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During UV disinfection, the required UV dose in terms of fluence depends upon the species of bacteria spore and protozoa. To rank their UV disinfection sensitivity, spore sensitivity index (SPSI) and protozoan sensitivity index (PSI) are defined. For spores, shoulder effect exists, therefore, SPSI is defined as the ratio between the ki of any spores for the linear portion of the dose response curve to the kir of Bacillus subtilis as the reference spore. After statistical analysis, the fluence of any spore can be predicted by SPSI through equation, H = (0.8358 ± 0.126)*LogI*SPSI + H0. PSI is defined as the ratio between the inactivation rate constants of a protozoa in reference to that of Cryptosporidium parvum. The equation predicting the fluence of any protozoa in reference to Cryptosporidium parvum is: H = 107.45*(3.86 ± 2.68)*LogI/PSI. Two regression equations suggest that protozoa require significantly higher UV dose than bacteria spores.

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  • UV sensitivity index of bacteria spore and protozoa were defined.

  • The UV fluence could be predicted by the UV sensitivity indexes.

  • Protozoa required significantly higher UV dose than that required by spores.

Graphical Abstract

Graphical Abstract
Graphical Abstract
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Graphical Abstract
Graphical Abstract
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Bacillus subtilis and Cryptosporidium parvum as reference, protozoan, sensitivity index, spore, UV disinfection
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UV disinfection technology becomes more and more important in water and wastewater industries, because UV radiation is an effective inactivation process against pathogenic micro-organisms such as Cryptosporidium and Giardia which poses a major threat to the safety of drinking water (Lonnen et al. 2005). To determine the inactivation equivalent fluence in UV disinfection system is more complex than medium pressure mercury vapor polychromatic. Because the spectral sensitivity of the microorganisms should be known toward the various wavelengths emitted by the medium pressure lamp as well as the spectral transmittance of the water (Mamane-Gravetz et al. 2005). Different spores and protozoa require different UV irradiation doses, depending upon the cultivation method used. The difference in UV susceptibility may also be related to the individual spectral UV sensitivity of the spores and protozoa (Cabaj et al. 2001, 2002).

Currently, the relationship between the fluence required for different spores and protozoan at a specific Log I have been reported in various publications. Some papers reported the UV dose and response data. The UV disinfection of different spores and protozoa at different degrees of Log I was published by Malayeri et al. (2016). This current research aims to develop a simple and universal model to systematically predict the fluence required to achieve specific reduction log I by using the spores sensitive index (SPSI) and protozoan sensitive index (PSI) during UV disinfection. Two independent universal equations were developed for fluence required to achieve a specific inactivation level Log I for different spores and protozoan in wastewater by using Bacillus subtilis and Cryptosporidium parvum as reference spores and protozoan, respectively.

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Databases

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The database developed by Malayeri et al. (2016) was used to obtain a uniform set of first-order inactivation rate constants of spores and protozoa during UV disinfection. The inactivation rate constants of other spores and protozoa were divided by the mean kr as a reference spores and protozoa to derive their corresponding SPSI. The SPSI developed was then used to derive the statistical equation between Hi/Hr and SPSI and Log I.

Spores mathematic model

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Shoulder effect during UV disinfection refers to the initial delay of inactivation of bacteria spores (spores for simplicity) to achieve observable inactivation rate of Log I (Severin et al. 1983, 1984). Shoulder effect can be mathematically described as follows:
(1)
where N0 is the initial spore concentration before UV disinfection, Nd is the spore concentration after it received UV fluence of H. When fluence equals zero, the shoulder effect d is the log (Nd/N0), which will be referred to as Log I for simplicity. kH is the first order initial rate constant (cm2/mJ) of the linear portion of log (Nd/N0) vs. H.
To simplify the mathematical model of Equation (1), a spore survival curve during UV disinfection can be considered as two portions (Chick 1908; Watson 1908). First, shoulder portion of the curve can be approximated as shoulder broadness (SB), H0, which is the minimal fluence required to have observable Log I. Mathematically, H0 is the intercept of H when log (Nd/N0) equal to zero. The actual SB would be either less or greater than the H0 which is obtained from the intercept from the linear portion of the survival curve. However, the predicted H could be either less or greater than actually observed fluence H. Second, after the initial shoulder, the linear portion follows the first order kinetics which is characterized by the inactivation rate constant, kH. As a result, a simple kinetic model is expressed as follows:
(2)
where log I is log (Nd/N0). kH is the first order initial constant (cm2/mJ) of the linear portion of log(Nd/N0) vs. H. b is the intercept on the y-axis of Log I of the spore survival dose cure.
Equation (2) can be solved to get H:
(3)
where Hi is the fluence required at a given Log I. ki equals 1/kH. H0 is the shoulder broadness and equals b/kH.
Similarly, Equation (3) can be also applied to a reference spore such as Bacillus subtilis, which is recommended as a reference spore by the US EPA, as follows:
(4)
To obtain a simplified predictive model, Equations (3) and (4) can be re-arranged as follows:
(5)
(6)
When Equation (5) is divided by Equation (6) at the both sides at the same inactivation Log I, a simple linear equation is obtained:
(7)

Equation (7) suggests that the ratio between the fluence differences required for any spore is proportional to the ratio of their inactivation rate constants at the linear portion, if the same level inactivation rate of Log I is to be achieved for the specific spore.

In this study, a new concept of SPSI similar to bacteria sensitivity index Tang & Sillanpää (2015) is defined as the ratio between the ki of any spores for the linear portion of the dose response curve to the kir of the reference spores as follows:
(8)
With this definition, the ratio between the fluence differences required to achieve a specific inactivation Log I, ΔH/ΔHr can be theoretically related to SPSI as follows:
(9)
This equation suggests several important points between ΔH/ΔHr and SPSI at a specific Log I: first, ΔH/ΔHr should be linearly proportion to SPSI; second, the slope of the equation should be one in theory. In reality, however, the uncertainty during the measurement of H and the determination of the corresponding inactivation rate constants ki, which depends upon the accuracy of fluence measured will have slope different from one; third, when the approximated shoulder H0 from the intercept of the linear portion at the Log I = 0 is used to replace the actual SB, the uncertainty of the coefficient, α, also increase. All of these uncertainty factors will affect the regression coefficient, α, which will deviate from one. To determine the coefficient α, regression analysis is carried out according to the following linear model:
(10)
After regression analysis, the equation can be re-written as follows:
(11)
Substituting Equation (4) into the above equation:
(12)
Finally, a predictive equation is obtained as follows:
(13)

Since the shoulder broadness, Hor, was cancelled to each other, Equation (13) indicates that the predictive model is independent of Hor.

Protozoa mathematic model

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During UV disinfection of protozoa, no shoulder effect was reported. Therefore, the disinfection kinetic model of protozoa is described by the first-order kinetics as proposed by Chick (1908) and Watson (1908) as follows:
(14)
where N0 is the initial concentration of protozoa to applying UV, N is the number of protozoa after exposure time t to UV, kt is the disinfection rate constant of a protozoa and C is the concentration of a disinfectant. For UV disinfection, the concentration is replaced by UV irradiance intensity (mW/cm2). The product of UV intensity and the exposure time is defined as fluence (H), which has the unit of mJ/cm2. Cryptosporidium parvum is used as the reference protozoa because the US EPA had specific concern and regulation of the protozoa, therefore:
(15)
(16)
Dividing Equation (3) by Equation (4) at the both sides, the following equation resulted:
(17)
To achieve the same level of Log I for both a specific protozoa and Cryptosporidium parvum, the left side of the equation becomes unity 1. Inspecting Equation (17), a new concept of PSI is defined as the ratio between the ki of any protozoa to the kr of a reference protozoa, Cryptosporidium parvum, as follows:
(18)
Therefore, the relative fluence required to achieve a given order of inactivation Log I, Hi/Hr can be theoretically related to PSI according to the theoretical Equation (17) as follows:
(19)
Similarly, this equation suggests two important points about the relationship between Hi/Hr and 1/PSI at the same order of Log I: first, the slope of the equation should be 1 and linearly proportional to 1/PSI; second, for the reference protozoa Cryptosporidium parvum, both sides become one. In reality, the uncertainty in the measurement of H and the uncertainty in the quantification of inactivation rate constants ki will result in a slope different from one. To determine the coefficient β, regression analysis is carried out according to the following linear model:
(20)

Statistic analysis

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By using the database which compiled by Malayeri et al. (2016), the inactivation UV dose at different Log I was modelled through a linear correlation analyses using SPSS of the IBM. The inactivation rate constant of each spore and protozoan were divided by the corresponding inactivation rate constants of the reference spores such as Bacillus subtilis, or the reference protozoa such as Cryptosporidium parvum, respectively. The regression analysis was conducted between Hi/Hr and SPSI using linear to determine which model fits best to the data sets. Once the model was chosen, it was used throughout the rest of the statistical analysis. The same statistical analysis procedure was applied for regression analysis between the required fluence and the 1/PSI.

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Spores sensitivity index

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The calculated values of kH and b are listed under their corresponding spores in the second and third column, respectively. To facilitate the linear regression, the coefficients of ki = 1/kH(mJ/cm2) and the shoulder broadness, H0 = b/kH (mJ/cm2), of Equation (3) are presented in the Table 1 so that SPSI can be defined for each spores.

Table 1

Transformation of kH into ki during UV disinfection of spores

Inactivation kinetics-Log I = -kH + b
H = kiLog I + H0
Reference
kH(cm2/mJ)Bki = 1/kH(mJ/cm2)H0 = b/kH(mJ/cm2)
Bacillus subtillis as reference 11.235 8.372 0.089 0.745  
Spores for model development      
Clostridium pasteurianum 1.65 1.83 0.606 1.109 Clauß (2006)  
Streptomyces griseus ATCC10137 3.25 5.67 0.308 1.745 Clauß (2006)  
Bacillus strophaeus ATCC9372 8 1.33 0.125 0.166 Sholtes et al. (2016)  
Sterne 12 15 0.083 1.25 Nicholson & Galeano (2003)  
Bacillus astrophaeus ATCC9372 16.5 5.33 0.061 0.323 Zhang et al. (2014)  
34F2(sterne) method: Schaeffer's sporulation medium 28.5 10.67 0.035 0.374 Rose & O'Connell (2009)  
Thermoactionmyces 30 26.67 0.033 0.889 Clauß (2006)  
Bacillus cereus ATCC11778 44 7 0.023 0.159 Clauß (2006)  
Bacillus pumilus ATCC27142 68 0.67 0.015 0.010 Boczek et al. (2016)  
Aspergillus brasiliensis ATCC16404 85.5 42.67 0.011 0.499 Taylor-Edmonds et al. (2015)  
Inactivation kinetics-Log I = -kH + b
H = kiLog I + H0
Reference
kH(cm2/mJ)Bki = 1/kH(mJ/cm2)H0 = b/kH(mJ/cm2)
Bacillus subtillis as reference 11.235 8.372 0.089 0.745  
Spores for model development      
Clostridium pasteurianum 1.65 1.83 0.606 1.109 Clauß (2006)  
Streptomyces griseus ATCC10137 3.25 5.67 0.308 1.745 Clauß (2006)  
Bacillus strophaeus ATCC9372 8 1.33 0.125 0.166 Sholtes et al. (2016)  
Sterne 12 15 0.083 1.25 Nicholson & Galeano (2003)  
Bacillus astrophaeus ATCC9372 16.5 5.33 0.061 0.323 Zhang et al. (2014)  
34F2(sterne) method: Schaeffer's sporulation medium 28.5 10.67 0.035 0.374 Rose & O'Connell (2009)  
Thermoactionmyces 30 26.67 0.033 0.889 Clauß (2006)  
Bacillus cereus ATCC11778 44 7 0.023 0.159 Clauß (2006)  
Bacillus pumilus ATCC27142 68 0.67 0.015 0.010 Boczek et al. (2016)  
Aspergillus brasiliensis ATCC16404 85.5 42.67 0.011 0.499 Taylor-Edmonds et al. (2015)  
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Depending on the coefficient of reference data and Table 1, SPSI can be defined in Table 2.

Table 2

Definition of SPSI

SPSI = ki/kir
Reference spores: Bacillus subtilisSPSIReference
Clostridium pasteurianum ATCC6013 6.809 Clauß (2006)  
Streptomyces griseus ATCC10137 3.457 Clauß (2006)  
Bacillus astrophaeus ATCC9372 1.404 Sholtes et al. (2016)  
Sterne 0.936 Nicholson & Galeano (2003)  
Bacillus astrophaeus ATCC9372 0.680 Zhang et al. (2014)  
34F2 (sterne) method: Schaeffer's sporulation medium 0.394 Rose & O'Connell (2009)  
Thermoactinomyces vulgaris ATCC43649 0.374 Clauß (2006)  
Bacillus cereus ATCC11778 0.255 Clauß (2006)  
Bacillus pumilus ATCC27142 0.165 Boczek et al. (2016)  
Aspergillus brasiliensis ATCC16404 0.131 Taylor-Edmonds et al. (2015)  
SPSI = ki/kir
Reference spores: Bacillus subtilisSPSIReference
Clostridium pasteurianum ATCC6013 6.809 Clauß (2006)  
Streptomyces griseus ATCC10137 3.457 Clauß (2006)  
Bacillus astrophaeus ATCC9372 1.404 Sholtes et al. (2016)  
Sterne 0.936 Nicholson & Galeano (2003)  
Bacillus astrophaeus ATCC9372 0.680 Zhang et al. (2014)  
34F2 (sterne) method: Schaeffer's sporulation medium 0.394 Rose & O'Connell (2009)  
Thermoactinomyces vulgaris ATCC43649 0.374 Clauß (2006)  
Bacillus cereus ATCC11778 0.255 Clauß (2006)  
Bacillus pumilus ATCC27142 0.165 Boczek et al. (2016)  
Aspergillus brasiliensis ATCC16404 0.131 Taylor-Edmonds et al. (2015)  
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Histogram with probability density function (PDF) and cumulative distribution function (CDF) of SPSI using the fluence required for Bacillus subtilis as the reference in Figure 1 shows that up to five spores have the same inactivation rate constants as the linear portion of the survival curve as that of the reference spores Bacillus subtilis.
Figure 1
Histogram with probability density function (PDF) and cumulative distribution function (CDF) of SPSI using the fluence required for Bacillus subtilis.
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Histogram with probability density function (PDF) and cumulative distribution function (CDF) of SPSI using the fluence required for Bacillus subtilis.

Figure 1
Histogram with probability density function (PDF) and cumulative distribution function (CDF) of SPSI using the fluence required for Bacillus subtilis.
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Histogram with probability density function (PDF) and cumulative distribution function (CDF) of SPSI using the fluence required for Bacillus subtilis.

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Transformation of H into ΔH/ΔHr

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To assess which set of SPSI is the best, following the Equation (3), Table 3 is presented. Through Table 4, H can be transformed to ΔH/ΔHr as shown in Table 4.

Table 3

SPSI in reference to Bacillus subtilis

Fluence differenceΔH = H-H0
Log I0123Reference
34F2(sterne) method: Schaeffer's sporulation medium 0.374 22.625 35.625 79.626 Rose & O'Connell (2009)  
Aspergillus brasiliensis ATCC16404 0.499 121.501 225.501 292.501 Taylor-Edmonds et al. (2015)  
Bacillus astrophaeus ATCC9372 0.323 21.676 37.677 54.677 Zhang et al. (2014)  
Bacillus cereus ATCC11778 0.159 51.841 92.841 139.841 Clauß (2006)  
Bacillus pumilus ATCC27142 0.010 67.834 137.990 203.990 Boczek et al. (2016)  
Bacillus strophaeus ATCC9372 0.166 9.833 15.833 25.83375 Sholtes et al. (2016)  
Bacillus subtilis 0.745 17.1 28.09 38.753  
Clostridium pasteurianum 1.109 2.291 4.191 5.591 Clauß (2006)  
Sterne 1.25 26.75 35.75 50.75 Nicholson & Galeano (2003)  
Streptomyces griseus ATCC10137 0 6.755 11.255 13.255 Clauß (2006)  
Thermoactionmyces 1.745 54.111 89.111 114.111 Clauß (2006)  
Fluence differenceΔH = H-H0
Log I0123Reference
34F2(sterne) method: Schaeffer's sporulation medium 0.374 22.625 35.625 79.626 Rose & O'Connell (2009)  
Aspergillus brasiliensis ATCC16404 0.499 121.501 225.501 292.501 Taylor-Edmonds et al. (2015)  
Bacillus astrophaeus ATCC9372 0.323 21.676 37.677 54.677 Zhang et al. (2014)  
Bacillus cereus ATCC11778 0.159 51.841 92.841 139.841 Clauß (2006)  
Bacillus pumilus ATCC27142 0.010 67.834 137.990 203.990 Boczek et al. (2016)  
Bacillus strophaeus ATCC9372 0.166 9.833 15.833 25.83375 Sholtes et al. (2016)  
Bacillus subtilis 0.745 17.1 28.09 38.753  
Clostridium pasteurianum 1.109 2.291 4.191 5.591 Clauß (2006)  
Sterne 1.25 26.75 35.75 50.75 Nicholson & Galeano (2003)  
Streptomyces griseus ATCC10137 0 6.755 11.255 13.255 Clauß (2006)  
Thermoactionmyces 1.745 54.111 89.111 114.111 Clauß (2006)  
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Table 4

Δh/ΔHr at specific inactivation log I of Bacillus subtilis as reference

Fluence differenceΔH = H-H0
Log I0123Reference
ΔHr, Bacillus subtilis as reference      
Bacillus subtilis 0.745 16.354 37.703 52.009 Zhang et al. (2014)  
Thermoactionmyces 1.745 0.302 0.423 0.455 Clauß (2006)  
Aspergillus brasiliensis ATCC16404 0.499 0.135 0.167 0.177 Taylor-Edmonds et al. (2015)  
34F2(sterne) method: Schaeffer's sporulation medium 0.374 0.722 1.058 0.653 Rose & O'Connell (2009)  
Bacillus astrophaeus ATCC9372 0.323 0.754 1 0.951 Zhang et al. (2014)  
Bacillus strophaeus ATCC9372 0.166 1.663 2.381 2.013 Sholtes et al. (2016)  
Bacillus cereus ATCC11778 0.159 0.315 0.406 0.371 Clauß (2006)  
Clostridium pasteurianum 1.109 7.139 8.996 9.302 Clauß (2006)  
Sterne 1.25 0.611 1.954 1.024 Nicholson & Galeano (2003)  
Bacillus pumilus ATCC27142 0.010 0.241 0.273 0.254 Boczek et al. (2016)  
Streptomyces griseus ATCC10137 0 2.421 3.349 3.923 Clauß (2006)  
Fluence differenceΔH = H-H0
Log I0123Reference
ΔHr, Bacillus subtilis as reference      
Bacillus subtilis 0.745 16.354 37.703 52.009 Zhang et al. (2014)  
Thermoactionmyces 1.745 0.302 0.423 0.455 Clauß (2006)  
Aspergillus brasiliensis ATCC16404 0.499 0.135 0.167 0.177 Taylor-Edmonds et al. (2015)  
34F2(sterne) method: Schaeffer's sporulation medium 0.374 0.722 1.058 0.653 Rose & O'Connell (2009)  
Bacillus astrophaeus ATCC9372 0.323 0.754 1 0.951 Zhang et al. (2014)  
Bacillus strophaeus ATCC9372 0.166 1.663 2.381 2.013 Sholtes et al. (2016)  
Bacillus cereus ATCC11778 0.159 0.315 0.406 0.371 Clauß (2006)  
Clostridium pasteurianum 1.109 7.139 8.996 9.302 Clauß (2006)  
Sterne 1.25 0.611 1.954 1.024 Nicholson & Galeano (2003)  
Bacillus pumilus ATCC27142 0.010 0.241 0.273 0.254 Boczek et al. (2016)  
Streptomyces griseus ATCC10137 0 2.421 3.349 3.923 Clauß (2006)  
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Correlation analysis between ΔH/ΔHr and SPSI

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According to Equation (10), ΔH/ΔHr should linearly correlate with SPSI. Figures 2,3–4 are plots a typical predicted output ΔH/ΔHr against the observed ΔH/ΔHr at 1 Log I, 2 Log I and 3 Log I, respectively. It shows that the correlation is very robust with R = 0.9642, R = 0.9713 and R = 0.9917 between ΔH/ΔHr which suggests that the theoretical equation is valid. On the other hand, it means the H0 and Hr are not the major errors to effect the UV disinfection efficiency. Such robust linear relationship suggests that Equation (10) should have robust predictive power of the fluence requirement for specific inactivation rate of Log I as long as SPSI is defined. According to the results, the equation can be obtained to predict the required fluence of any spores as follows:
(21)
Figure 2
Hpredicted vs. Hobserved at 1 Log I.
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Hpredicted vs. Hobserved at 1 Log I.

Figure 2
Hpredicted vs. Hobserved at 1 Log I.
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Hpredicted vs. Hobserved at 1 Log I.

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Figure 3
Hpredicted vs. Hobserved at 2 Log I.
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Hpredicted vs. Hobserved at 2 Log I.

Figure 3
Hpredicted vs. Hobserved at 2 Log I.
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Hpredicted vs. Hobserved at 2 Log I.

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Figure 4
Hpredicted vs. Hobserved at 3 Log I.
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Hpredicted vs. Hobserved at 3 Log I.

Figure 4
Hpredicted vs. Hobserved at 3 Log I.
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Hpredicted vs. Hobserved at 3 Log I.

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Protozoa sensitivity index

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The protozoa sensitivity index can be defined by Equation (3). In Table 5 are listed the ki and b, and after linear regression, ki and H0 can be calculated.

Table 5

Transformation of kH into ki during UV disinfection of protozoa

-Log I = -kH + b
H = kiLog I + H0
Inactivation kineticskH(cm2/mJ)bki = 1/kH(mJ/cm2)H0 = b/kH(mJ/cm2)Reference
Cryptosporidium parvum as reference 0.475 0.869 2.105 1.829  
Protozoa for model development      
Acanthamoeba castellanii CCAP15342 (life stage: cysts) 23 24.33 0.043 1.058 Cervero-Aragó et al. (2014)  
Acanthamoeba spp. 155 (life stage: trophozoites) 19 3.67 0.053 0.193 Cervero-Aragó et al. (2014)  
Acanthamoeba spp. 155 (life stage: cysts) 32.5 1.67 0.031 0.051 Cervero-Aragó et al. (2014)  
Giardia lamblia 1.25 0 0.8 0 Cervero-Aragó et al. (2014)  
Giardia lamblia 1 0.53 1 0.53 Campbell & Wallis (2002)  
Naegleria fowleri 5 3 0.2 0.6 Mofidi et al. (2002)  
Toxoplasma gondii oocysts 4.9 2.6 0.204 0.530 Mofidi et al. (2002)  
Toxoplasma gondii 3.3 0.13 0.303 0.039 Amoah et al. (2005)  
Vermamoeba vermiformis CCAP 15434 7.5 3.67 0.133 0.489 Ware et al. (2010)  
Vermamoeba vermiformis 195 (life stage: trophozoites) 7 3 0.143 0.429 Cervero-Aragó et al. (2014)  
Vermamoeba vermiformis 195 (life stage: cysts) 22 12 0.045 0.545 Cervero-Aragó et al. (2014)  
-Log I = -kH + b
H = kiLog I + H0
Inactivation kineticskH(cm2/mJ)bki = 1/kH(mJ/cm2)H0 = b/kH(mJ/cm2)Reference
Cryptosporidium parvum as reference 0.475 0.869 2.105 1.829  
Protozoa for model development      
Acanthamoeba castellanii CCAP15342 (life stage: cysts) 23 24.33 0.043 1.058 Cervero-Aragó et al. (2014)  
Acanthamoeba spp. 155 (life stage: trophozoites) 19 3.67 0.053 0.193 Cervero-Aragó et al. (2014)  
Acanthamoeba spp. 155 (life stage: cysts) 32.5 1.67 0.031 0.051 Cervero-Aragó et al. (2014)  
Giardia lamblia 1.25 0 0.8 0 Cervero-Aragó et al. (2014)  
Giardia lamblia 1 0.53 1 0.53 Campbell & Wallis (2002)  
Naegleria fowleri 5 3 0.2 0.6 Mofidi et al. (2002)  
Toxoplasma gondii oocysts 4.9 2.6 0.204 0.530 Mofidi et al. (2002)  
Toxoplasma gondii 3.3 0.13 0.303 0.039 Amoah et al. (2005)  
Vermamoeba vermiformis CCAP 15434 7.5 3.67 0.133 0.489 Ware et al. (2010)  
Vermamoeba vermiformis 195 (life stage: trophozoites) 7 3 0.143 0.429 Cervero-Aragó et al. (2014)  
Vermamoeba vermiformis 195 (life stage: cysts) 22 12 0.045 0.545 Cervero-Aragó et al. (2014)  
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Using reference data and Table 5, PSI can be defined in Table 6.

Table 6

PSI of reference dose required data

PSI = ki/kir
Reference protozoa: cryptosporidium parvumPSI1/PSIReference
Giardia lamblia 0.475 2.105 Mofidi et al. (2002)  
Toxoplasma gondii 0.144 6.947 Ware et al. (2010)  
Toxoplasma gondii oocysts 0.097 10.316 Amoah et al. (2005)  
Naegleria fowleri 0.095 10.526 Mofidi et al. (2002)  
Vermamoeba vermiformis 195 (life stage: trophozoites) 0.068 14.737 Cervero-Aragó et al. (2014)  
Vermamoeba vermiformis CCAP 15434 0.063 15.789 Cervero-Aragó et al. (2014)  
Vermamoeba vermiformis 195 (life stage: cysts) 0.055 46.316 Cervero-Aragó et al. (2014)  
Giardia lamblia 0.38 2.632 Campbell & Wallis (2002)  
Acanthamoeba spp. 155 (life stage: trophozoites) 0.025 40.000 Cervero-Aragó et al. (2014)  
Acanthamoeba castellanii CCAP15342 (life stage: trophozoites) 0.023 42.105 Cervero-Aragó et al. (2014)  
Acanthamoeba castellanii CCAP15342 (life stage: cysts) 0.021 48.421 Cervero-Aragó et al. (2014)  
Acanthamoeba spp. 155 (life stage: cysts) 0.015 68.421 Cervero-Aragó et al. (2014)  
PSI = ki/kir
Reference protozoa: cryptosporidium parvumPSI1/PSIReference
Giardia lamblia 0.475 2.105 Mofidi et al. (2002)  
Toxoplasma gondii 0.144 6.947 Ware et al. (2010)  
Toxoplasma gondii oocysts 0.097 10.316 Amoah et al. (2005)  
Naegleria fowleri 0.095 10.526 Mofidi et al. (2002)  
Vermamoeba vermiformis 195 (life stage: trophozoites) 0.068 14.737 Cervero-Aragó et al. (2014)  
Vermamoeba vermiformis CCAP 15434 0.063 15.789 Cervero-Aragó et al. (2014)  
Vermamoeba vermiformis 195 (life stage: cysts) 0.055 46.316 Cervero-Aragó et al. (2014)  
Giardia lamblia 0.38 2.632 Campbell & Wallis (2002)  
Acanthamoeba spp. 155 (life stage: trophozoites) 0.025 40.000 Cervero-Aragó et al. (2014)  
Acanthamoeba castellanii CCAP15342 (life stage: trophozoites) 0.023 42.105 Cervero-Aragó et al. (2014)  
Acanthamoeba castellanii CCAP15342 (life stage: cysts) 0.021 48.421 Cervero-Aragó et al. (2014)  
Acanthamoeba spp. 155 (life stage: cysts) 0.015 68.421 Cervero-Aragó et al. (2014)  
View Large

Histogram with probability density function (PDF) and cumulative distribution function (CDF) of PSI using the fluence required for Cryptosporidium parvum as the reference in Figure 5 shows two protozoas have the same inactivation rate constants of the linear portion of the survival curve as that of the reference protozoa Cryptosporidium parvum.
Figure 5
Histogram with probability density function (PDF) and cumulative distribution function (CDF) of PSI using the fluence required for Cryptosporidium parvum.
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Histogram with probability density function (PDF) and cumulative distribution function (CDF) of PSI using the fluence required for Cryptosporidium parvum.

Figure 5
Histogram with probability density function (PDF) and cumulative distribution function (CDF) of PSI using the fluence required for Cryptosporidium parvum.
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Histogram with probability density function (PDF) and cumulative distribution function (CDF) of PSI using the fluence required for Cryptosporidium parvum.

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Transformation of H into H/Hr

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To assess which set of PSI is the best, following the Equation (3), Table 7 is presented. Through Table 7, H can be transformed to H/Hr as shown in Table 8.

Table 7

Fluence required at different Log I of protozoa

Fluence difference
Log I123Reference
Hr, Cryptosporidium parvum as reference     
Cryptosporidium parvum     
Acanthamoeba castellanii CCAP15342 (life stage: trophozoites) 31.4 51.4 71.4 Cervero-Aragó et al. (2014)  
Acanthamoeba castellanii CCAP15342 (life stage: cysts) 43.942 73.942 89.942 Cervero-Aragó et al. (2014)  
Acanthamoeba spp. 155 (life stage: trophozoites) 27.807 30.807 65.807 Cervero-Aragó et al. (2014)  
Acanthamoeba spp. 155 (life stage: cysts) 33.948 66.949 98.948 Cervero-Aragó et al. (2014)  
Giardia lamblia 8 10 20 Cervero-Aragó et al. (2014)  
Giardia lamblia 0.97 1.47 3.47 Mofidi et al. (2002)  
Naegleria fowleri 7.4 12.4 17.4 Mofidi et al. (2002)  
Toxoplasma gondii oocysts 6.67 12,469 16.469 Amoah et al. (2005)  
Toxoplasma gondii 3.361 6.761 9.961 Ware et al. (2010)  
Vermamoeba vermiformis CCAP 15434 10.511 18.511 25.510 Cervero-Aragó et al. (2014)  
Vermamoeba vermiformis 195 (life stage: trophozoites) 9.571 16.571 23.571 Cervero-Aragó et al. (2014)  
Vermamoeba vermiformis 195 (life stage: cysts) 31.455 59.454 75.455 Cervero-Aragó et al. (2014)  
Fluence difference
Log I123Reference
Hr, Cryptosporidium parvum as reference     
Cryptosporidium parvum     
Acanthamoeba castellanii CCAP15342 (life stage: trophozoites) 31.4 51.4 71.4 Cervero-Aragó et al. (2014)  
Acanthamoeba castellanii CCAP15342 (life stage: cysts) 43.942 73.942 89.942 Cervero-Aragó et al. (2014)  
Acanthamoeba spp. 155 (life stage: trophozoites) 27.807 30.807 65.807 Cervero-Aragó et al. (2014)  
Acanthamoeba spp. 155 (life stage: cysts) 33.948 66.949 98.948 Cervero-Aragó et al. (2014)  
Giardia lamblia 8 10 20 Cervero-Aragó et al. (2014)  
Giardia lamblia 0.97 1.47 3.47 Mofidi et al. (2002)  
Naegleria fowleri 7.4 12.4 17.4 Mofidi et al. (2002)  
Toxoplasma gondii oocysts 6.67 12,469 16.469 Amoah et al. (2005)  
Toxoplasma gondii 3.361 6.761 9.961 Ware et al. (2010)  
Vermamoeba vermiformis CCAP 15434 10.511 18.511 25.510 Cervero-Aragó et al. (2014)  
Vermamoeba vermiformis 195 (life stage: trophozoites) 9.571 16.571 23.571 Cervero-Aragó et al. (2014)  
Vermamoeba vermiformis 195 (life stage: cysts) 31.455 59.454 75.455 Cervero-Aragó et al. (2014)  
View Large
Table 8

H/Hr data specific inactivation log I of Cryptosporidium parvum as reference

Fluence
Log I123Reference
ΔHr, Cryptosporidium parvum as reference     
Acanthamoeba castellanii CCAP15342 (life stage: trophozoites) 54.286 299.570 192.153 Cervero-Aragó et al. (2014)  
Acanthamoeba castellanii CCAP15342 (life stage: cysts) 75.970 430.951 242.054 Cervero-Aragó et al. (2014)  
Acanthamoeba spp. 155 (life stage: trophozoites) 48.074 179.549 177.100 Cervero-Aragó et al. (2014)  
Acanthamoeba spp. 155 (life stage: cysts) 58.692 390.191 266.292 Cervero-Aragó et al. (2014)  
Giardia lamblia 13.831 58.282 53.824 Cervero-Aragó et al. (2014)  
Giardia lamblia 1.677 8.567 9.338 Mofidi et al. (2002)  
Naegleria fowleri 12.793 72.270 46.827 Mofidi et al. (2002)  
Toxoplasma gondii oocysts 11.530 72.674 44.322 Amoah et al. (2005)  
Toxoplasma gondii 5.810 39.402 26.806 Ware et al. (2010)  
Vermamoeba vermiformis CCAP 15434 18.171 107.884 68.654 Cervero-Aragó et al. (2014)  
Vermamoeba vermiformis 195 (life stage: trophozoites) 16.547 96.582 63.436 Cervero-Aragó et al. (2014)  
Vermamoeba vermiformis 195 (life stage: cysts) 54.380 346.514 203.065 Cervero-Aragó et al. (2014)  
Fluence
Log I123Reference
ΔHr, Cryptosporidium parvum as reference     
Acanthamoeba castellanii CCAP15342 (life stage: trophozoites) 54.286 299.570 192.153 Cervero-Aragó et al. (2014)  
Acanthamoeba castellanii CCAP15342 (life stage: cysts) 75.970 430.951 242.054 Cervero-Aragó et al. (2014)  
Acanthamoeba spp. 155 (life stage: trophozoites) 48.074 179.549 177.100 Cervero-Aragó et al. (2014)  
Acanthamoeba spp. 155 (life stage: cysts) 58.692 390.191 266.292 Cervero-Aragó et al. (2014)  
Giardia lamblia 13.831 58.282 53.824 Cervero-Aragó et al. (2014)  
Giardia lamblia 1.677 8.567 9.338 Mofidi et al. (2002)  
Naegleria fowleri 12.793 72.270 46.827 Mofidi et al. (2002)  
Toxoplasma gondii oocysts 11.530 72.674 44.322 Amoah et al. (2005)  
Toxoplasma gondii 5.810 39.402 26.806 Ware et al. (2010)  
Vermamoeba vermiformis CCAP 15434 18.171 107.884 68.654 Cervero-Aragó et al. (2014)  
Vermamoeba vermiformis 195 (life stage: trophozoites) 16.547 96.582 63.436 Cervero-Aragó et al. (2014)  
Vermamoeba vermiformis 195 (life stage: cysts) 54.380 346.514 203.065 Cervero-Aragó et al. (2014)  
View Large

Correlation analysis between H/Hr and 1/PSI

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According to Equation (10), H/Hr should linearly correlate with 1/PSI regardless which set of reference fluence is used; Figures 6,7–8 are plots of a typical predicted output H/Hr against the observed H/Hr at 1 Log I, 2 Log I and 3 Log I, respectively. It shows that the correlation is not more robust than SPSI. R = 0.8702, R = 0.8925 and R = 0.9646 between H/Hr which suggests that the theoretical equation is valid. According to the results as before mentioned, the equations can be obtained to predict the required fluence of any protozoa by using three different sets of fluence requirements of Cryptosporidium parvum as follows:
(22)
Figure 6
Linear correlation between H/Hr and 1/PSI at 1 Log I.
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Linear correlation between H/Hr and 1/PSI at 1 Log I.

Figure 6
Linear correlation between H/Hr and 1/PSI at 1 Log I.
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Linear correlation between H/Hr and 1/PSI at 1 Log I.

Close modal
Figure 7
Linear correlation between H/Hr and 1/PSI at 2 Log I.
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Linear correlation between H/Hr and 1/PSI at 2 Log I.

Figure 7
Linear correlation between H/Hr and 1/PSI at 2 Log I.
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Linear correlation between H/Hr and 1/PSI at 2 Log I.

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Figure 8
Linear correlation between H/Hr and 1/PSI at 3 Log I.
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Linear correlation between H/Hr and 1/PSI at 3 Log I.

Figure 8
Linear correlation between H/Hr and 1/PSI at 3 Log I.
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Linear correlation between H/Hr and 1/PSI at 3 Log I.

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Comparison with different bateria and virus

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SPSI compare with bacteria sensitivity index (BSI)

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For the previous study, the BSI used E. coli as the reference bacteria, the fluence recommended by the US EPA is used in the correlation analysis to obtain the following equation:

(23)

Compared with SPSI, the UV fluence is lower than BSI. As a result, it would significantly reduce the trial and error experiment in deciding which fluence should be used to achieve a specific inactivation rate Log I for a specific spores providing the corresponding SPSI is known.

PSI compare with virus sentivity index (VSI)

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Without shoulder broadness, VSI was used to predict the required UV fluence for virus to be inactivated at Log I. Log I is log inactivation and VSI is the VSI in reference to MS2-phage as follows:
(24)

Obviously, to disinfect protozoa, more UV fluence is needed than bacteria spores. The major advantage of the method developed in this study is rooted in its dimensionless parameters such as Hi/Hr versus PSI.

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Scientific analysis unveils a linear relationship between fluence required for inactivation of any spores and that required by reference spores such as Bacillus subtillis is proportional to the ratio of their corresponding inactivation rate constant ki/kir. The SPSI has been successfully used to predict the fluence. The developed model tends to overpredict the fluence required at low Log I while it would underpredict the fluence required as Log I level increased. Up to 3 Log I, the model underpredicts all the fluence with the maximal errors less than 15%. The PSI was defined as the ratio between the inactivation rate constants of a protozoa in reference to that of Cryptosporidium parvum. PSI can be used to rank the relative UV disinfection sensitivity. For example, most protozoa have a PSI greater than that of Cryptosporidium parvum, and if there are no protozoa, which has very low PSI, Cryptosporidium parvum should be used as an adequate indicator in the validation of a UV disinfection system. Using statistical equations developed in this paper, PSI can be used to accurately predict the fluence required, Hi, for any given protozoa at a specific Log I by using Equation (22).

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Zhao Wang: statistical analysis and writing. Walter Z. Tang: conceptualization, methodology, statistical analysis, investigation, writing, review and editing, and supervision. Mika Sillanpää: review and editing, Jinze Li: review and editing.

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All relevant data are included in the paper or its Supplementary Information.

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The authors declare there is no conflict.

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© 2022 The Authors
This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY 4.0), which permits copying, adaptation and redistribution, provided the original work is properly cited (http://creativecommons.org/licenses/by/4.0/).