# Time Series Analysis On The Total Number Of Patients Treated For Malaria Fever

## Abstract

This project work reveled the rate at which people are infected with malaria the least square method used for analysis showed that people are infected with malaria irrespective of the time and seasons of a successive year,

There is no noticeable direction as regarding the number of patient treated for malaria over time.

Also, the analysis from autoregressive moving average report shows that both autoregressive and moving average of order four were both appropriate while the report from autocorrelation and autocovanance does not indicate any noticeable trend in the number of patients treated for malaria.

## Chapter One

### Introduction

#### 1.0 Introduction

The term time series refers to one the quantitative method used in determination pattern in data collected over time e.g weekly monthly, quarterly or yearly.

Time service is the statistic tool or methodology that can be used to transform past experience to predict future event which would enable the researcher or organization to plan.

It gives information about how the particular case of study has been behaving in the past and present and such information can be used in prediction The number of people treated for malaria fever at the otan Ayegbaju management hospital. Comprehensive health centre otan. We are going to seen how change occur over mouths in each year in the occurrence of the disease in the hospital. As a result of this, we will be able to know certain factor responsible for increase or decrease in the rate of infection of the disease over the period of time.

Record of time series data can be made in the following ways:-

##### A. Through Cumulative Figures:

these represent value of input through the quarter. We must always bear in mind the different when handling time series data and as certain which particular type we are dealing with in every case.

##### B. Cumulative Type Added Compilation:

some cases when an added compilation introduced for the cumulative type of data the figure which are related to month of the year and not the total for month. further more the characteristic movement, seasonal variation Irregular variation in the analysis of time series, we have two types of model are generally accepted as good approximation of the true data association among the component of observed data, they are the most commonly assumed relationship between time series and its components. These are additive model and Multiplicative mode. All time series contain at least on of four of its components.

These components are:-

- Long term trend
- Seasonal variation
- Cyclical variation
- Irregular or random variation value

##### Irregular Or Random Component

This venation cannot BE attributed to any of three previously discussed component in the sense that is unpredictable.

Irregulars flotation can be cause by many factor such as war, flood drought and other human as action. Two type of irregular variation may exit in a time series viz. minor and major irregularities minor irregularities show up as serivtooth like pattern are under the long term trend. These irregularited are in organization long term operation:

##### Models of Time Series

We usually denote the component of time series as T,TS,C and I: There Are Two Types Of Modern That Are Appropriate For Joining Component Of Time Series these moderns are additive and multiplicative modern.

The additive moder assumes that the valve of the original data is the sum total of other four elements it is:

T=T+S+C+I where

**T**is value of the originally conserved data (dependent)**T**is the value of secular or trend**S**is the value ofr cyclical venation and**I**is the value of irregular venation

Mufti active modern on the other hand assumes that the value of the observed data is the Y = TSCI

#### 1.1 Background of Study

one of the factor that determine the population of a country, state local government e.t.c is death rate, that is to say, the more the disease infected the population of such an area and vice-versa. The fact prompted the writer into the study of quarterly number of people given treatment for malaria at the comprehensive health centre otan ayegbaju, in addition to that it is done to know weather infected people come to the hospital fur test or they stay back due to the old custom self medication.

In order to carry our the analysis data will be collected from daily record of the hospital at record department over some years to get all necessity information so as to carry out computation and predict about the nearest future by using secondary method of data collection.

#### 1.2 Scope and Coverage of the Study

This project work was carried out on the number of people treated for malaria fever between year 2001 to 2010. The data was collected from the comprehensive health centre Otan Ayegbaju osun state.

#### 1.3 Aim and Objective of the Study

- To know whether the yearly spread of malaria is increasing pr decreasing.
- To formulate a model that can best explain the relationship between malaria increases over the years
- To use the modern to forecast the occurrence of malaria
- To plot the graph of the original data i.e occurrence of malaria against year correlogram and moving average.

#### 1.4 Sources of Data Collection

Data used for research are of two main sources: these source are primary and secondary data.

Primary data are fresh data which are collected for the task at hand. An example of such is census registration for cards.

Secondary data on the other hand are data dreaded in existence. They are originally collected for some purpose other than research current problem. They can be collected from school, hospital organization, government agencies, newspaper, monthly or annual report e.t.c thus a secondary data is used in this project.

#### 1.5 Limitation of the Study

As we know that a researcher is bound to face certain problem. various problem were encountered before during and after data collection

##### The problem are:-

Poor storage, which make the transfer of data difficult Data were not properly recorded and in some cases, we have missing value.

Also data for some period are missing from the record office: those were available were poorly recorded this establishing one of the major.

##### Disadvantage of a secondary data usage data

collection :- before the data was released to me, I had to present a cover letter from the HOD and my student identify card and also promised that the data would be used for statistical purpose only.

## Chapter Five

### 5.0 Summary, Conclusions and Recommendations

#### 5.1 Discussion of Results

The study shows that in the first quarter of 2001, the month January recorded the highest prevalence of malaria cases (655). In the second quarter of that same year, the highest reported case was in June with a total number of 897. The highest number of reported cases in third quarter was in September with a total number of 572. In the last quarter of that same year, the highest number of reported cases was in December. In all, the highest number of reported cases in the whole year was in December (1161) and the least number was in the month of July with a total number of 475. The number of reported cases per month was 717.3.

In the year 2002, the highest number of reported cases in the first quarter was in the month of January with a number of 966. June had the highest number of cases in the second quarter with a total number of 1182. In the third quarter, the highest number was 1202 and it is recorded in July. In the fourth quarter, the highest number was 1391 in December. In all, the highest number of reported cases in 2002 was in the month of December. The least number of reported cases was 451 and it was recorded in February. The average monthly number of reported cases in the year was 1058.8. In the year 2003, the study indicates that the highest number of reported cases in the first quarter was in the month of March with a total of 1059 cases. The highest number in the second quarter was 1037 cases in the month of June. The third quarter recorded the highest number in September with a total of 1224 cases. The highest number of cases in the fourth quarter was in December with a total of 1377. The highest number of reported cases in the whole year was in December and the least number of reported cases was 992 which occurred in January. The average reported a case per month of the year was 1130.3.

The study also shows that the highest number of reported cases in 2004 for the first quarter was in the month of March with a total of 997 cases. The second quarter had the highest value in April with a total of 976 cases. In the third quarter, the highest number of reported cases was 917 in September. The fourth quarter had a total of 1402 cases in December. The highest number of reported cases for the whole year was in January with a total of 1402 cases. The least number of reported cases in the whole year was 379 in the month of May. The average monthly reported cases were 870.6.

In 2005, the highest value in the first quarter was in the month of March with a total of 1721 cases. The second quarter had its highest value in the month of June with a total of 2023 cases. The highest number of reported cases for the third quarter was in the month of June with a total of 2023 cases. The fourth quarter had a record of 2029 cases in the month of December as the highest number of reported cases. The highest number of reported cases for the whole year of 2005 was 2038 in the month of August. The number of reported cases per month in that year was 1875.9. The rest of the analysis can be referenced from Tables 4.1 and 4.2 respectively.

Comparatively, the number of reported cases per month (717) in 2001 indicates the lowest among all the years. This figure indicates that on the average, 717 people had malaria in each month in 2001. The average monthly reported case in 2002 is 1059.This implies that 1059 had malaria every month in 2002. This indicates an increase in 342 the average reported cases. This probably could be attributed to the increase in the population of the people in that area. In 2003, the reported cases per month further increased to 1130. In 2004 the number of reported cases per month was 871. This figure however indicates a drop in the number of reported cases. In 2005, an average of 1876 cases was recorded. Comparing the number of reported cases per month in 2005 with 2004, there is a further increase in the number of reported cases. The least number of reported cases per month is in 2001. Observing the trend of the reported cases from 2001 to 2004, it is most likely that the number of reported cases of the disease will increase in 2010 with the implementation of the National Health Insurance scheme.

Comparing the number of reported cases per month in 2001 with that of 2002, the result indicates that there is a significant difference in the number of reported cases. The number of reported cases in 2001 is lower than that of 2002. One is 95% confident that the difference in the means of 2001 and 2002 is between -672.76 and -10.07. The interval does not contain zero and this confirms the fact that the number of reported cases per month between these years are significantly different from zero. Comparing the number of reported cases in 2001 with that of 2003 indicates that the number of reported cases in 2001 is significantly different from that of 2003. One can say there is 95% confidence that the difference in the number of reported cases per month in 2001 and 2003 is between-744.26 and -81.57. Also comparing the number of reported cases in 2005 with 2008 and 2009 indicate the average number of monthly reported cases in 2005 is significantly different from those of 2008 and 2009. The number of reported cases per month in 2005 is lower than those of 2008 and 2009. There is 95% confidence that the difference in the number of reported cases per month in 2005 and 2008 is between -792.66 and -129.99. There is 95% confidence that the difference in the number of reported cases per month in 2005 and 2009 is between -1265.76 and 603.07.

Comparing the number of monthly reported cases per month in 2006 and 2001 to 2004 it is realized that there is no significant difference in their means. There is 95% confidence that the average number of reported cases per month is between 1390.57and 2053.26, 1049.15 and 1711.85, 977.65 and 1640.35, 1237.32 and 1900.35 respectively.

However, considering the number of reported cases per month in 2006 and 2007, there is statistical evidence that the average number of reported cases in 2006 is different from that of 2007. The average number of reported cases in 2006 is 2439 and that of 2007 is 2114.67. So in 2006, the average number of reported cases is higher than that of 2007. There is 95% confidence that the difference in means is between -6.76 and 655.93. Considering the number of reported cases per month in 2006 and 2008, there is statistical evidence that the average number of reported cases in 2006 is different from that of 2008. The average number of reported cases in 2006 is 2439 and that of 2008 is 2337.25. So in 2006, the average number of reported cases are higher than that of 2008. There is 95% confidence that the difference in means is between -229.35 and 433.35. There is evidence that the difference in the average number of reported cases in 2006 and 2009 is significantly different from zero. The average number of reported cases in 2009 is 2810. There is 95% confidence that the difference in the average number of cases in 2006 and 2009 is between-

702.43 and -39.74. There is the evidence that the difference in the number of reported cases per month in 2007 and 2008 is different from zero. There is 95% confidence that the difference in the number of reported cases per month is between -553.93 to 108.76. In 2007 and 2009, there is evidence that the difference in the number of reported cases per month is significantly different from zero. There is 95% confidence that the difference in the number of reported cases in the years 2007 and 2009 is between -1027.01 and -364.32. There is statistical evidence that the number of reported cases per month in 2008 and 2009 is significantly different from zero. There is 95% confidence that the difference in the number of reported cases per month in 2008 and 2009 is between -804.43 and -141.74.

The time series model developed for predicting the number of reported cases of malaria in the Otan Ayegbaju osun state is ARIMA (2, 1, 0). This model can be used by researchers for forecasting malaria reported cases in the district. However, it should be updated from time to time with the incorporation of current data.

#### 5.2 Findings

The study reveals that the introduction of the National Health Insurance Scheme is having positive impact on the malaria reported cases in the District. Since its inception in 2002, the reported cases per month in subsequent years from 2001 to 2010 have increased significantly. Despite the fact that people have been complaining about the low-cost drugs administer at the health centre under health insurance scheme, they still breathe a sigh of relief for the fact that many people are able to access health care with a minimum cost.

In general, Malaria is not only a health problem but also a developmental problem in Nigeria. It imposes significant financial hardships on households and the national economy. The burden of malaria is, therefore, a challenge to human development manifesting itself as a cause and consequence of under-development. Malaria‟s impact on households and society can be assessed in at least three important dimensions namely, health, social and economic. The impact of malaria in all the dimensions is to a large extent little appreciated, especially with the emergence of the HIV/AIDS pandemic.

#### 5.3 Summary of Results

Comparing the average monthly reported cases of 2001 with each year‟s reported cases, it is realized that the number of reported cases has been increasing significantly over the years. The number of reported cases from 2007 to 2010 is higher than that of preceding years, the factor attributable to increase in population over the years and also for the fact that the community has seen the usefulness of the National Health Insurance scheme and now access the health facilities more than ever before. For details check from Appendix B

The ARIMA model developed for predicting the monthly reported malaria cases is ARIMA (2, 1, 0):

(5.1)

The model was used to predict a five-month lead period of the reported cases. See Appendix A for details.

#### 5.4 Conclusion

The model was essentially a stand-alone model since no relevant inputs for the model were available. Nevertheless, reasonable fitting accuracy (R square = 0.053, MAPE =14.358) was achieved for 120 months of historical data and the generated forecasts were adequately accurate. Based on the accuracy of forecasts obtained from the various models built in this thesis, it was demonstrated that Box and Jenkins ARIMA model can be successfully employed for the purpose of forecasting time dependent series.

The results of this work demonstrates the usefulness and motivates the need of employing the statistical technique of ARIMA methodology in forecasting time series applications, either independently or in conjunction with the traditional methods, to result in a less computationally and data intensive method. Nevertheless, some work still needs to be done to validate further the use of such techniques in various other scenarios faced by time series forecasting.

It can be concluded that the Otan Ayegbaju osun state has conditions that favour the breeding of mosquitoes, the vector that causes malaria. The prevalence of malaria is more pronounced among certain population subgroups. Malaria presents significant costs to the affected households since it is possible to experience multiple and repeated attacks in a year. The district, which has the two rainy seasons, is the hardest hit by these vectors because of the weather. In this case, the district must be given priority attention in annual budgets to enable it combat the disease. In particular, there is the need for a strong collaboration among major stakeholders including the Government, District Assemblies, Non-Governmental Organisations and the community to devise holistic, effective, and cost-saving methods for prevention, control and treatment of the disease. Though the use of insecticides for example coils, sprays are identified as the major method of protection due to their availability and affordability for many households, the efficacy of some of these numerous brands on the market may be questionable. In the short- term, the efficacy of these products needs to be assessed by concerned authorities in order not to endanger the health of the people.

#### 5.5 Recommendations

While advocating continuation of education on the use of the ITNs, it is recommended that efforts must be seriously made by the major players in the health sector to make the net readily available in the communities at low prices to enable the ordinary Nigeriaian to purchase it.

The decision to seek medical care from a health provider is influenced by several factors but the perceived quality of the provider and the proximity of the health facility are major determinants of health seeking behaviours. The proximity of the facility affects the cost of transportation and more importantly the cost of time. In order to improve timeliness of treatment, the service consequently would have to be closer to patients especially those in the remote and malarious endemic areas like the Asukorkor, Apemso, Naama, Ahensan etc in the district. The mobile outreach programme of the Nigeria Health Service must be well equipped so that difficulty could be minimised at the service. Malaria reduction strategies should be incorporated into Nigeria‟s

Poverty Reduction Strategy. It is anticipated that with a considerable reduction in poverty levels, households and communities would become increasingly responsible for the improvement of their health status and quality of life.

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