**5. Multiple linear regression model**

From this data set and temporal series, some tentative models were developed for a better understanding to the disease dynamics. Assuming that the proportion of susceptible individuals is a constant value a reported to a large population (eventually of genetic origin), this could explain the main feature of the epidemic process of meningococcal disease and ecological characteristics of meningococcus commensality.

Also, meningococcus as a species may exist as a non-pathogenic microorganism. IMD will then arise only among susceptible people who have a genetic predisposition while in any large population, such a percentage is very small (<1%).

In order to calculate the percentage of susceptible population to IMD, it is possible to calculate it as a risk of susceptibility (RS), the percentage of susceptible, i.e. approximate proportion of the population susceptible" (APPS) to IMD. In order to calculate APPS, we first calculate the annual estimated number of carriers, AAQC (infected people without clinical manifestations):

$$\text{APPS} \quad = \text{ (IMD number:} AA\text{QC)} \times 100\% \tag{1}$$

where AAQC = annual approximate quantity of carriers (infected people without clinical manifestations); CPR = carrier prevalence rate (from the ratio of the carriers detected among people examinees); N = the census of the population of the studied territory; 365 = days (i.e., a year); D = average duration of carriage status (not detected after 14 days).

where AAQC formula is derived from PR formula:

**4. Clinics**

as pneumonia or mixed clinical forms.

clinical forms (n = 538).

h after onset.

to the frequency of septicemia.

nated intravascular coagulation syndrome, among others.

**5. Multiple linear regression model**

cal characteristics of meningococcus commensality.

large population, such a percentage is very small (<1%).

Among the 18,914 cases of IMD reported in Ukraine, 38.4% were meningococcemia, 29.9% were meningococcemia with meningitis, 27.9% meningitis and others 2.8% were of different minor etiologies. Other clinical forms have not been also clearly recognized and characterized

18 Meningoencephalitis - Disease Which Requires Optimal Approach in Emergency Manner

Also, the distribution of clinical forms of IMD in Ukraine is very different from the one observed in the EU countries in which meningitis prevails for 43.0%. Meningococcemia and meningococcemia with meningitis represent, respectively, 21.0 and 29.0% of total IMD in the EU [10]. Case fatality rate (CFR) of Meningococcal disease in Ukraine for the period considered (1992–2012) was of: 12.1% for IMD (n = 18,914); 18.9% for Meningococcemia (n = 7448); 10.1% for Meningococcemia (n = 5660); 5.94% of Meningitis (n = 5273); and 5.6% for others undefined

In 2012, overall CFR in EU/EEA countries was 7.9%, (3185 confirmed IMD cases). The highest CFR reported (n = 1563) among cases presenting septicemia was 18.8%, followed by cases meningitis with septicemia of 11.1%, and then by cases with meningitis (3.7%) [11]. In Ukraine, the higher observed overall CFR of IMD greater than in the EU can be attributed

Meningococcal disease CFR among children in Ukraine during the period of 2010–2015 ranged from 14.7 to 19.1% occurring as follows with respect to the age class: first year of life, 66%; 1–3 year old, 30%; over three-year old, 4%. Among 77% of patient death occurred during the first 24

According to the children's infectious hospital of Kiev, for the past 15 years, serotypes prevail as follows: meningococcal serogroup B, 57%; serogroup A, 19%; serogroup C, 20%; and other serogroup, 4%. Meningococcemia was diagnosed in 47% of patient with meningococcemia, 41% meningitis, while 12–76% of children with meningococcal disease had a complicated course of the disease, including septic shock, brain edema, multiple organ failure, dissemi-

From this data set and temporal series, some tentative models were developed for a better understanding to the disease dynamics. Assuming that the proportion of susceptible individuals is a constant value a reported to a large population (eventually of genetic origin), this could explain the main feature of the epidemic process of meningococcal disease and ecologi-

Also, meningococcus as a species may exist as a non-pathogenic microorganism. IMD will then arise only among susceptible people who have a genetic predisposition while in any

\*\*Wire ANAQC\*\* \*\*nulina\*\* is \*\*neline 100\*\* i \*\*nulina\*\*.\*\*

$$\text{AAQC} = \frac{\text{CPR} \times \text{N} \times 365}{\text{D}}\tag{2}$$

where PR = prevalence rate; IR = incidence rate; D = average day duration for one case of carriage [12].

Ultimately, AAQC formula allows to convert the data of sample surveys (i.e., prevalence of meningococcal carriage showed (**Figure 9**) to indicators of incidence (or the annual approximate number of carriers). Thus, we calculated the AAQC among healthy children for the period 1992–2012 years. The AAQC of children was calculated from 2,206,475 persons. The proportion of IMD cases (i.e., % susceptible) presented an average of 0.0360% ± 0.0189, that is: in overall, one IMD patient associated with 5271 carriers in during 1990–2012.

Moreover, this way we calculated indicators for period of time from 1992 to 2012 for the general population. The annual average number of carriers in the general healthy population was 24,990,502 persons (variation of 15,480,263–34,746,741 per year). The proportion of IMD cases (i.e., % susceptible) had an average of 0.0036% (0.0022–0.0058% per year), that is: one IMB patient associated an average of 29,729 carriers.

In overall, this is consistent with the fact that the IMD incidence among children exceeds IMD incidence in the general population (or adult) by 10-fold or more.

The total risk of disease (RD) is expressed as a product of risk of infection (RI) to risk of susceptibility (RS) where RD = RI × RS. Thus, in our paradigm, RS and RI are the final and necessary causes of IMD emergence and spread to human population. All other causes that may affect IMD incidence will act indirectly through RI and RS.

Therefore, we built multiple regression models of the epidemic process of MI, where the incidence of IMD is the dependent variable, while independent variables are the level of meningococcal carriage (RI) and the proportion of the susceptible population (RS). The construct of the regression model was by deriving multiple regression method [12]. Multiple linear regression models of IMD in Ukraine were therefore developed [13]. We used for the model the data presented in the figures 6 and 10.

Our first model takes the following form of the regression equation:

$$\text{Y1} = -7.43 + 8.26 \,\text{X}\_1 + 227.63 \,\text{X}\_2 \tag{3}$$

where Y1 = IMD incidence per 100,000 children 0–14 years; −7.43 (or "a") = constant, which corresponds to the mathematical expectation Х<sup>1</sup> and Х<sup>2</sup> if Y = 0; Х<sup>1</sup> = prevalence of carriage among healthy children aged 0–14 (%); Х<sup>2</sup> = approximate proportion of the population susceptible to the IMD among children aged 0–14, or APPS (%); 8.26 (or "b<sup>1</sup> ") = regression coefficient showing the change of level Y, if Х<sup>1</sup> is changed to 1%; 227.63 (or "b<sup>2</sup> ") = regression coefficient showing the change of level Y, if Х<sup>2</sup> is changed to 1%.

Note that the influence of the regression coefficients (b<sup>1</sup> and b2 ) and constant "a" at incidence Y is statistically significant (Student exact test: b<sup>1</sup> = 14.56 with p = 2.13 × 10−11; b<sup>2</sup> = 15.39 with p = 8.38 × 10−12; a = 7.54 with p = 5.59 × 10−7).

In the model, the coefficient of multiple correlation R = 0.9697 and its standard error is equal to 0.5069 (R<sup>2</sup> = 0.9404, i.e. 94.04%) that statistically significance explains IMD incidence and shows the high descriptive properties of the model. Ultimately, this model appears highly significant (Fisher's exact test = 142.04 p < 0.05 at 95% confidence) describing the totality of the properties of the epidemic process of MD among children aged 0–14. Analysis of the residuals values of the model did not find any autocorrelation. Overall, the model encompasses all properties and is statistically significant.

Our second model takes the following form of the regression equation:

$$\text{Y2} = -1.59 \, + \, 0.89 \, \text{X}\_{\text{i}} \, + 469.13 \, \text{X}\_{\text{2}'} \, \tag{4}$$

where Y2 = IMD incidence per 100,000 population; Х<sup>1</sup> = prevalence of carriage among persons who had contact with IMD patients (or among total population), %; Х<sup>2</sup> = approximate proportion of the population susceptible to the IMD among total population, APPSIMD, %. The model has excellent descriptive properties and statistically significant. The coefficient of multiple correlation r = 0.9937 and its standard error is equal to 0.0645, accordingly with r<sup>2</sup> = 0.9875. Residuals analysis of the model did not find any autocorrelation (i.e., almost normal distribution.)

Model limitation: Our models use aggregated data form a survey, and therefore, our model does not allow for an adequate formal residual analysis. In order to perform such type of analysis, it requires to build at least 50 times of such models from necessary data sets. Also, our models do not take into account the potential heterogeneity of the pathogen.

## **6. Conclusion**

Altogether the present and past surveillance of bacterial meningitis in Ukraine provide a unique source for a comprehensive understanding of the disease dynamics and, most importantly, allow to develop tools and strategies for control and prevention.

Thus, the results of mathematical modeling of IMD using the available time series of data suggest that the nature of the main manifestations of the epidemic caused by the MI process demonstrates the prevalence of meningococcal carriage and provides a measure of the of susceptible populations, which are both factors strongly associated and allow the assessment of immediate risk of IMD in country. The proposed multiple linear regression model of epidemic process of meningococcal disease will improve epidemiological surveillance of the disease. Moreover, such models will provide a strong mean for assessing the quality of vaccination against invasive bacterial infections as well as diphtheria.
