A Game Theoretic Analysis of Competition Between Vaccine and Drug Companies during Disease Contraction and Recovery.

BACKGROUND: Infectious diseases such as COVID-19 and HIV/AIDS are behaviorally challenging for persons, vaccine and drug companies, and donors. METHODS: In 3 linked games in which a disease may or may not be contracted, N persons choose risky or safe behavior (game 1). Two vaccine companies (game 2) and 2 drug companies (game 3) choose whether to develop vaccines and drugs. Each person chooses whether to buy 1 vaccine (if no disease contraction) or 1 drug (if disease contraction). A donor subsidizes vaccine and drug developments and purchases. Nature probabilistically chooses disease contraction, recovery versus death with and without each drug, and whether vaccines and drugs are developed successfully. COVID-19 data are used for parameter estimation. RESULTS: Each person chooses risky behavior if its utility outweighs safe behavior, accounting for nature's probability of disease contraction which depends on how many are vaccinated. Each person buys a vaccine or drug if the companies produce them and if their utilities (accounting for side effects and virus mutation) outweigh the costs, which may be subsidized by a sponsor. DISCUSSION: Drug purchases depend on nature's recovery probability exceeding the probability in the absence of a drug. Each company develops and produces a vaccine or drug if nature's probability of successful development is high, if sufficiently many persons buy the vaccine or drug at a sales price that sufficiently exceeds the production price, and if the donor sponsors. CONCLUSION: Accounting for all players' interlinked decisions allowing 14 outcomes, which is challenging without a game theoretic analysis, the donor maximizes all persons' expected utilities at the societal level to adjust how persons' purchases and the companies' development and production are subsidized. HIGHLIGHTS: A game theoretic approach can help explain the production decisions of vaccine and drug companies, and the decisions of persons and a donor, impacted by Nature.In 3 linked games, N persons choose risky behavior if its utility outweighs safe behavior.Vaccine and drug companies develop vaccines and drugs sponsored by a donor if profitable, allowing 14 outcomes.

Decisions of persons, the pharmaceutical industry, and donors in disease contraction and recovery assuming virus mutation.

BACKGROUND: The article develops an eight-period game between N persons and a pharmaceutical company. The choices of a donor and Nature are parametric. METHODS: Persons choose between safe and risky behavior, and whether or not to buy drugs. The pharmaceutical company chooses whether or not to develop drugs. The donor chooses parametrically whether to subsidize drug purchases and drug developments. Nature chooses disease contraction, recovery, death, and virus mutation. The game is solved with backward induction. RESULTS: The conditions are specified for each of seven outcomes ranging from safe behavior to risky behavior and buying no or one or both drugs. The seven outcomes distribute themselves across three outcomes for the pharmaceutical company, which are to develop no drugs, develop one drug, and develop two drugs if the virus mutates. For these three outcomes the donor's expected utility is specified. CONCLUSION: HIV/AIDS data is used to present a procedure for parameter estimation. The players' strategic choices are exemplified. The article shows how strategic interaction between persons and a pharmaceutical company, with parametric choices of a donor and Nature, impact whether persons choose risky or safe behavior, whether a pharmaceutical company develops no drugs or one drug, or two drugs if a virus mutates, and the impact of subsidies by a donor.

Evolutions in the physiology of skiing, skating and running in the Olympics.

Cross-country skiing, biathlon, Nordic combined, short track speed skating, and speed skating (12+11+3+8+14=48 events), i.e. five of the 15 disciplines in the 2018 Winter Olympics, require participants to reach the finish line in minimum time, while exerting mechanical propulsion power through flat terrain, uphill, and downhill. This article compares distances and times for these disciplines systematically with each other and with running, walking, and swimming in the Summer Olympics. Regarding physiological implications, the absence of distances below 6 km in biathlon, 5 km in Nordic combined, 1.2-1.5 km in cross-country skiing, and 0.5 km in speed skating means recruiting fewer competitors with sprint characteristics (type IIx fast isoforms muscles, etc.). The absence of distances above 10 km in speed skating and Nordic combined, and 20 km in biathlon, means recruiting fewer or other kinds of competitors with long distance characteristics. For example, high anaerobic threshold is important at greater distances, and high VO2max is important above intermediate distances. A new recruitment criterion for Olympic events is proposed, argued to recruit athletes fairly and be fair to spectators. The new criterion supplements current criteria such as popularity, relevance, and cooperation. The article recommends assessing 26 new events for future Winter Olympics within the five disciplines, equivalently for men and women. Formats are specified for the new events. Regarding equal distances for men and women, women use 8.7-13.6% more time than men in most events, except when upper-body power is important (above 13.6%) and in ultraendurance events (below 5.3%).

Formalizing the Precautionary Principle Accounting for Strategic Interaction, Natural Factors, and Technological Factors.

Four dimensions of the precautionary principle (PP), involving threat, uncertainty, action, and command, are formalized at the level of set theory and the level of individual players and natural and technological factors. Flow and decision diagrams with a feedback loop are developed to open up a new research agenda. The role of strategic interaction and games in the PP is underdeveloped or nonexistent in today's literature. To rectify this deficiency, six kinds of games are identified in the four PP dimensions. The games can be interlinked since player sets can overlap. Characteristics are illustrated. Accounting for strategic interaction, the article illustrates uncertainty in the PP regarding which game is played, which players participate in which game, strategy sets, payoffs, incomplete information, risk attitudes, and bounded rationality. The insurance and lottery games analyzed earlier for the safe minimum standard (SMS) for species extinction are revisited and placed into a broader context illustrating strategic interaction. Uncertainty about payoffs illustrates transformations back and forth between the chicken game, battle of the sexes, assurance game, and prisoner's dilemma.

Defense Strategies for Asymmetric Networked Systems with Discrete Components.

We consider infrastructures consisting of a network of systems, each composed of discrete components. The network provides the vital connectivity between the systems and hence plays a critical, asymmetric role in the infrastructure operations. The individual components of the systems can be attacked by cyber and physical means and can be appropriately reinforced to withstand these attacks. We formulate the problem of ensuring the infrastructure performance as a game between an attacker and a provider, who choose the numbers of the components of the systems and network to attack and reinforce, respectively. The costs and benefits of attacks and reinforcements are characterized using the sum-form, product-form and composite utility functions, each composed of a survival probability term and a component cost term. We present a two-level characterization of the correlations within the infrastructure: (i) the aggregate failure correlation function specifies the infrastructure failure probability given the failure of an individual system or network, and (ii) the survival probabilities of the systems and network satisfy first-order differential conditions that capture the component-level correlations using multiplier functions. We derive Nash equilibrium conditions that provide expressions for individual system survival probabilities and also the expected infrastructure capacity specified by the total number of operational components. We apply these results to derive and analyze defense strategies for distributed cloud computing infrastructures using cyber-physical models.

Policy makers, the international community and the population in the prevention and treatment of diseases: case study on HIV/AIDS.

A four-period game is developed between a policy maker, the international community, and the population. This research supplements, through implementing strategic interaction, earlier research analyzing "one player at a time". The first two players distribute funds between preventing and treating diseases. The population reacts by degree of risky behavior which may cause no disease, disease contraction, recovery, sickness/death. More funds to prevention implies less disease contraction but higher death rate given disease contraction. The cost effectiveness of treatment relative to prevention, country specific conditions, and how the international community converts funds compared with the policy maker in a country, are illustrated. We determine which factors impact funding, e.g. large probabilities of disease contraction, and death given contraction, and if the recovery utility and utility of remaining sick or dying are far below the no disease utility. We also delineate how the policy maker and international community may free ride on each other's contributions. The model is tested against empirical data for 43 African countries. The results show consistency between the theoretical model and empirical estimates. The paper argues for the need to create commitment mechanisms to ensure that free riding by both countries and the international community is avoided.

On the Effectiveness of Security Countermeasures for Critical Infrastructures.

A game-theoretic model is developed where an infrastructure of N targets is protected against terrorism threats. An original threat score is determined by the terrorist's threat against each target and the government's inherent protection level and original protection. The final threat score is impacted by the government's additional protection. We investigate and verify the effectiveness of countermeasures using empirical data and two methods. The first is to estimate the model's parameter values to minimize the sum of the squared differences between the government's additional resource investment predicted by the model and the empirical data. The second is to develop a multivariate regression model where the final threat score varies approximately linearly relative to the original threat score, sectors, and threat scenarios, and depends nonlinearly on the additional resource investment. The model and method are offered as tools, and as a way of thinking, to determine optimal resource investments across vulnerable targets subject to terrorism threats.

The influence of slope and speed on locomotive power in cross-country skiing.

PURPOSE: A model was developed for cross-country skiing where locomotive power depends on speed and slope as variables, and further depends on snow friction, gravitation, mass, air drag, wind, and air density. Model parameters were estimated experimentally. METHODS: Two differential equations were developed for how locomotive power depends on speed and slope. The equations are of the logistic form with a threshold determined by the skier's technique, intensity, mass, metabolic rate, gross efficiency, and lactate threshold. Three parameters were estimated by minimizing the average summed square difference between the simulated speed, using the model, and experimental speed of an elite male skier in a 4218 m track. Distance and height along the track were measured using a measuring wheel and an inclinometer generating 52 datapoints. Research assistants measured time from start at 14 different positions. Parameter values were determined from the literature. RESULTS: We illustrated how speed and slope impact locomotive power. The model was shown to be superior to a model where locomotive power is a function of speed only. The joint dependence of locomotive power on speed and slope is crucial in the non-stationary conditions where the skier passes high and low points along the track where both speed and slope change rapidly. CONCLUSION: The model is useful to predict the impact of altering a subset of the 23 variables and parameters on the remaining variables, for example the impact of changed friction or terrain slope on the skier's speed and thus time to complete a ski race.

Using the power balance model to simulate cross-country skiing on varying terrain.

The current study adapts the power balance model to simulate cross-country skiing on varying terrain. We assumed that the skier's locomotive power at a self-chosen pace is a function of speed, which is impacted by friction, incline, air drag, and mass. An elite male skier's position along the track during ski skating was simulated and compared with his experimental data. As input values in the model, air drag and friction were estimated from the literature based on the skier's mass, snow conditions, and speed. We regard the fit as good, since the difference in racing time between simulations and measurements was 2 seconds of the 815 seconds racing time, with acceptable fit both in uphill and downhill terrain. Using this model, we estimated the influence of changes in various factors such as air drag, friction, and body mass on performance. In conclusion, the power balance model with locomotive power as a function of speed was found to be a valid tool for analyzing performance in cross-country skiing.

Measuring patient participation in surgical treatment decision-making from healthcare professionals' perspective.

AIMS AND OBJECTIVES: To develop, empirical test, and validate an instrument measuring patient participation in surgical treatment decision-making from healthcare professionals' perspective. BACKGROUND: Since the advent of New Public Management in many Western countries, patient participation in healthcare decision-making has been considered to be a best practice. A common notion is that well-educated and well-informed public want to choose their own treatments and providers and want to ask questions about the quality of their health services. DESIGN: Survey. METHODS: A self-report-measuring instrument was designed and administered to 620 healthcare professionals. Items were developed, validated and tested by 451 nurses and physicians working in six surgical wards in a University Hospital in Norway. RESULTS: A 16-item scale with the following four dimensions was developed: information dissemination, formulation of options, integration of information and control. Factor analysis procedures and reliability testing were performed. A one-way, between-groups analysis of variance was conducted to compare doctors' and nurses' opinions on four dimensions of patient participation in surgical treatment decision-making. CONCLUSIONS: This article shows that patient participation in surgical treatment decision-making can be measured by a 16-item scale and four distinct dimensions. The analysis demonstrated a reasonable level of construct validity and reliability. Nurses and physicians have a positive attitude towards patient participation overall, but the two groups differ in the extent to which they accept the idea of patient participation in treatment decision-making. RELEVANCE TO CLINICAL PRACTICE: The instrument can be a tool for managers and healthcare professionals in the implementation of patient participation in clinical practice. Data from the instrument can be useful to identify health services being provided and what areas that could strengthen patient participation.

Patient participation, decision-makers and information flow in surgical treatment.

AIMS AND OBJECTIVES: To clarify patient participation by specifying three kinds of information flows between healthcare professionals and patients in four models such as the paternalistic, shared, informed and nonpaternalistic models. BACKGROUND: The relationship between healthcare professionals and patients has evolved from a traditional paternalistic model where 'doctors know best' and patients are passive recipients, to a partnership where patients act as active participants. DESIGN: A qualitative study. METHODS: Qualitative data from interviews with four doctors, seven nurses and seven patients illustrate these relationships. RESULTS: A 3 × 3 matrix is developed where healthcare professionals can make decisions unilaterally, patients can make decisions unilaterally, or these can make decisions jointly. Information can flow from healthcare professionals to patient, from patient to healthcare professionals or both ways. CONCLUSIONS: This conceptualisation provides a rich understanding of decision-making and information flow in surgical hospitals. RELEVANCE TO CLINICAL PRACTICE: The paper illustrates how practice can be assessed empirically to determine how it fits into the structure. Strategies can be implemented to move practice from one part of the structure to another part.

Models, phases and cases of patient participation in decision-making in surgical treatment in Norway: a qualitative study.

This study improves our understanding of patients' participation in hospital treatment-decision processes. We explored the degree of patient participation perceived by both patients and healthcare professionals in four phases of the decision process: information dissemination, formulation of options, integration of information, and control within four models of interactions between healthcare professionals and patients: the paternalistic model, the shared model, the informed model, and the non-paternalistic model. The analysis was based on 18 in-depth, exploratory interviews with patients and healthcare professionals in six surgical units in Norway. Knowledge about how patients and healthcare professionals interact in the surgical-decision process is important for developing systems and arenas for patient participation in practice, and for a climate and culture to further support the implementation.

A qualitative identification of categories of patient participation in decision-making by health care professionals and patients during surgical treatment.

The aim of this article is to identify how health care professionals and patients experience patient participation in decision-making processes in hospitals. Eighteen semi-structured interviews with experts from different disciplines such as medicine and nursing in surgical departments as well as patients who have undergone surgical treatment constitute the data. By content analysis four categories of patient participation were identified: information dissemination, formulation of options, integration of information, and control. To meet the increasing demands of patient participation, this categorization with four identified critical areas for participation in decision-making has important implications in guiding information support for patients prior to surgery and during hospitalization.

A simulation of cross-country skiing on varying terrain by using a mathematical power balance model.

The current study simulated cross-country skiing on varying terrain by using a power balance model. By applying the hypothetical inductive deductive method, we compared the simulated position along the track with actual skiing on snow, and calculated the theoretical effect of friction and air drag on skiing performance. As input values in the model, air drag and friction were estimated from the literature, whereas the model included relationships between heart rate, metabolic rate, and work rate based on the treadmill roller-ski testing of an elite cross-country skier. We verified this procedure by testing four models of metabolic rate against experimental data on the treadmill. The experimental data corresponded well with the simulations, with the best fit when work rate was increased on uphill and decreased on downhill terrain. The simulations predicted that skiing time increases by 3%-4% when either friction or air drag increases by 10%. In conclusion, the power balance model was found to be a useful tool for predicting how various factors influence racing performance in cross-country skiing.

Patient participation in surgical treatment decision making from the patients' perspective: validation of an instrument.

The aim of this paper is to describe the development of a new, brief, easy-to-administer self-reported instrument designed to assess patient participation in decision making in surgical treatment. We describe item generation, psychometric testing, and validity of the instrument. The final scale consisted of four factors: information dissemination (5 items), formulation of options (4 items), integration of information (4 items), and control (3 items). The analysis demonstrated a reasonable level of construct validity and reliability. The instrument applies to patients in surgical wards and can be used to identify the health services that are being provided and the areas that could strengthen patient participation.

On the kinetics of anaerobic power.

BACKGROUND: This study investigated two different mathematical models for the kinetics of anaerobic power. Model 1 assumes that the work power is linear with the work rate, while Model 2 assumes a linear relationship between the alactic anaerobic power and the rate of change of the aerobic power. In order to test these models, a cross country skier ran with poles on a treadmill at different exercise intensities. The aerobic power, based on the measured oxygen uptake, was used as input to the models, whereas the simulated blood lactate concentration was compared with experimental results. Thereafter, the metabolic rate from phosphocreatine break down was calculated theoretically. Finally, the models were used to compare phosphocreatine break down during continuous and interval exercises. RESULTS: Good similarity was found between experimental and simulated blood lactate concentration during steady state exercise intensities. The measured blood lactate concentrations were lower than simulated for intensities above the lactate threshold, but higher than simulated during recovery after high intensity exercise when the simulated lactate concentration was averaged over the whole lactate space. This fit was improved when the simulated lactate concentration was separated into two compartments; muscles + internal organs and blood. Model 2 gave a better behavior of alactic energy than Model 1 when compared against invasive measurements presented in the literature. During continuous exercise, Model 2 showed that the alactic energy storage decreased with time, whereas Model 1 showed a minimum value when steady state aerobic conditions were achieved. During interval exercise the two models showed similar patterns of alactic energy. CONCLUSIONS: The current study provides useful insight on the kinetics of anaerobic power. Overall, our data indicate that blood lactate levels can be accurately modeled during steady state, and suggests a linear relationship between the alactic anaerobic power and the rate of change of the aerobic power.

Resource distribution in multiple attacks with imperfect detection of the attack outcome.

This article extends the previous research of consecutive attacks strategy by assuming that an attacker observes the outcome of each attack imperfectly. With given probabilities it may wrongly identify a destroyed target as undestroyed, and wrongly identify an undestroyed target as destroyed. The outcome of each attack is determined by a contest success function that depends on the amount of resources allocated by the defender and the attacker to each attack. The article suggests a probabilistic model of the multiple attacks and analyzes how the target destruction probability and the attacker's relative resource expenditure are impacted by the two probabilities of incorrect observation, the attacker's and defender's resource ratio, the contest intensity, the number of attacks, and the resource distribution across attacks. We analyze how the attacker chooses the number of attacks, the attack stopping rule, and the optimal resource distribution across attacks to maximize its utility.

Systematization of a set of closure techniques.

Approximations in population dynamics are gaining popularity since stochastic models in large populations are time consuming even on a computer. Stochastic modeling causes an infinite set of ordinary differential equations for the moments. Closure models are useful since they recast this infinite set into a finite set of ordinary differential equations. This paper systematizes a set of closure approximations. We develop a system, which we call a power p closure of n moments, where 0≤p≤n. Keeling's (2000a,b) approximation with third order moments is shown to be an instantiation of this system which we call a power 3 closure of 3 moments. We present an epidemiological example and evaluate the system for third and fourth moments compared with Monte Carlo simulations.

Defense resource distribution between protection and redundancy for constant resource stockpiling pace.

The article considers the optimal resource distribution in a parallel system between increasing protection and providing redundancy in a situation when the attacker's and defender's resources are stockpiling and the resource increment rate is constant. It is assumed that the system must perform within an exogenously given time horizon and the attack time probability is uniformly distributed along this horizon. The defender optimizes the resource distribution in order to minimize the system destruction probability during the time horizon. First, we find the optimal pace of construction of the new redundant elements assuming that the construction must start in the initial stage of the stockpiling process. We show that starting construction of new elements in the beginning of the system's existence results in its high initial vulnerability. Introducing the time delay before starting the construction can reduce the initial system vulnerability and the entire system destruction probability. The problem of optimization of time delay and new element construction pace is considered with and without constraint on the initial system vulnerability. Examples illustrating the methodology of the optimal defense strategy analysis are presented.

Inpatient service providers' perspectives on service user involvement in Norwegian community mental health centres.

BACKGROUND: For two decades, mental health services in Norway have focused on service user involvement. Despite this, there is little knowledge about how inpatient mental health services have promoted user involvement. AIM: To examine service providers' reports of service user involvement at the individual and departmental levels in Norwegian community mental health centres (CMHCs). METHODS: One hundred and eighty six (186) inpatient service providers in five CMHCs filled out a questionnaire. RESULTS: Confirmatory factor analysis showed that service provider perceptions and awareness of service user involvement can be measured by three subscales: organizational user involvement; patient collaboration; and assisted patient involvement. Little user involvement was reported at the departmental level. Providers more often reported user involvement at the individual level. Providers in two of the CMHCs reported a somewhat higher degree of departmental-level user involvement. There were no significant differences across gender, age, leader position, profession and job tenure, though evening/night shift workers reported a lesser degree of user involvement. CONCLUSION: The results suggest that user involvement at the departmental level needs to be addressed in future efforts to promote user involvement in CMHCs.