Zdrav Vestn 2008; 77: 487–98 487 Research article/Raziskovalni prispevek MODELLING OF THE RISK FACTORS AND CHRONIC DISEASES THAT INFLUENCE THE DEVELOPMENT OF SERIOUS HEALTH COMPLICATIONS MODELIRANJE DEJAVNIKOV TVEGANJA IN KRONIČNIH BOLEZNI, KI VPLIVAJO NA RAZVOJ HUJŠIH ZDRAVSTVENIH ZAPLETOV Maja Atanasijević-Kunc1, Jože Drinovec2, Simona Ručigaj3, Aleš Mrhar3 1 Faculty of Electrical Engineering, University of Ljubljana, Tržaška 25, 1000 Ljubljana 2 Faculty of Medicine, University of Maribor, Slomškov trg 15, 2000 Maribor 3 Faculty of Pharmacy, University of Ljubljana, Aškerčeva 7, 1000 Ljubljana Abstract Background Some chronic diseases, like diabetes type 2 and hypertension, and risk factors, such as obesity, hypercholesterolemia, and smoking, are strongly correlated with the potential development of serious health complications that can threaten a patient’s life or significantly influence the quality of life, while at the same time representing an enormous economic burden. Such complications include, for example, stroke, coronary heart disease, peripheral arterial vascular disease, end-stage renal disease and congestive heart failure. Methods For a quantitative evaluation of the mentioned patient groups, the age distribution and an estimation of the treatment expenses a dynamic mathematical model was developed, where special attention was devoted to its structure, as it should enable the sequential construction and representation of different forms of data information. The model was realized in the Matlab program package with the Simulink Toolbox. Conclusions A dynamic mathematical model is described that enables the observation of patients (in percentage terms) with diabetes type 2 and obesity, as well as those who smoke, have hyper-cholesterolemia and hypertension and all possible combinations of these problems, related to their age. Taking into account the Slovenian demographic data and annual treatment expenses, we were able to quantitatively evaluate these factors, not only in Slovenia, but also in other developed regions where the demographic and economic situations are similar. It is also possible to extend the model to patients with serious complications, also taking into account the population dynamics, which is the goal of the next steps in our investigation. Regarding the presented results, it is estimated that from a group of a million people, those requiring treatment for diabetes type 2 cost as much as € 19.5 millions per year, since the treatment of one patient for one year is € 355. If all the sufferers requiring such treatment were located, as a consequence of more systematic medical examinations, an additional € 16 millions would be needed. In this group of one million people, as many as 40 % are expected to develop hyper-cholesterolemia, of which 26 % are diagnosed and treated adequately. The annual cost for the treatment of one patient is € 313, which means that for a group of a million people the costs would be € 82 millions per year. An additional € 43.5 millions would be needed if all the sufferers with hypercholesterolemia were treated. Another chronic disease is hypertension. The annual cost for treating one patient is estimated to be € 271, and so for a group of a million people the treatment costs would be € 69.5 millions. If this were extended to include so far undiscovered sufferers with this chronic disease an additional € 14.5 millions would be needed. Corresponding author / Avtorica za dopisovanje: Doc. dr. Maja Atanasijević-Kunc, Faculty of Electrical Engineering, University of Ljubljana, Tržaška 25, 1000 Ljubljana 488 Zdrav Vestn 2008; 77 The treatment expenses for all mentioned chronic diseases in Slovenia amount to over € 340 millions per year, with an additional € 148 millions needed for those sufferers who remain undiagnosed. Furthermore, it is well known that serious health complications are significantly reduced if these chronic diseases are adequately treated. From this point of view diagnosing and treating these chronic sufferers is, of course, efficient. But with a further development of the model we can also have an economic evaluation, indicating the potential savings, resulting from an early treatment and the consequently decreasing serious health problems. Key words modelling; simulation; diabetes type 2; obesity; smoking; hypercholesterolemia; hyperten- sion Izvleček Izhodišča Nekatere kronične bolezni, kot so diabetes tipa 2 in hipertenzija ter dejavniki tveganja, kamor uvrščamo debelost, dislipidemijo in kajenje, so tesno povezani z razvojem hudih zdravstvenih zapletov, ki lahko ogrozijo pacientovo življenje oz. bistveno vplivajo na kvaliteto življenja, hkrati pa pomenijo izjemno veliko ekonomsko breme. Med tovrstne zaplete sodijo npr. možganska kap, koronarna srčna bolezen, srčno popuščanje, periferna arterijska žilna bolezen pa tudi končna odpoved ledvic. Metode Da bi lahko tudi kvantitativno ovrednotili razširjenost in starostno porazdelitev posa- meznih skupin pacientov ter stroškov zdravljenja, smo razvili dinamični matematični model, pri čemer je bila posebna pozornost posvečena njegovi strukturi, ki omogoča postopen razvoj ter upoštevanje in prikaz informacij različnih oblik. Model je realiziran v programskem paketu Matlab z orodjem Simulink. Opisani dinamični matematični model razvoja diabetesa tipa 2, debelosti, kajenja, dislipi-demije in hipertenzije omogoča opazovanje opisanih bolezni in dejavnikov tveganja relativno, v procentih, glede na starost pacientov, pri čemer smo pri modeliranju upoštevali tudi vse možne kombinacije omenjenih skupin pacientov. Dodajanje informacij, povezanih z demografskimi razmerami v Sloveniji ter letno ceno zdravljenja posameznih bolezni, je omogočilo tudi kvantitativno vrednotenje razmer, in sicer tako v Sloveniji kot tudi v razvitih deželah, kjer sta demografska struktura prebivalstva in ekonomski razvoj primerljiva. Možno pa je tudi dopolnjevanje modela z vključitvijo hujših zdravstvenih zapletov in napovedmi spreminjanja števila prebivalstva, kar bo predmet naših nadaljnjih raziskav. Na osnovi predstavljenih rezultatov modeliranja je mogoče pričakovati, da je v populaciji z milijon prebivalci za letno zdravljenje diabetesa 2 namenjeno 19,5 milijona €, oz. 355 € na pacienta, še dodatnih 16 milijonov € pa bi potrebovali, če bi s sistematskimi pregledi odkrili vse paciente. V isti skupini prebivalcev lahko pričakujemo kar 40 % pacientov z dislipedimijo, med katerimi je odkritih in ustrezno zdravljenih 26 %. Ker znaša letna cena zdravljenja te kronične bolezni na pacienta 313 €, je na milijon prebivalcev za zdravljenje dislipidemije potrebnih 82 milijonov €, še dodatnih 43,5 pa bi potrebovali, če bi bili zdravljeni vsi pacienti. Zelo razširjena kronična bolezen je tudi hipertenzija. Letno zdravljenje enega pacienta znaša 271 €, kar pomeni 69,5 milijona € na milijon prebivalcev, še dodatnih 14,5 milijona pa bi jih potrebovali, če bi bili z bolj sistematičnimi pregledi odkriti vsi pacienti. Za zdravljenje omenjenih kroničnih bolezni je torej potrebnih v Sloveniji preko 340 milijonov €, še dodatnih 148 pa bi jih morali nameniti zaenkrat neodkritim pacientom. Poznano je, da so hudi zdravstveni zapleti med ustrezno zdravljenimi kroničnimi bolniki izrazito redkejši, tako da je z etičnega stališča odkrivanje tovrstnih pacientov seveda upravičeno. Z nadaljnjim razvojem modela pa bomo skušali ovrednotiti tudi ekonomske prihranke, ki bi nastopili z zdravljenjem vseh obravnavanih kroničnih bolnikov zaradi zmanjšanja hudih obolenj. Ključne besede modeliranje; simulacija; diabetes tipa 2; debelost; kajenje; dislipidemija; hipertenzija Zaključki Atanasijević-Kunc M et al. Modelling of the risk factors and chronic diseases 489 Introduction Methodology It is well known that chronic diseases like, for exam- When developing a model it is very important to take ple, diabetes type 2, hypercholesterolemia and hyper- into account the purpose of the model’s usage, the tension are frequent in large numbers in countries all reliability of the data on which it is constructed, the over the world, and Slovenia is no exception. Some mathematical correctness of its interpretation, its suitreports suggest that these diseases have already ability for manipulation and the possibility to evalu-reached epidemic proportions.1–3 In developed re- ate the results.6 Therefore, the structure of our model gions regular examinations discover many sufferers was developed in such a manner that it allows the who are afterwards advised to undertake a particular sequential adding of each phenomenon in the whole diet and, if necessary, also treatment with drugs. Due observed population, while the evaluation of the moto the range of these diseases the costs of treatment del’s results are compared with different data forms cannot be ignored, as they represent a serious eco- and sources. nomic burden, not only for governments, hospitals The concept used regarding the development of the and medical insurance companies, but also for indi- model is illustrated in Figure 1, where all three mod-viduals, especially when taking into account the im- elling phases are also indicated. portant influence of these diseases, and risk factors The first phase of the modelling, which is described like obesity and smoking, on serious health compli- in detail, enables the observation of the mentioned cations that can threaten a person’s life or dramatical- diseases and the percentage risk factors in terms of ly lower the quality of life. This is true without taking the age of the sufferers, the relations between the ob-into account the additional treatment expenses, which served groups of sufferers, and their possible over-are usually a few times higher than those for the treat- lapping. These results can be further used for the pre-ment of chronic diseases. diction of more serious complications (which are still The goal of this study was to develop a dynamic mo- under investigation) but they can also represent the del that would make it possible to: input data for an estimation of the size of the observed – identify the main dynamic properties of the ob- groups of people, taking into account the chosen geo-served diseases and risk factors, graphical area. In our case the results are evaluated – estimate the number of sufferers in terms of age, for Slovenia and developed regions where the age – identify any possible overlapping of the observed distribution and the distribution of diseases is simi-groups of sufferers, lar. This part of results was calculated inside the third – estimate the healing effects and treatment costs for design phase, where the cost evaluation of a suitable each of the observed diseases, disease treatment was also realised. – predict the social burden of the treatment, The presented modelling results were obtained with – model extensions that would enable an estimation the Matlab program package.7, 8 of the influence of chronic diseases and risk fac- The concept of the first phase is presented in more tors on serious health complications, estimate and detail in Figure 2. It is separated into five main design evaluate possible savings, and study the ageing steps. The result of the first step gives the information population’s influence on the distribution of dis- about the distribution of the sufferers with diabetes eases and the economic burden. Such types of modelling results are not directly available in the literature. They often cover some of the mentioned aspects, but are usually connected with a specific region or country.4 In this paper the results are evaluated for Slovenia, and then an extrapolation is suggested, which can be applied to countries with a similar demographic and social situation.5 It is, we believe, reasonable to assume that the circumstances are similar in practically all of the countries of the EU. The study is organized as follows. First, the main modelling steps are described, where special attention is given to the model’s structure. This enables the sequential building of a dynamic system, taking into account all the observed risk factors, diseases, the population distribution and the treatment costs. In the next step, the simulation results and the model predictions are presented and discussed. The paper ends with concluding remarks and some suggestions for future work. type 2 (D2) in the observed population. In the next Relative (expressed as percentage) distribution of patients regarding their age Prevalenca pacientov v odvisnosti od starosti, izražena v odstotkih 3rd PHASE 3. FAZA numerical and numerično in price-treatment ekonomsko evaluation vrednotenje Relative (expressed as percentage) distribution of patients regarding their age Prevalenca pacientov v odvisnosti od starosti, izražena v odstotkih 1st PHASE 2nd PHASE chronical diseases and serious disease risk factors complications 1. FAZA 2. FAZA kronične resni bolezni in zdravstveni dejavniki tveganja zapleti Figure 1. The concept of the model’s construction. Sl. 1. Koncept izgradnje modela. 490 Zdrav Vestn 2008; 77 diabetes type 2 diabetes tipa 2 => obesity debelost ^> smoking kajenje ^> hypercholesterolemia dislipidemija ^> hypertension hipertenzija Figure 2. The structure of the first modelling phase. Sl. 2. Struktura prve faze modeliranja. step the set of obese people is introduced. In the third step it is taken into account that in the observed population there is also a group of people who are smokers, while in the fourth and fifth steps the model is additionally extended to describe people with hyper-cholesterolemia and hypertension. Results and discussion The development of diabetes type 2 in the population The distribution of diabetes type 2 (D2) has been reported by different data sources.9,10 In,9 for example, it is possible to find the information, presented in the third column of Table 1, where the simplifying assumption that between the ages of 0 and 24 the number of people with D2 can be neglected is introduced. Table 1. Data comparison from9 and10 regarding the prevalence of people with D2. Razpr. 1. Primerjava prevalenčnih podatkov iz9 in10 pacientov z D2. Age group Age in years % D2 (due to 9) % D2 (due to 10) Starostna skupina Starost v letih % D2 (glede na 9) % D2 (glede na 10) 1. 0-24 0 0 2. 25-29 0.8 3.5 3. 30-34 0.3 3.5 4. 35-39 1.4 4.2 5. 40-44 2.6 4.2 6. 45-49 5.4 8.9 7. 50-54 5.6 8.9 8. 55-59 10 15.5 9. 60-64 9.3 15.5 10. 65-69 19 11. 70-74 19 12. 75-79 19 13. 80-84 19 14. 85-89 20 15. 90-94 20 16. 95 and over 95 in več 20 It is evident that the data from9 differ a good deal from those in.10 The reason can probably be explained by the relatively small number of people investigated in.9 This was also the reason why the data from10 were used for modelling purposes. Regarding the last column of Table 1, it is again taken into account that the number of people with D2 up to the age of 24 is negligible, while the number between the ages of 75 and 84 is 19 % of people, and for the older population this number can be increased to 20 %. These data indicate, of course, the people who were diagnosed with the disease. However, based on some estimations11 there are approximately two times as many people who are not diagnosed and therefore not adequately treated. The number of people in this group is not the same for all age groups. It is probably that their number decreases with age, due to the fact that different health problems stimulate detailed analyses and the discovery of D2. Taking into account all the data and the assumptions, a mathematical model for diabetes type 2 was developed, where the independent variable is not the group of people from the chosen time interval but the age in years, as the changes inside each group can be significant. Of course, the mean values of the percentage function from the model and the data should be as similar as possible. The prediction of the model is illustrated in Figure 3, where the curve D2NEZDRA represents the undiagnosed and, therefore, untreated sufferers, D2ZDRA is the treated sufferers, while D2 indicates all the people with diabetes type 2. The demographic data are illustrated in Figure 4, where the population for Slovenia in 2003 for males and females is shown. By combining the two it is possible to quantify the number of observed sufferers, as presented in Figure 5, where, again, the treated (D2ZDRA) and untreated (D2NEZDRA) sufferers are shown. In the study12 it was estimated that the annual cost for the D2 treatment for one patient is on average € 355. This price includes all the expenses for the examinations and drug treatments (general practitioner, 4 times/year; laboratory, 2 times/year; drugs). From this the annual cost of D2 treatment in Slovenia was estimated, as shown in Figure 6, for the different ages of patients. The lower curve indicates the costs for the treated patients, while the upper line is an estimation of the increase in costs if all sufferers with D2 were to be diagnosed and, therefore, also treated. Figure 3. Percentage distribution of D2 (D2ZDRA – diagnosed patients, D2NEZDRA – undiagnosed sufferers, D2 – all with diabetes type 2). Sl. 3. Procentualna porazdelitev D2 (D2ZDRA – odkriti pacienti, D2NEZDRA – neodkriti pacienti, D2 – vsi pacienti z diabetesom tipa 2). Atanasijević-Kunc M et al. Modelling of the risk factors and chronic diseases 491 ktattMU (¦mm o****"-. \ ¦** l^C1"*K !¦¦¦¦ •» ":•' '", 1 •*................ 1 r:::"":' »* * ft % 'h -c ¦ i P 2 p 3 3 4P » KI n> 5ü » : 3 Figure 4. Population of Slovenia in 2003 sex and age. Sl. 4. Prebivalci Slovenije leta 2003, porazdeljeni po spolu in starosti. Figure 5. Number of inhabitants in Slovenia with D2 (all) (D2ZDRA – treated and D2NEZDRA – untreated) by age. Sl. 5. Število sladkornih bolnikov v Sloveniji v odvisnosti od starosti (D2 – vsi, D2ZDRA – zdravljeni, D2NEZDRA – nezdravljeni). Figure 6. D2 treatment costs in euros. Sl. 6. Cena zdravljenja pacientov z D2 v €. On the basis of the presented results the following can be concluded: 1. In Slovenia there are around 100,000 people, or 5.5 % of the population, with diabetes type 2 (the model predicts 110,086) who are being treated. 2. Approximately 90,000 people (the model predicts 90,697), or 4.5 % of the population, are undia-gnosed. 3. Approximately 200,000 people (the model predicts 200,783) or 10 % of the population have diabetes type 2. 4. Of all the D2 sufferers there are 54.83 % being treated and 45.17 % not being treated. 5. The annual cost for D2 treatment is around € 39 millions (the model predicts € 39,080,530). 6. If all the sufferers were to be diagnosed and treated, the annual cost of treatment would increase to approximately € 71 millions, which represents a cost increase of € 32 millions (the model predicts € 32,197,435). As Slovenia can be regarded as a developed country in terms of lifestyle and nutrition,5 it can be concluded that in similar countries the following can be expected: 1. For every 1 million people there are 5.5 % with diagnosed diabetes D2 and 4.5 % who are not diagnosed and therefore not treated. 2. The annual cost for D2 treatment is approximately € 19.5 millions per million people. 3. If all sufferers of D2 were diagnosed the annual cost would increase by € 16 millions. Obesity The outputs from the first step are three signals representing the following: the patients being treated for D2 (D2ZDRA); the sufferers who have not been diagnosed (D2NEZDRA); and the people without D2. These three signals are then entered into the second subsystem (Figure 2), where the observed population is further transformed into the group of people with a healthy weight and the group of people who are overweight. The outputs from this block are six signals, representing all the groups of people. Several studies13–15 show a significant correlation between obesity and diabetes type 2. As a measure of obesity the body mass index (BMI) is normally used.15 In order to keep the situation simple and because the vast majority of obese people belong to that group with a BMI between 25 and 30, all the people with a BMI > 25 are regarded as a single group. Table 213 shows the distribution of overweight people. It is, therefore, to be expected that 22.2 % (between the ages of 20 and 39) to 29.2 % (between the ages of 40 and 59) of the population is overweight, while over the age of 60 it is to be expected that the number decreases to an average of 24.4 % of people being described as obese. Looking at the whole population, the ratio of those classed as overweight to those with a healthy weight equals 25.3 %/74.7 % = 0.3387. The modelling results for this design step are illustrated in Figures 7 and 8. Regarding the situation in Figure 7, it can be concluded that the group of young, obese people (PTT) is made up mainly of those without D2 (BREZD2inPTT). This situation is to be expected as D2 starts later in life than obesity. Over time the size of this group of people decreases as they begin to join the group with D2 (D2VSIinPTT). Over the age 492 Zdrav Vestn 2008; 77 Table 2. Percentage distribution of the overweight and obese population and the population with a healthy weight, by age and on average. Razpr. 2. Procentualna razporejenost ljudi s prekomerno in primerno telesno maso glede na starost in v povprečju. Age % of overweight % of healthy weight % ljudi s prekomerno % ljudi z zdravo Starost telesno maso telesno maso 20–39 22.2 77.8 40–59 29.2 70.8 60 and over 24.4 75.6 60 in več Over 20 on average by age 25.3 74.7 Nad 20 povprečno, glede na starost Figure 7. Percentage distribution of obese people (PTT) with and without D2 (PTT – obese, BREZD2inPTT – obese without D2, D2VSIinPTT – obese with D2, D2ZDRAinPTT – obese with treatment for D2, D2NEZDRAinPTT – obese with untreated D2). Sl. 7. Procentualna porazdelitev ljudi s prekomerno telesno težo (PTT), ki imajo oz. nimajo D2 (PTT – vsi s prekomerno telesno težo, BREZD2inPTT – brez D2 in s PTT, D2VSIinPTT – z D2 in PTT, D2ZDRAinPTT – D2 zdravljeni in s PTT, D2NEZDRAinPTT – D2 nezdravljeni in s PTT). Figure 8. The ratio of people with and without D2 for the obese population. Sl. 8. Zastopanost ljudi z diabetesom 2 v skupini ljudi s prekomerno telesno maso. of 60 the size of group decreases due to the normalization of body weight. Between the ages of 30 and 60 the group of obese people begin to join those with diagnosed and undiagnosed D2, while later on this is true mainly for the diagnosed and, therefore, treated patients (D2ZDRAinPTT). In Figure 8 the following ratios are illustrated: D2ZDRAinPTT/PTT represents the ratio between obese patients with treated D2 and all obese people, D2NEZDRAinPTT/PTT represents the ratio between obese people with untreated D2 and all obese people, while D2VSIinPTT/PTT represents the ratio between all the obese people with D2 and all the obese people. Taking into account counting data (Figure 4) and the obesity-modelling results (Figure 7) the number of overweight people in Slovenia can be estimated. The results suggest that more than 400,000 people in Slovenia are overweight (the model predicts 434,681) or almost 22 % of the population. Smoking The model’s structure is further extended with the division into the groups of smokers and non-smokers, using the data presented in Table 3.16 Table 3. Percentage distribution of smokers by age and on average. Razpr. 3. Procentualna porazdelitev kadilcev glede na starost in povprečno. Age (irrespective of sex) % of smokers Starost (ne glede na spol) % kadilcev 18–44 24.1 45–64 21.9 65 and over 8.6 65 in več Over 20 – balanced regarding age 20.8 Nad 20 – uravnoteženo glede na starost The structure and parameters were defined with respect to the data, while at the same time the fact that D2 is more frequently detected in the population of smokers than among people who are not smoking was taken into account. Figures 9 and 10 show the results predicted by this modelling phase. From Figure 9 it is obvious that the group of young smokers is mainly made up of those people without D2. Later on, however, the share of D2 sufferers becomes significant. After the age of 60 the group of smokers with D2 begins to decrease due to the fact that a large number of people give up smoking when they get older. When the situation with regard to smokers is defined, the circumstances relating to non-smokers are also known. Figure 10 shows the ratios that are informative with regard to the occurrence of D2 sufferers among the smokers and non-smokers. It is obvious that the curve r1 = smokers with D2 / smokers is, over time (in other words, age), significantly higher than r2 = non-smokers with D2 / non-smokers. The average value of the ratio r1/r2 is 1.68 between the ages of 25 and 95. The Atanasijević-Kunc M et al. Modelling of the risk factors and chronic diseases that influence the development of serious health complications 493 model’s responses are, therefore, a very good match for the data in,16 where the results indicate that the risk factor among smokers is, on average, 1.68 times higher than among non-smokers (1.42 for women and 1.94 for men). Regarding the modelling results (Figure 9) and the counting data (Figure 4) the distribution of the smoking population in Slovenia was defined. According to the modelling results there are over 340,000 people who smoke in Slovenia (the model predicts 342,941) or the group of smokers represents 17.18 % of population. In the interval between the ages of 25 and 70 the model predicts more than 23 % of smokers. Figure 9. Smokers with and without D2 (D2NEZDRA – untreated D2, D2ZDRA – treated D2). Sl. 9. Kadilci z in brez D2 (D2NEZDRA – nezdravljen D2, D2ZDRA – zdravljen D2). \ / afa \ ¦ ./ / - twwrttpOZA mkn \ \ \ s \ 11 9 3 a 3 & * 0 = D 6 •ir*] 0 I 0 s 0 i & 1 » Figure 10. Ratios: r1 = smokers with D2 / smokers, r2 = non-smokers with D2 / non-smokers, ratio = r1/r2. Sl. 10. Razmerji: r1 = kadilci z D2 / kadilci, r2 = nekadilci z D2 / nekadilci, razmerje = r1 / r2. Hypercholesterolemia The model was then expanded to also incorporate the people with hypercholesterolemia (H). This means that the whole population (in all its subgroups) is further divided into three groups: to those without hypercholesterolemia (BREZH), to the group with the treated disease (HZDRA) and to those sufferers who are not diagnosed and are therefore untreated (HNEZDRA). This step of the model was constructed on the basis of the data presented in Table 4.17, 18 Table 4. Percentage of people with hypercholesterol-emia with regard to age and concomitant D2. Razpr. 4. Procentualna razporeditev pacientov z dis-lipidemijo glede na starost in procentualna razporeditev pacientov, ki imajo hkrati H in D2. Age (men and women in average) Starost (moški in ženske povprečno) % of people with hypercholesterolemia % ljudi z dislipidemijo % of people with hypercholesterolemia and D2 % ljudi, ki imajo hkrati dislipidemijo in D2 18–24 25–34 35–44 45–54 55–64 65–74 75 and over 75 in več 9.3 17.2 26.5 37.7 50.3 50.6 50.6 44.1 44.1 44.1 59.7 59.7 58.7 53.5 During modelling the following simplifying assumptions were taken into account: – when one of the observed diseases is discovered, this stimulates a more detailed examination of the patient and, consequently, other diseases are also diagnosed and are therefore treated, – all the people with D2 who are not treated also develop hypercholesterolemia. The modelling results are illustrated in Figures 11 and 12. Figure 11 shows the patients with hyperchole-sterolemia (H) as well as the sufferers (HNEZDRA) and treated patients (HZDRA). In Figure 12 it is possible to observe those who also have D2 and hypercho-lesterolemia (D2andH), with the distinction among those who are treated (D2andHZDRA) and those who are not (D2andHNEZDRA). Figure 11. Hypercholesterolemia (H), diagnosed and, consequently, treated (HZDRA), untreated (HNEZDRA). Sl. 11. Dislipidemija (H), odkriti in zdravljeni (HZDRA), neodkriti in nezdravljeni (HNEZDRA). Taking into account the situation in Figures 11 and 4 the number of treated and untreated sufferers with hypercholesterolemia can be calculated as presented in Figure 13. The annual cost for treating this disease 494 Zdrav Vestn 2008; 77 is € 31312 (general practitioner, 4 times/year; laboratory, 2 times/year; drugs). Figure 14 shows the annual cost for treating this disease with regard to the age of the sufferer. Figure 12. D2 in combination with hypercholesterol-emia (D2andH) (D2andHZDRA – treated, D2andHNEZDRA – untreated). Sl. 12. Pacienti, ki imajo hkrati D2 in dislipidemijo (D2andH) (D2andHZDRA – zdravljeni, D2andHNEZDRA – nezdravljeni). Figure 13. Number of people with hypercholesterol-emia (H) in Slovenia (treated – HZDRA, undiagnosed and untreated – HNEZDRA, and all – H). Sl. 13. Število pacientov z dislipidemijo (H)v Sloveniji (zdravljeni – HZDRA, neodkriti in nezdravljeni – HNEZDRA, vsi – H). On the basis of the presented results the following can be concluded: 1. In Slovenia there are over 500,000 treated sufferers (the model predicts 525,632) with hypercholestero-lemia, which means 26.33 % of the population. 2. The number of undiagnosed sufferers exceeds 280,000 (the model predicts 280,168 prediction), which means 14.03 % of the population of Slovenia. 3. Over 40 % of the population, or over 800,000 people, are, therefore, suffering with hypercholeste-rolemia. 4. The annual cost for treating this disease in Slovenia is over € 160 m (the model predicts € 164,522,816). Figure 14. Annual treatment costs for sufferers of hypercholesterolemia (diagnosed – lower curve, all – upper curve). Sl. 14. Letna cena zdravljenja pacientov z dislipidemijo (odkritih pacientov – spodnja krivulja, vseh – zgornja krivulja). 5. For the case of all the sufferers being diagnosed and treated the cost would increase by 53.3 % (the model predicts a total of € 252,215,400). Therefore, in developed regions the following can be expected: 1. 40 % of the population are suffering from hyper-cholesterolemia, 2. 26 % are diagnosed and are receiving treatment, 3. an annual cost of € 82 m per one million people can be anticipated, 4. for the case of all the sufferers being diagnosed and treated, the treatment cost would increase by € 44 m per one million people. Hypertension The first modelling phase was completed by a further separation of the observed population, taking into account hypertension. Again, a distinction was made between people who are diagnosed and treated (TZDRA) and those who are not being treated (TNEZDRA). These two groups form the group of people with hypertension (T), while the others are not suffering from hypertension (BREZT). The assumption was made that when one of the observed diseases is diagnosed, so are the others, and that smoking and an increased body mass are not treated and are taken into account. For modelling purposes the data as presented in Table 519 were used. These data report the percentage of diagnosed sufferers with hypertension. It is estimated that in Slovenia there is an additional, approximately 20 % of people with undiagnosed hypertension. Taking into account this assumption and the fact that their number is decreasing with the sufferers’ age, this group was included in the model. The results of this modelling step are illustrated in Figures 15 to 19. In Figure 15 the people with hypertension (T) are presented with regard to their age. This group consists of those patients who are discovered and are therefore treated (TZDRA) and of those who are not treated because they are not diagnosed Atanasijević-Kunc M et al. Modelling of the risk factors and chronic diseases 495 Table 5. Percentage of people with hypertension with regard to age. Razpr. 5. Procentualna razporeditev ljudi s hiperten-zijo glede na starost. Age % of men % of women % in average Starost % moških % žensk % povprečno 16-24 10.6 1.5 6.05 25-34 13.6 4.9 9.25 35-44 21.3 10.4 15.85 45-54 36.7 24.3 30.5 55-64 53.2 48.2 50.7 65-74 66.6 67.3 66.95 75 and more 75 in več 66.7 76.6 71.65 (TNEZDRA). The presented curves match the source data very well. Figure 15 also shows the situation with regard to diabetes type 2. All the patients with D2 (D2), the set of patients with D2 and hypertension (D2andT) and those who have hypertension but not diabetes type 2 (BREZD2inT) are shown. In Figure 16 the following ratios are illustrated: r1=D2inT/D2VSI [solid line] r2=(D2inT/D2VSI)/(BREZD2inT) [dotted line] It is evident that among patients with diabetes, hypertension is approximately two times more frequent than among the healthy population. Finally, also the time-varying ratios of treated hypertension patients / all with hypertension and untreated sufferers / all with hypertension were defined as shown in Figure 17. It is evident that at the beginning the group of undiagnosed and untreated sufferers is greater, but with time the sufferers are discovered directly or indirectly because of other health problems. Figure 15. Percentage of patients with hypertension and with combination of T and D2 regard to age (T – all with hypertension, TZDRA – treated patients with hypertension, TNEZDRA – untreated sufferers with hypertension, BREZT – people without hypertension, BREZD2inT – people without D2 and with T, D2inT – people with D2 and T). Sl. 15. Prevalenca pacientov s hipertenzijo in kombinacijo T in D2 glede na starost (T – vsi hipertoniki, TZDRA – zdravljeni hipertoniki, TNEZDRA – nezdrav-ljeni hipertoniki, BREZT – ljudje brez hipertenzije, BREZD2inT – ljudje brez D2 in s T, D2inT – ljudje z D2 in s T). ri -D2HIT 1D2VSIA U-îDirtT .IMVSI l.uBREZDSwIJflrtrtB* VlfeM-1.7792 t> ftd9« ri ri ¦ "¦»i____ ---- 0 » I 0 Figure 16. Hypertension and D2 – ratios: r1=D2inT/ D2VSI and r2=D2inT/D2VSI)/(BREZD2inT). Sl. 16. Hipertenzija in D2 – razmerja: r1=D2inT/D2VSI in r2=D2inT/D2VSI)/(BREZD2inT). Figure 17. The ratios of treated and untreated sufferers with hypertension, for all sufferers of hypertension. Sl. 17. Razmerji zdravljenih in nezdravljenih pacientov s hipertenzijo glede na vse hipertonike. »of »un •nini»» *¦ \\.*- • * T \ \ Z.' "•v \ \ \ *¦ * ¦ * i '" TMCZDRA ^ / .C: ...j / é "k. V *••. ¦ ! i 0 1 1 4 * ~2 I I a T 9 9 3 ? ° ™ Figure 18. Number of sufferers with hypertension in Slovenia (treated – TZDRA, undiagnosed and untreated – TNEZDRA, all – T). Sl. 18. Število pacientov s hipertenzijo v Sloveniji (zdravljeni – TZDRA, neodkriti in nezdravljeni – TNEZDRA, vsi – T). The mean value of the population with hypertension is 31.14 %, according to the model forecast. 496 Zdrav Vestn 2008; 77 Using the information as presented in Figures 15 and 4, the number of treated and untreated sufferers with hypertension can be calculated, as illustrated in Figure 18. The estimated average annual cost for hypertension treatment is € 271 per person12 (general practitioner, 4 times/year; laboratory, once/year; drugs). On the basis of this data it is possible to calculate of the annual cost of hypertension treatment in Slovenia, as illustrated in Figure 19. On the basis of presented results the following can be concluded: Figure 19. Annual cost for hypertension treatment with regard to age (actual cost – lower curve, total cost for the case of treating all sufferers – upper curve). Sl. 19. Letna cena zdravljenja hipertenzije glede na starost pacientov (dejanska cena – spodnja krivulja, cena zdravljenja vseh pacientov – zgornja krivulja). 1. In Slovenia there are over 500,000 patients with hypertension (the model predicts 513,561) being treated; the mean value in therefore 25.7 %. 2. Over 108,000 sufferers, or 5.4 % of the population are undiagnosed, and are therefore untreated. 3. A total of 31 % of the population of Slovenia is hypertonic, which means over 600,000 sufferers (the model predicts 621,695). 4. The annual cost of hypertension treatment in Slovenia is over € 139 millions (the model predicts € 139,175,031). 5. For the case of all the sufferers being diagnosed the cost would increase to € 168 m (the model predicts € 168,479,345), which means a 21 % increase. In developed countries the following can be expected: 1. over 30 % of the population have hypertension, 2. the diagnosed and treated are 25 to 26 %, 3. an annual cost of € 69.5 m for a population of million people can be expected, 4. for the case of all sufferers being diagnosed the annual cost for hypertension treatment would increase by € 14.5 m per million people. Conclusions Recent estimates suggest that 195 million people throughout the world have diabetes and that this number will increase to 330, maybe even to 500 million, by 2030.20 The prevalence of type 2 diabetes increases with age, especially in Europe.21 The most common cause of death in European adults with diabetes is coronary artery disease. Several studies have demonstrated that D2 increases a risk for two to three times in comparison with people without diabetes.22 In combination with other chronic diseases, like hypertension and hypercholesterolemia, and risk factors, like obesity and smoking, the development of other serious health complication can also be expected (stroke, coronary heart disease, end-stage renal disease and congestive heart failure). Such a range of epidemic chronic diseases indicates that they have become (in a direct and indirect manner) significant social and economic burdens, important for governments, hospitals, health-insurance companies and, regarding educational programs, for the whole population. In many countries (especially smaller) national registers for such health problems do not exist (or are available only for some diseases). So expectations have to be estimated with regard to epidemio-logical statistical data. In this paper the results of nonlinear, dynamic, mathematical modelling are presented, which make it possible to track sufferers with diabetes type 2, hyper-cholesterolemia, hypertension, overweight people and smokers. Also, all possible combinations were taken into account, which means that the output of the last block of the first design phase consists of 108 time signals for each observed group. A complete mathematical description is given in Appendix.23 These groups are presented with regard to age and percentage. The obtained information was used as a direct input to the third modelling phase, where it was combined with demographic data and with the estimated treatment costs. From this the number of sufferers and patients the economic burden were also derived for Slovenia and other developed countries. The modelling results are summarized in Tables 8 and 9. From the presented results it is obvious that the number of patients with chronic diseases and risk factors is very large. The situation should in fact be treated as an epidemic, especially when we realise that the trends suggest an even worse situation in the future. In spite of the fact that obesity and smoking were, in this study, not evaluated as an economic burden (the potential treatment costs for these two risk factors were not included) the treatment cost per year for the observed chronic diseases is estimated to be € 491 m. In the case where all sufferers were to be diagnosed (i.e., a more systematic examination) and therefore also correspondingly treated, this economic burden would initially increase by an additional € 148 m. But as mentioned, diseases and risk factors are strongly correlated with the potential development of a stroke, coronary heart disease, peripheral arterial-vascular disease, end-stage renal disease and congestive heart failure, and so such an investment could be justified from the economic point of view. The treatment costs for these complications are significantly higher than the treatment costs of initial diseases. Atanasijević-Kunc M et al. Modelling of the risk factors and chronic diseases 497 Table 8. Number of sufferers, patients and the annual treatment cost in Slovenia. Razpr. 8. Število bolnikov (neodkritih in odkritih) in letna cena zdravljenja v Sloveniji. Disease or risk factor and annual treatment cost for one patient Letna cena zdravljenja za enega pacienta za posamezno bolezen ali dejavnik tveganja Treatment annual Number of Number of diagnosed cost (€) for diagnosed undiagnosed sufferers in SLO patients in SLO sufferers in SLO Število Letna cena zdravljenja Število diagnosticiranih (€) odkritih bolnikov nediagnosticiranih bolnikov v SLO v SLO bolnikov v SLO Treatment annual cost Cost increase in the in SLO for all patients case that all sufferers (€) Letna cena zdravljenja v SLO za vse bolnike (€) were to be treated (€) Povečanje letne cene zdravljenja za primer, če bi bili odkriti vsi bolniki (€) D2 (€ 355) over / preko 110,000 over / preko 39 m over / preko 90,000 over / preko 71 m over / preko 32 m Obese population Populacija s prekomerno telesno maso over / preko 430,000 //// Smokers Kadilci over / preko 342,000 //// Hypercholesterolemia Dislipidemija (€ 313) over / preko 525,000 over / preko 164 m over / preko 280,000 over / preko 252 m over / preko 87 m Hypertension Hipertenzija (€ 271) over / preko 513,561 over / preko 139 m over / preko 108,000 over / preko 168 m over / preko 29 m Table 9. Percentage of sufferers, patients and treatment cost in a population of a million people in developed regions. Razpr. 9. Procentualna zastopanost opazovanih pacientov in cena zdravljenja na milijon prebivalcev v razvitih območjih. Disease or risk factor and annual treatment cost for one patient Letna cena zdravljenja za enega pacienta za posamezno bolezen ali dejavnik tveganja % of diagnosed sufferers Treatment annual cost (€) for diagnosed patients % of undiagnosed sufferers Treatment annual cost for all sufferers (€) % diagnosticiranih Letna cena zdravljenja % neodkritih bolnikov (€) odkritih bolnikov bolnikov Cost increase in the case that all sufferers were to be treated (€) Povečanje letne cene Letna cena zdravljenja zdravljenja za primer, za vse bolnike (€) če bi bili odkriti vsi bolniki (€) D2 (€ 355) 5.5 % 19.5 m 4.5 % 35.5 m 16 m Obese population Populacija s prekomerno telesno maso 22 % //// Smokers Kadilci 17.2 % (23 % between the age of 25 and 70) (23 % v starosti med 25 in 70) //// Hypercholesterolemia Dislipidemija (€ 313) 26.33 % 82 m 14 % 126 m 44 m Hypertension Hipertenzija (€ 271) 25.7 % 69.5 m 5.4 % 8.4 m 14.5 m References 1. International Diabetes Foundation. Diabetes prevalence. 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