-modθle pour la fiθvre de Lassa (LF) chez les humains et d'en tirer les prιdicteurs de l'ιvolution des tendances dans le temps point de distribution de LF cas au Libιria en vue de la situation de sous-dιclaration et de la santι publique dιfi posι par la maladie dans le pays.
Matιriels et Mιthodes: Une rιtrospective 5 ans donnιes de LF distribution countrywide parmi les humains ont ιtι utilisιs pour former un modθle tendance de la maladie au Libιria. Un temps de tendance modθle quadratique a ιtι sιlectionnι en raison de sa qualitι de l'ajustement (R 2 = 0,89, P < 0,05) et ΰ la meilleure performance par rapport au linιaire et exponentielle modθles. Paramθtre prιdicteurs ιtaient exιcuter sur mιthode des moindres carrιs pour prιdire LF cas pour un futur pιriode de 5 ans, couvrant 2013-2017.
Rιsultats: La phase deux modθle prιdictif de LF cas-pattern entre 2013 et 2017 a ιtι caractιrisιe par un dιclin ιventuel dans le sud-ouest du comtι de Grand Bassa au cours de la pιriode de prιvision et un vers le haut cas-tendance dans le nord du comtι de Nimba. Cas spιcifique augmentation exponentielle a ιtι prιvue pour les 2 premiθres annιes (2013- 2014) avec une progression gιomιtrique au cours des 3 prochaines annιes (2015- 2017) dans le comtι de Nimba.
Conclusion: Ce document dιcrit une application en translation de l'espace-temps rιpartition de LF ιpidιmies, 2008-2012 a rapportι au Libιria, sur lequel un modθle prιdictif a ιtι dιveloppι. Nous avons proposι une infaisable faisable deux-stade espace-temps approche permutation d'estimer le temps de tendance et paramθtres conduite infιrence prιdictive sur LF au Libιria.
Mots-clιs: Cas-pattern, la fiθvre de Lassa, modθle de prιvision, de prospective, de tendance temporelle modθle

Keywords: Case-pattern, Lassa fever, predictive model, prospective, time-trend model

How to cite this article:
Olugasa BO, Odigie EA, Lawani M, Ojo JF. Development of a time-trend model for analyzing and predicting case-pattern of Lassa fever epidemics in Liberia, 2013-2017. Ann Afr Med 2015;14:89-96

How to cite this URL:
Olugasa BO, Odigie EA, Lawani M, Ojo JF. Development of a time-trend model for analyzing and predicting case-pattern of Lassa fever epidemics in Liberia, 2013-2017. Ann Afr Med [serial online] 2015 [cited 2023 Mar 28];14:89-96. Available from:

   Introduction Top

Lassa fever (LF) is an acute and sometimes fatal viral hemorrhagic illness that is endemic in West Africa. [1] The disease is caused by the Lassa virus (LASV), an RNA virus of the family Arenaviridae. LF usually manifests with fever, muscle aches, sore throat, nausea, vomiting, chest, and abdominal pain. [2],[3] The autochthonous peri-domestic rodent Mastomys natalensis is the natural reservoir of LASV. [4],[5] Mastomys exhibit persistent, asymptomatic infection, and profuse urinary virus excretion. Contamination of human food with LASV-infected urine of Mastomys is considered to be the most common route of transmission. Nosocomial epidemics with case fatality up to 65% have been reported in Liberia [2],[6] and Nigeria. [7],[8],[9] The disease has two geographically endemic areas separated by 2000 km with little evidence of virus circulation in Benin, Ghana, Cote d'Ivoire, and Mali. [10] LF is known to account for some 300,000-500,000 cases and 5000 deaths yearly among humans. It is nevertheless, recognized that most cases of LASV infection in communities along the LF belt in West Africa are probably mild. [11],[12]

Lassa fever has continued to be a public health challenge, and gained expanded area of endemicity into the South-coast area of Liberia, [13],[14] following prolonged (1990-2004) civil conflict, and at certain other parts of West Africa. [15] Beyond the public health challenge, LF poses "one-health" educational challenge in the West African sub-region. This has been notable as the absence of virus positive Mastomys between two endemic zones (2000 km apart), and poor virus diversity in the Mano River area compared to the Lake Chard area, has been considered to be a unique import of LASV from Nigeria to Sierra Leone in the 19 th century. [10] The time-dependent transmission process of LF and its increasing spread within the sub-region has been characterized by under-reporting. [14] There is a need for studies to focus on tracking and monitoring of LASV dynamics in the sub-region, with particular attention to time and trend plots. Thus, this study was designed to develop a time-trend model for analysis and prediction of LF case-pattern in Liberia.

Time-trend modeling is a crucial tool in preventive medicine, as it promotes awareness and capacity building toward the ambitious aim of "arriving at the site of an outbreak before the pathogen." It also contributes to identify the pattern of biological risk and how to manage the risk. [16],[17],[18],[19] In recent years, diverse approaches have been employed, with various levels of inter-disciplinary collaboration to improve LF surveillance and control in West Africa. The merit of such collaboration is in the novelty it offers to elucidate possible solutions to protracted problems among human and animal population. [17],[19],[20] An addition to what has been achieved through inter-disciplinary collaborations is the use of geospatial techniques to map LF cases and identify their pattern of spread. [13],[20] The confirmation of an expanding area of endemicity of LF [13],[14],[15] calls for more effective and efficient surveillance and control of LF in all of West Africa, especially Liberia. This paper, therefore, aims to describe the development of a time-trend model for analyzing and predicting LF case-patterns, in Liberia.

   Materials and Methods Top

Study design

The study employed a retrospective review of LF hospital-based records in Liberia between 2008 and 2012. In addition, it uses the data captured to train time and trend models for the analysis and prediction of case-pattern of suspected and confirmed LF cases for the next 5 years, 2013-2017.

Data source

The source of this data was earlier presented and described by Olugasa et al.[14] The secondary dataset was the Liberian Lassa fever geospatial observational data (LI-LASFGOLD) profile, 2008-2012 that was developed at the Center for Control and Prevention of Zoonoses, the University of Ibadan by a joint study group on LF from Cuttington University (Liberia), and University of Ibadan (Nigeria), together with the Liberian Ministry of Health and Social Welfare and the Liberian Ministry of Agriculture. The primary data used in developing the LI-LASFGOLD profile were sourced from the Liberian National Diagnostic Unit. The dataset comprised all clinically suspected, probable, and laboratory confirmed cases of LF that were reported during the 5 years period between January 1, 2008 and December 31, 2012 countrywide. The residential addresses of LF cases were available in most instances.

An LF case was established based on the World Health Organization (WHO) definition. [20] A confirmed case of LF was a person that was confirmed in the laboratory, or that met the clinical illness case defined by WHO and was not laboratory confirmed case but epidemiologically linked to a confirmed case. A probable case was a person with clinical illness, not laboratory confirmed, and was not epidemiologically linked to a confirmed case, but had appropriate exposure history. A suspected case, however, was a person with acute illness of <3 weeks duration, with temperature of 38°C and above, showing no response to effective antimalarial treatment after the first dose and no response to chloramphenicol treatment after 48 h.

Statistical analysis

Time plot

We first explored the time series data with the plot of its series over time and then a sample descriptive measure of the main properties of the series was generated. [21] This rests on the assumption of independence of exponential or quadratic association. Observation was made on the dataset for presence of outliers, troughs, and turning points that may be pronounced on the time plot. Where exponential or a quadratic series exists but is not accounted for would lead to biased parameter estimates and incorrect inference. [22] Thus, an exponential or quadratic model, if necessary was based on goodness-of-fit test. [23] We tested goodness-of-fit for this data set on linear, exponential, and quadratic models.

Trend models

We have considered mainly the linear, quadratic, and exponential trend models for this study. Trend refers to the general direction in which the graph of a set of observations made successfully in time (usually at equal intervals) tends to be going over a long period of time. The period of time could be 5, 10, 15, or more years. The time period to be made use of, however, depends on the objectives of the study. In addition, the nature of the study will dictate whether to observe the sets of observations monthly or annually. For the purpose of this study, annual values were used because it gives the overall view of the LF cases than could be obtained in the case of the monthly series.

Since several of the time-trend curves in all human endeavors have the tendency to either grow increasingly or decreasingly in absolute terms or fluctuate over the period of time so considered, such trend series can be described using appropriate mathematical models called trend models.

Quadratic trend model

The model of LF trend was performed using the quadratic trend curve [22],[23] when the trend fails to exhibit a straight line pattern. The parameters of the quadratic model were estimated using the method of least squares. We plot the quadratic trend curve for the set of LF cases recorded between 2008 and 2012.

The quadratic trend model was defined by:

Tt = b0 + b1t + b2t2


Tt (trend value) is an N by 1 LF case

t is the time index/year

t2 is the square of the i th time/year

b0 is the intercept

b1 is the slope attached to time trend index/year

b2 is the slope attached to the square of the i th time/year.

Model estimation

The model examines the effects of the time trend on quadratic plot of cases. There were three parameters in the quadratic trend model and estimation of these parameters was done through the least squares method. Conventionally, using least squares method, three normal equations were required. These were obtained by normalizing the error, through differentiating with respect to b0 , b1 , and b2 . The derived three normal equations are as follows:

Spatio-temporal scan statistic

The detection of prospective (2013-2017) high-risk space-time cluster of LF was performed using Kulldorff's two-dimensional prospective spatio-temporal scan statistic. [24] SatScan version 9.1.1 (SaTScan™ statistics software, Martin Kulldorff and Information Management Services Inc, Cambridge, Massachusetts, US) was used to compute prospective space-time clusters of confirmed LF cases using the space-time permutation model as described by Kulldorff. [24] The space-time permutation model automatically adjusts for both purely spatial and purely temporal clusters. This model requires information about the spatial location and time for each case defined by a cylindrical window with circular (or elliptical) geographic base and height corresponding to time. The number of observed cases in a cluster are compared to what would have been expected if the spatial and temporal locations of all cases were independent of each other in which a disease cluster was defined as an unusually high concentration of disease events in a region unlikely to have occurred by chance. Hence, a cluster was any area within the study region of significant elevated risk for a disease with a higher proportion of its cases in that time period compared to the remaining geographic areas. The scan window was limited to 50% of the total population and the time precision specified in months at a statistical significance of P < 0.05. The most likely cluster was the function with the maximum test statistics (hypothetical probability that an event has already occurred or would yield a specific outcome).

Map design was performed using ArcGIS 10.1® (Environmental Systems Research Institute, Redlands, California, US).

   Results Top

Model parameters

The first-stage of model development was the generation of model parameter estimates. We obtained values for slope attached to time-trend index/year and slope attached to the square of the i th time/year (b1 and b2 ), respectively, where b1 was − 20.829 and b2 was 2.571, on quadratic trend model. Quadratic trend model performed best, compared to linear and exponential model on goodness-of-fit (R2 = 0.895, P < 0.05) as indicated by the computed coefficient of determination. The lower results of model parameter estimates derived from a linear and exponential trend models are presented in [Table 1]. The goodness-of-fit (R2 ) of model parameter estimates on quadratic time-trend model was consistently high. The quadratic model thus, offered the best explanation of the observed variation in the time-trend model, and its parameter estimates were employed in the second-stage of LF case value prediction.
Table 1: Summary and parameter estimates of LF time-trend model, Liberia, 2008-12

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Time and trend curves derived from retrospective LF data between 2008 and 2012 upon which the parameter estimations were made are presented in [Figure 1] and [Figure 2]. A general decline in suspected and confirmed LF cases was observed in Grand Bassa County and Nimba County during this period. An upward trend was observed in Nimba County after 2011 LF cases.
Figure 1: (a) Retrospective time plot of confi rmed Lassa fever (LF) cases in identifi ed counties in Liberia, 2008-2012; (b) Trend plot of confirmed LF cases in Grand Bassa, 2008-2012; (c) Time plot for gender that was tested for LF in Grand Bassa County; and (d) Time plot for laboratory test result for suspected LF cases in Grand Bassa County

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Figure 2: (a) Retrospective time plot of confirmed Lassa fever (LF) cases in Nimba County, Liberia, 2008-2012; (b) Trend plot of confirmed LF cases in Nimba County, 2008-2012; (c) Time plot for gender that was tested for LF in Nimba County; and (d) Trend plot for forecasted LF cases in Nimba County, 2013-2017

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Case-pattern forecast

The second-stage of model development was that of computation of case-pattern over 2013-2017. Using the formulary,

we computed prospective LF case-pattern for a 5 years forecast period from 2013 to 2017 [Table 2],[Table 3] and [Table 4]. The model forecasts zero case on Grand Bassa County in each of the 5 years (for both suspected and confirmed LF cases). Nimba County, however, had a case specific exponential trend that increased from 14 LF cases forecasted for 2013-121 LF cases in 2017. The exponential increase in 2013-2015 became a geometric increase between 2015 and 2017.
Table 2: Retrospective and prospective time-trend case pattern of LF, Liberia, 2008-2017

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Table 3: Expanded details on time-trend estimators for LF cases, 2008-2012 with 5 years prediction covering 2013-2017, Grand Bassa County, Liberia (0.1≤P≤0.5)

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Table 4: Expanded details on time-trend estimators for LF cases, 2008-2012 with 5 years prediction covering 2013-2017, Nimba and grand Bassa, Liberia

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Prospective space-time scan statistic of confirmed LF cases identified a most likely cluster (test statistic = 5.28, P = 0.041) of cases in Nimba County, with 2 years recurrence interval.

   Discussion Top

To our knowledge, this is the first attempt to predict the trend of LF in Liberia using a standardized approach. The combined time-trend model derived from least square estimation of the quadratic model procedure revealed a good degree of agreement with the trend of LF cases reported to the Ministry of Health, between 2013 and 2014. Although the number of officially reported LF cases are likely to represent only a small proportion of those that actually occurred. This finding shows that the trend of LF differs remarkably between counties. For example, while there was a negative downward curve of cases in Grand Bassa County, with resultant predicted self-termination of cases of LF in this region, Nimba County has a positive upward curve with a sharp increase in cases of LF predicted for the 5 years period, 2013-2017.

The LF time-trend curve seen in Grand Bassa County (2008-2012) was a typical pattern of an epidemic event in outlook. [25] The cases increased through 2009-2010 and declined until 2012. This event was an expanded spread of LF Southward in Liberia. [13],[14] During an outbreak, spread to neighboring communities was found. This finding has been corroborated by the 2014 confirmed sporadic and first time of reporting LF case in Margibi County, by the WHO, [26] being yet another county where outbreak had never been previously reported. Thus, the model here developed is functionally adequate for predicting case-pattern of LF in Liberia. An increased tendency for LF epidemics to spread into adjacent communities was earlier reported by Olugasa et al. [14] Evidence for habitat suitability for the three major means of transmission of LASV-infection, namely rodent-to-humans, humans-to-humans, and humans-to-rodents have also been reported. [10],[27],[28] Hence, there is a high likelihood of LF to become endemic in the Southern Counties of Liberia, just as obtained in the Northern parts of the country, including Nimba County with exponential outbreaks. In the event of no interventions, there may be a continuation of the expanded areas of endemicity into the Southern part of Liberia beyond 2017.

The status of LF in Liberia, therefore, calls for prioritization of its control intervention. Especially, the presence of LF epicenter in the Northern counties (Nimba, Lofa, and Bong) for some two to four decades, [13],[28],[29],[30] and the additional expanded area of epidemics identified in the Southern part of the country. [13],[14]

The case specific time-trend pattern in Nimba County, however, suggests an exponential increase in LF outbreaks in the first 2 years (2013-2015), with subsequent geometric increases during 2016-2017. This computation also agrees with the space-time prospective scan statistic that revealed a significant cluster of LF in Nimba County. It was logical to expect that movement of persons that may be incubating LF, or that may be infected by the virus could occur at any time within Liberia, especially from an endemic area of the country to a nonendemic area for various reasons, which may include being in search of the job, family re-union, seeking healthcare services, and resettlement following civil-conflict displacement during 1990-2004. This underscores the critical need to strengthen disease surveillance with the goal of early detection, early warning, and early intervention toward control of LF in various parts of Liberia.

   Conclusion Top

Using a two-staged quadratic time-trend model with a standard linear regression model, gave highly significant regression coefficient for the analysis and prediction of LF case-patterns in Liberia. Based on the countrywide dataset (n = 73), the following equation to predict LF case-pattern was developed:

It was, therefore, possible to analyze and predict case-pattern of LF over the next 5 years, from the available retrospective 5 years data, with a high level of goodness-of-fit. It is recommended that the results of this technique should be compared to annual reports of LF as they occur in Liberia to aid in building more effective containment for future outbreaks. Thus, the likelihood of being able to arrive at the site of an outbreak before the pathogen gets there is underway. To our knowledge, this is the first attempt to predict the trend of LF in Liberia using a standardized approach.

   References Top

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  [Figure 1], [Figure 2]

  [Table 1], [Table 2], [Table 3], [Table 4]

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