Mariusz Górajski

Optimal double control problem for a PDE model of goodwill dynamics

We propose a new optimal control model of product goodwill in a segmented market where the state variable behaviour is described by a partial differential equation of the Lotka–Sharp–McKendrick type. In order to maximize the sum of discounted profits over a finite time horizon, we control the marketing communication activities which influence the state equation and the boundary condition. Moreover, we introduce the mathematical representation of heterogeneous electronic word of mouth. Based on the semigroup approach, we prove the existence and uniqueness of optimal controls. Using a maximum principle, we describe a numerical algorithm to find the optimal solution. Finally, we examine several examples on the optimal goodwill model and discover two types of marketing strategies.

Knowledge and Attitudes of Dentists with Respect to the Risks of Blood-Borne Pathogens—A Cross-Sectional Study in Poland

Background: To analyze dentists’ knowledge of blood-borne infections, their attitudes towards infected patients, and to determine the frequency of the contact with infectious material; Methods: We surveyed 192 dentists using an anonymous questionnaire. Results: Only a quarter of dentists responded correctly to all questions. 96% of the examined dentists confirmed that they were more cautious during treatment of patients with HBV, HCV and HIV. 25% of all respondents refuse to help infected patients due to concerns about their own health. The dentists occasionally removed protective clothing to make it “easier” to perform specific procedures. The dentists experienced contact with infectious material most frequently by splashes onto the conjunctiva or as a result of superficial injuries. The risk of injury by a medical tool increased with the years of employment. Re-capping needles was associated with an increased risk of injury; Conclusions: Despite the widespread tolerance of people infected with blood-borne viruses and the well-proven low infection risk to medical personnel, dentists continue to be prejudiced and concerned about their own health and may refuse to treat infected patients. It may be assumed that the proportion of refusing treatment is even greater. This attitude should imply the implementation of training in the field of pathogen transmission and the real risk of infection.

On the Equivalence of Solutions for a Class of Stochastic Evolution Equations in a Banach Space

We study a class of stochastic evolution equations in a Banach space E driven by cylindrical Wiener process. Three different analytical concepts of solutions: generalised strong, weak and mild are defined and the conditions under which they are equivalent are given. We apply this result to prove existence, uniqueness and continuity of weak solutions to stochastic delay evolution equations. We also consider two examples of these equations in non-reflexive Banach spaces: a stochastic transport equation with delay and a stochastic delay McKendrick equation.

The effects of technological shocks in an optimal goodwill model with a random product life cycle

Abstract We consider the optimal goodwill control problem in a segmented market where the length of the product life cycle is affected by unpredictable technological turbulence. In order to maximize profit over a random time horizon, a company controls the marketing efforts directed to each market segment. Assuming an exponential distribution for the product life cycle, we modify the optimal goodwill model into the infinite time horizon control problem. Based on the semigroup approach, we prove the existence and uniqueness of the optimal solution. We formulate optimality conditions for the problem and we prove the existence of a stationary long-run equilibrium. Next, we construct a numerical algorithm to find the optimal solution. Finally, we examine several scenarios of optimal marketing strategies.

Awareness of the Risk of Exposure to Infectious Material and the Behaviors of Polish Paramedics with Respect to the Hazards from Blood-Borne Pathogens—A Nationwide Study

(1) Background: To determine paramedics’ frequency of contact with blood and other body fluids, as well as the analysis of knowledge of paramedics about blood-borne infections, their attitudes to patients infected with blood-borne viruses, and the post-exposure procedures implemented by paramedics; (2) Methods: An anonymous questionnaire among 190 paramedics working in various health care facilities in Poland (adjusted response rate, 76.3%); (3) Results: 78% of paramedics had contact with potentially infectious material at least several times a week. Paramedics’ knowledge on transferring infection was insufficient. Paramedics with longer employment time and better professional experience suffered fewer injuries with used needles/medical tools (p = 0.079). Most frequently reported factors that prevented the use of personal protective equipment were emergency situations (19.5%), skin irritations and contact allergies (19%) and, in the case of protective gloves, reduced manual dexterity (16%). In total, 82% of paramedics were concerned about the risk of being infected with HIV, HBV or HCV as a result of performing their job. In total, 97% of paramedics behaved more carefully while caring for infected patients. In total, 90% of the paramedics never refrained from performing the specific procedures necessary to help the patient whom they knew to be infected; (4) Conclusions: Despite the paramedics’ insufficient theoretical knowledge about the risk of blood-borne infections, the emphasis in the training of future paramedics should be on classes perfecting practical skills, because growing experience significantly reduces the risk of injury.

Occupational Safety and Hygiene of Dentists from Urban and Rural Areas in Terms of Sharp Injuries: Wound Structure, Causes of Injuries and Barriers to Reporting—Cross-Sectional Study, Poland

(1) Background: Frequent contact of the dentist with potentially infectious material (PIM) is undeniable. The aim of the study was to determine the frequency and type of injuries, as well as to identify barriers to reporting and barriers to the implementation of post-exposure prophylaxis (PEP) among dentists from urban and rural areas. (2) Methods: We surveyed 192 dentists using an anonymous questionnaire. (3) Results: During the 12 months preceding the survey, 63% of dentists from the village and 58.8% of dentists from the city suffered at least one superficial cut, and deep cuts 15.1% and 17.6% respectively. Contact with PIM through spitting on the conjunctiva was 58.9% and 52.1% (village vs. city). Needle stick injuries were 50.4% and fingers were affected in 48.8% cases. The causes of injuries were: inattention 54.7%, rush 27%, unpredictable behavior of the patient 19%, recapping 18.2%. Work in the countryside was associated with a 1.95-times greater chance of not reporting injuries. The distance from a hospital with antiretroviral treatment may be a barrier to the implementation of PEP. (4) Conclusion: The circumstances of the injuries and the reasons for not applying for antiretroviral treatment point to the areas of necessary dentist education in this topic.

Measuring expected time to default under stress conditions for corporate loans

We present a new measure of extreme credit risk in the time domain, namely the conditional expected time to default (CETD). This measure has a clear interpretation and can be applied in a straightforward way to the analyses of loan performance in time. In contrast to the probability of default, CETD provides direct information on the timing of a potential loan default under some stress scenarios. We apply a novel method to compute CETD using Markov probability transition matrices, a popular approach in survival analysis literature. We employ the new measure to the analysis of changing credit risk in a large portfolio of corporate loans.

Did legal regulations change the reporting frequency of sharp injuries of medical personnel? Study from 36 hospitals in Łódź Province, Poland

OBJECTIVES The aim of the study has been to analyze the epidemiological data on sharp injuries among health care workers before and after the implementation of regulations related to the conduct of the register of sharp injuries. MATERIAL AND METHODS We hypothesized that the introduction of legislation would change the existing low reportability of sharp injuries and reporting incidents would increase. In Poland the binding regulations, dating back to 2013, require the employer to keep a record of sharp injuries. Therefore, we compared the data from before and after the entry regulations. Data was collected from the records of occupational exposure/accidents at work in hospitals in the Łódź Province during 2010-2014. The feedback came from 36 hospitals (return index = 51.5%), representing a total annual average of 13 211 medical workers. RESULTS The incidence of injuries did not change significantly over the period 2010-2014, and the number of reported injuries in 2014 (the year when the Regulation had already been effective) was even lower than in the previous years. The average annual injury index was 12.31 injuries per 1000 employees (95% confidence interval: 11.48-13.16/1000). The incidence of injuries among nurses was significantly higher than in other groups of medical professionals (p < 0.05). These injuries most often occur while using needles (p < 0.05). CONCLUSIONS The obligation to record occupational exposures set forth in current regulations is not likely to improve the reliability of reporting the incidents actually taking place. Further research should focus on identifying barriers to reporting cases of exposure to potentially infectious material. Action should be taken to raise awareness of medical personnel about the possible effects of exposure to infectious material, in particular, the benefits of the implementation of early post-exposure procedures. Perhaps it will increase the reporting frequency of sharp injuries of medical personnel. Int J Occup Med Environ Health 2018;31(1):37-46.