An extended logistic model of photodynamic inactivation for various levels of irradiance using the example of Streptococcus agalactiae

Irradiance is an important factor influencing the acceleration of microorganism mortality in photodynamic inactivation (PDI) processes. Experimental observations of PDI processes indicate that the greater the irradiation power is, the faster the decrease in the population size of microorganisms. However, commonly used mathematical models of PDI processes usually refer only to specific values of irradiance without taking into account the influence of change in irradiance on the dynamic properties of inactivation. The main goal of this paper is to analyze the effect of irradiance on the PDI process and attempt to mathematically model the obtained dependencies. The analysis was carried out using the example of photodynamic inactivation of the bacterium Streptococcus agalactiae with the adopted Logistic PDI model optimized for several selected levels of irradiance. To take into account the impact of changes in irradiation power on the PDI model, the selected parameters were made appropriately dependent on this factor. The paper presents several variants of parameter modification with an evaluation of the model fitting quality criterion. The discussion on appropriate selection of parameters to be modified was carried out as a comparative analysis of several case studies. The extended logistic PDI model obtained in the conducted research effectively describes the dynamics of microorganism mortality in the whole tested irradiation power range.