Human emissions of size-resolved fluorescent bioaerosols in control situations.

Human bioaerosols contribute significantly to indoor air quality. This study used a Wideband Integrated Bioaerosol Sensor (WIBS-4A) instrument for real-time measurement of particle size distribution and count to differentiate fluorescent bioaerosols from non-fluorescent aerosols. Through an experiment involving 12 subjects (six men and six women) wearing standard cotton clothing in a 2 m × 2 m × 2 m environmental chamber, we established a quantitative method to obtain the bioaerosol emission rate of a single subject, aiming to explore the effects of masks and sex on bioaerosol emissions from different individuals. The mean emission rates of fluorescent bioaerosols in the particle size ranges of 0.5-2.5 µm and 2.5-10 µm were 3.192±2.11×104 counts/(person·h) and 13.98±9.34×104 counts/(person·h), respectively. A comparison between those wearing and not wearing masks revealed no significant differences in the emissions of fluorescent bioaerosols. This suggests respiratory sources may not significantly impact the emissions of fluorescent bioaerosols from individuals under seated breathing conditions. Significant disparities in the fluorescent bioaerosol emission rates of different biological sexes were observed through independent sample analysis. Males exhibited 41 % and 15 % higher emission rates than females for particle size ranges of 0.5-2.5 µm and 2.5-10 µm, respectively, possibly because of different metabolic rates. A significant correlation between metabolic rates and fluorescent bioaerosols (sig = 0.044 < 0.05) was observed in all the subjects. These findings underscore the individual variations that affect bioaerosol emission rates. The data provided by this study will facilitate further analysis of the on-site measured data and source analysis.

Investigating the spatial distribution of volatile organic compounds in aircraft cabins from various emission sources.

Volatile organic compounds (VOCs) significantly affect the air quality in aircraft cabins, consequently affecting passenger health and comfort. Although VOC emission sources and their contributions have been studied extensively, the distribution characteristics of VOCs originating from diverse sources within cabins have received limited attention, and the correlation between VOC sources and concentrations in passenger breathing zones remains largely unexplored. To fill this knowledge gap, the concentration field of VOCs was investigated using a computational fluid dynamics model, and the results were experimentally validated in a typical single-aisle aircraft cabin with seven seat rows. The diffusion characteristics of different VOCs emitted by four typical sources in aircraft cabins (floors, human surfaces, seats, and respiratory sources) were analyzed and compared. The distribution of VOCs emitted by different sources was nonuniform and could be classified into two distinct categories. When the emission intensities of all sources were equal, the average concentration of VOCs emitted from the floor source were considerably lower in the passenger breathing zone (4.01 µg/m³) than those emitted from the human surface, seat, and respiratory sources, which exhibited approximately equal concentrations (6.82, 6.90, and 7.29 µg/m³, respectively). The analysis highlighted that the simplified lumped-parameter method could not accurately estimate the exposure concentrations within an aircraft cabin. To address this issue, we propose a correction method based on the emission intensity of each VOC source. This study provides critical insights into the diffusion characteristics of VOCs within aircraft cabins and VOC emissions from various sources.

Reducing airborne transmission of SARS-CoV-2 by an upper-room ultraviolet germicidal irradiation system in a hospital isolation environment.

Upper-room ultraviolet germicidal irradiation (UVGI) technology can potentially inhibit the transmission of airborne disease pathogens. There is a lack of quantitative evaluation of the performance of the upper-room UVGI for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) airborne transmission under the combined effects of ventilation and UV irradiation. Therefore, this study aimed to explore the performance of the upper-room UVGI system for reducing SARS-CoV-2 virus transmission in a hospital isolation environment. Computational fluid dynamics and virological data on SARS-CoV-2 were integrated to obtain virus aerosol exposure in the hospital isolation environment containing buffer rooms, wards and bathrooms. The UV inactivation model was applied to investigate the effects of ventilation rate, irradiation flux and irradiation height on the upper-room UVGI performance. The results showed that increasing ventilation rate from 8 to 16 air changes per hour (ACH) without UVGI obtained 54.32% and 45.63% virus reduction in the wards and bathrooms, respectively. However, the upper-room UVGI could achieve 90.43% and 99.09% virus disinfection, respectively, with the ventilation rate of 8 ACH and the irradiation flux of 10 µW cm-2. Higher percentage of virus could be inactivated by the upper-room UVGI at a lower ventilation rate; the rate of improvement of UVGI elimination effect slowed down with the increase of irradiation flux. Increase irradiation height at lower ventilation rate was more effective in improving the UVGI performance than the increase in irradiation flux at smaller irradiation height. These results could provide theoretical support for the practical application of UVGI in hospital isolation environments.

The impact of high background particle concentration on the spatiotemporal distribution of Serratia marcescens bioaerosol.

Airborne transmission is a well-established mode of dissemination for infectious diseases, particularly in closed environments. However, previous research has often overlooked the potential impact of background particle concentration on bioaerosol characteristics. We compared the spatial and temporal distributions of bioaerosols under two levels of background particle concentration: heavily polluted (150-250 µg/m3) and excellent (0-35 µg/m3) in a typical ward. Serratia marcescens bioaerosol was adopted as a bioaerosol tracer, and the bioaerosol concentrations were quantified using six-stage Andersen cascade impactors. The results showed a significant reduction (over at least 62.9%) in bioaerosol concentration under heavily polluted levels compared to excellent levels at all sampling points. The temporal analysis also revealed that the decay rate of bioaerosols was higher (at least 0.654 min-1) under heavily polluted levels compared to excellent levels. These findings suggest that background particles can facilitate bioaerosol removal, contradicting the assumption made in previous research that background particle has no effect on bioaerosol characteristics. Furthermore, we observed differences in the size distribution of bioaerosols between the two levels of background particle concentration. The average bioaerosols size under heavily polluted levels was found to be higher than that under excellent levels, and the average particle size under heavily polluted levels gradually increased with time. In conclusion, these results highlight the importance of considering background particle concentration in future research on bioaerosol characteristics.

Complex evolutionary interactions in multiple populations.

In competitive settings that entail several populations, individuals often engage in intra- and interpopulation interactions that determine their fitness and evolutionary success. With this simple motivation, we here study a multipopulation model where individuals engage in group interactions within their own population and in pairwise interactions with individuals from different populations. We use the evolutionary public goods game and the prisoner's dilemma game to describe these group and pairwise interactions, respectively. We also take into account asymmetry in the extent to which group and pairwise interactions determine the fitness of individuals. We find that interactions across multiple populations reveal new mechanisms through which the evolution of cooperation can be promoted, but this depends on the level of interaction asymmetry. If inter- and intrapopulation interactions are symmetric, the sole presence of multiple populations promotes the evolution of cooperation. Asymmetry in the interactions can further promote cooperation at the expense of the coexistence of the competing strategies. An in-depth analysis of the spatiotemporal dynamics reveals loop-dominated structures and pattern formation that can explain the various evolutionary outcomes. Thus, complex evolutionary interactions in multiple populations reveal an intricate interplay between cooperation and coexistence, and they also open up the path toward further explorations of multipopulation games and biodiversity.

Modeling the infection risk and emergency evacuation from bioaerosol leakage around an urban vaccine factory.

Mounting interest in modeling outdoor diffusion and transmission of bioaerosols due to the prevalence of COVID-19 in the urban environment has led to better knowledge of the issues concerning exposure risk and evacuation planning. In this study, the dispersion and deposition dynamics of bioaerosols around a vaccine factory were numerically investigated under various thermal conditions and leakage rates. To assess infection risk at the pedestrian level, the improved Wells-Riley equation was used. To predict the evacuation path, Dijkstra's algorithm, a derived greedy algorithm based on the improved Wells-Riley equation, was applied. The results show that, driven by buoyancy force, the deposition of bioaerosols can reach 80 m on the windward sidewall of high-rise buildings. Compared with stable thermal stratification, the infection risk of unstable thermal stratification in the upstream portion of the study area can increase by 5.53% and 9.92% under a low and high leakage rate, respectively. A greater leakage rate leads to higher infection risk but a similar distribution of high-risk regions. The present work provides a promising approach for infection risk assessment and evacuation planning for the emergency response to urban bioaerosol leakage.

Estimating the restraint of SARS-CoV-2 spread using a conventional medical air-cleaning device: Based on an experiment in a typical dental clinical setting.

OBJECTIVES: Droplets or aerosols loaded with SARS-CoV-2 can be released during breathing, coughing, or sneezing from COVID-19-infected persons. To investigate whether the most commonly applied air-cleaning device in dental clinics, the oral spray suction machine (OSSM), can provide protection to healthcare providers working in clinics against exposure to bioaerosols during dental treatment. METHOD: In this study, we measured and characterized the temporal and spatial variations in bioaerosol concentration and deposition with and without the use of the OSSM using an experimental design in a dental clinic setting. Serratia marcescens (a bacterium) and ΦX174 phage (a virus) were used as tracers. The air sampling points were sampled using an Anderson six-stage sampler, and the surface-deposition sampling points were sampled using the natural sedimentation method. The Computational Fluid Dynamics method was adopted to simulate and visualize the effect of the OSSM on the concentration spatial distribution. RESULTS: During dental treatment, the peak exposure concentration increased by up to 2-3 orders of magnitude (PFU/m3) for healthcare workers. Meanwhile, OSSM could lower the mean bioaerosol exposure concentration from 58.84 PFU/m3 to 4.10 PFU/m3 for a healthcare worker, thereby inhibiting droplet and airborne transmission. In terms of deposition, OSSM significantly reduced the bioaerosol surface concentration from 28.1 PFU/m3 to 2.5 PFU/m3 for a surface, effectively preventing fomite transmission. CONCLUSION: The use of OSSM showed the potential to restraint the spread of bioaerosols in clinical settings. Our study demonstrates that OSSM use in dental clinics can reduce the exposure concentrations of bioaerosols for healthcare workers during dental treatment and is beneficial for minimizing the risk of infectious diseases such as COVID-19.

Transmission characteristics of infectious pathogen-laden aerosols in a negative-pressure operating room.

The infectious pathogen-laden aerosols generated by infected patients have a significant impact on the safety of surgical staff in highly clean negative-pressure operating rooms. Understanding the transmission characteristics of infectious pathogen-laden aerosols is therefore essential. Therefore, in this study, we conducted experiments in a full-size negative-pressure operating room, and the Phi-X174 phage was used as a bioaerosol release source to investigate the migration and deposition of bioaerosols. The high-concentration spatial regions and high-concentration deposition surfaces of the bioaerosols in the operating room were determined. The results showed that there was a high concentration of bioaerosols in the vortex region below the medical lamp for extended periods of time. Three surgical staff members close to the patient's surgical site had high bioaerosol concentrations at their facial sampling points, with the highest concentration reaching 16,553 PFU/m³ . At the end of bioaerosol generation, 99.9% of the bioaerosols were discharged within 10 mins. The bioaerosol deposition rates per unit area were high at 1.48%/m2, 0.46%/m2 and 1.79%/m2 for the central control panel, storage cabinet, and door surface, respectively. This research can be used as a scientific reference for controlling bioaerosols and determining key disinfection parts in a negative-pressure operating room.

A model to evaluate ozone distribution and reaction byproducts in aircraft cabin environments.

Ozone and byproducts of ozone-initiated reactions are among the primary pollutants in aircraft cabins. However, investigations of the spatial distribution and reaction mechanisms of these pollutants are insufficient. This study established a computational fluid dynamics-based model to evaluate ozone and byproduct distribution, considering ozone reactions in air, adsorption onto surfaces, and byproduct desorption from surfaces. The model was implemented in an authentic single-aisle aircraft cabin and validated by measurements recorded during the aircraft cruise phase. Ozone concentrations in the supply air-dominated area were approximately 50% higher than that in the passenger breathing zone, suggesting that human surfaces represent a significant ozone sink. The deposition velocity onto human bodies was 21.83 m/h, surpassing 3.97 m/h on other cabin interior surface areas. Our model provides a mechanistic tool to analyze ozone and byproduct concentration distributions, which would be useful for assessing passenger health risks and for developing strategies for healthier aircraft cabin environments.

Bioaerosol distribution characteristics and potential SARS-CoV-2 infection risk in a multi-compartment dental clinic.

Dental clinics have a potential risk of infection, particularly during the COVID-19 pandemic. Multi-compartment dental clinics are widely used in general hospitals and independent clinics. This study utilised computational fluid dynamics to investigate the bioaerosol distribution characteristics in a multi-compartment dental clinic through spatiotemporal distribution, working area time-varying concentrations, and key surface deposition. The infection probability of SARS-CoV-2 for the dental staff and patients was calculated using the Wells-Riley model. In addition, the accuracy of the numerical model was verified by field measurements of aerosol concentrations performed during a clinical ultrasonic scaling procedure. The results showed that bioaerosols were mainly distributed in the compartments where the patients were treated. The average infection probability was 3.8% for dental staff. The average deposition number per unit area of the treatment chair and table are 28729 pcs/m2 and 7945 pcs/m2, respectively, which creates a possible contact transmission risk. Moreover, there was a certain cross-infection risk in adjacent compartments, and the average infection probability for patients was 0.84%. The bioaerosol concentrations of the working area in each compartment 30 min post-treatment were reduced to 0.07% of those during treatment, and the infection probability was <0.05%. The results will contribute to an in-depth understanding of the infection risk in multi-compartment dental clinics, forming feasible suggestions for management to efficiently support epidemic prevention and control in dental clinics.

Droplet aerosols transportation and deposition for three respiratory behaviors in a typical negative pressure isolation ward.

Negative pressure isolation wards could provide safety for health care workers (HCWs) and patients infected with SARS-CoV-2. However, respiratory behavior releases aerosols containing pathogens, resulting in a potential risk of infection for HCWs. In this study, the spatiotemporal distribution of droplet aerosols in a typical negative pressure isolation ward was investigated using a full-scale experiment. In this experiment, artificial saliva was used to simulate the breathing behavior, which can reflect the effect of evaporation on droplet aerosols. Moreover, numerical simulations were used to compare the transport of droplet aerosols released by the three respiratory behaviors (breathing, speaking, and coughing). The results showed that droplet aerosols generated by coughing and speaking can be removed and deposited more quickly. Because reduction in the suspension proportion per unit time was much higher than that in the case of breathing. Under the air supply inlets, there was significant aerosol deposition on the floor, while the breathing area possessed higher aerosol concentrations. The risk of aerosol resuspension and potential infection increased significantly when HCWs moved frequently to these areas. Finally, more than 20% of the droplet aerosols escaped from the ward when the number of suspended aerosols in the aerosol space was 1%.

Identification of key volatile organic compounds in aircraft cabins and associated inhalation health risks.

The identification of key VOCs during flights is important in creating a satisfactory aircraft cabin environment. Two VOC databases for the building indoor environment (from 251 occupied residences) and the aircraft cabin environment (from 56 commercial flights) were compared, to determine the common compounds (detection rate (DR) > 70%) in the two environments and the characteristic VOCs (only those with high DR during flights) in aircraft cabins. Possible VOC emission sources in flights were also discussed. As TVOC is usually viewed as a general indicator of air quality, the prediction of TVOC concentration was carried out using BP neural network algorithm, and the average error between the predicted and measured values was 55.35 µg/m3 (R2 = 0.80). Meanwhile, the VOCs' inhalation cancer/non-cancer risks to crew members and passengers were calculated on the basis of detection rates, exposure concentrations, and health risk assessments. Six compounds (i.e., formaldehyde, benzene, tetrachloroethylene, trichloromethane, 1,2-dichloroethane, and naphthalene) were proposed as the key VOCs in the existing aircraft cabin environment, presenting a risk to crew members that is higher than the US EPA proposed acceptable level (evaluated mean value > 1E-06). The estimated lifetime excess cancer/non-cancer risks for passengers were all below the assessment criteria. Based on a summary of various VOC limits in five built environments, hierarchical design of VOC concentration limits is recommended for the aircraft environment.

Influencing factors of carbonyl compounds and other VOCs in commercial airliner cabins: On-board investigation of 56 flights.

Volatile organic compounds (VOCs) as a non-negligible aircraft cabin air quality (CAQ) factor influence the health and comfort of passengers and crew members. On-board measurements of carbonyls (short-chain (C1 -C6 )) and other volatile organic compounds (VOCs, long-chain (C6 -C16 )) with a total of 350 samples were conducted in 56 commercial airliner cabins covering 8 aircraft models in this study. The mean concentration for each individual carbonyl compound was between 0.3 and 8.3 µg/m3 (except for acrolein & acetone, average = 20.7 µg/m3 ) similar to the mean concentrations of other highly detected VOCs (long-chain (C6 -C16 ), 97% of which ranged in 0-10 µg/m3 ) in aircraft cabins. Formaldehyde concentrations in flights were significantly lower than in residential buildings, where construction materials are known formaldehyde sources. Acetone is a VOC emitted by humans, and its concentration in flights was similar to that in other high-occupant density transportation vehicles. The variation of VOC concentrations in different flight phases of long-haul flights was the same as that of CO2 concentration except for the meal phase, which indicates the importance of cabin ventilation in diluting the gaseous contaminants, while the sustained and slow growth of the VOC concentrations during the cruising phase in short-haul flights indicated that the ventilation could not adequately dilute the emission of VOCs. For the different categories of VOCs, the mean concentration during the cruising phase of benzene series, aldehydes, alkanes, other VOCs (detection rate > 50%), and carbonyls in long-haul flights was 44.2 µg/m3 , 17.9 µg/m3 , 18.6 µg/m3 , 31.5 µg/m3 , and 20.4 µg/m3  lower than those in short-haul flights, respectively. Carbonyls and d-limonene showed a significant correlation with meal service (p < 0.05). Unlike the newly decorated rooms or new vehicles, the inner materials were not the major emission sources in aircraft cabins. Practical Implications. The on-board measurements of 56 flights enrich the VOC database of cabin environment, especially for carbonyls. The literature review of carbonyls in the past 20 years contributes to the understanding the current status of cabin air quality (CAQ). The analysis of VOC concentration variation for different flight phases, flight duration, and aircraft age lays a foundation for exploring effective control methods, including ventilation and purification for cabin VOC pollution. The enriched VOC data is helpful to explore the key VOCs of aircraft cabin environment and to evaluate the acute/chronic health exposure risk of pollutants for passengers and crew members.

Carbon dioxide in passenger cabins: Spatial temporal characteristics and 30-year trends.

Carbon dioxide (CO2 ) is an important environmental parameter in aircraft cabins. To understand the most recent, real-time CO2 concentration levels and their key influencing factors in aircraft cabins, we conducted in-flight measurements of 52 randomly selected commercial flights with different aircraft types and durations from August 2017 to August 2019. The spatial temporal characteristics of CO2 concentrations on board were analyzed and summarized. For the flight time scale, the CO2 concentrations during the boarding phase (1680 ± 558 ppmv) were notably higher than that in other phases, whereas the condition of the cruising phase was the lowest in most flights. The flight average CO2 concentrations of the cruising phase were 1253 ± 164 ppmv, and the corresponding estimated outside airflow rates were 6.2 ± 1.3 L/s/p in the economy class across all flights. Single-aisle and twin-aisle flights did not show noticeable differences for the same phases. Relatively uniform CO2 concentrations were observed at different positions of the same class. By comparing the results of this study with those previously reported, CO2 concentrations showed a slightly decreasing trend over the last 30 years. This suggested a slightly increased ventilation rate and potentially superior air quality on board.

A Novel Tissue-Based Liver-Kidney-on-a-Chip Can Mimic Liver Tropism of Extracellular Vesicles Derived from Breast Cancer Cells.

Extracellular vesicles (EVs) from cancer cells remodel distant organs to promote metastasis in vivo. A biomimetic microsystem may compensate costly and time-consuming animal models to accelerate the study of EV organotropism. A tissue-based liver-kidney-on-a-chip is developed with precision-cut tissue slices (PTSs) cultured to represent individual organs. The organotropism of breast cancer EVs is modeled using the biomimetic microsystem. A traditional animal model of EV organotropism is used to investigate the physiological similarity of the microfluidic model to animal models. It is demonstrated that breast cancer EVs show strong liver tropism rather than kidney tropism on both the microfluidic and animal models. It is found that the metastatic inhibitor AMD3100 inhibits liver tropism effectively in both the microfluidic and animal models. Overall, the tropism of EVs to different organs is reconstituted on the microfluidic model. The liver-kidney-on-a-chip may expand the capabilities of traditional cell culture models and provide a faster alternative to animal models for EV studies.

Human respiratory system as sink for volatile organic compounds: Evidence from field measurements.

Human exposure to volatile organic compounds (VOCs) via inhalation might increase the risk of specific diseases. Human breath has been widely investigated as a source of VOCs. However, the role of the human respiratory system as a sink for VOCs is much less studied. In this observational study, the VOC concentrations in inhaled and exhaled air in different environmental conditions were investigated. A total of 98 healthy non-smoking subjects who were exposed to a wide variation in levels of VOCs participated in this study. Individual and statistical results show that human breath could serve as a source for some VOCs and a sink for others, and even when human breath serves as a sink, not all VOCs were 100% absorbed. Interestingly, an increase in inhaled concentrations of toluene was observed to convert human breath from being a source to being a sink. Attention could be given to those VOCs for which humans act as a strong sink.

The importance of spatial heterogeneity and self-restraint on mutualism stability - a quantitative review.

Understanding the factors that enable mutualisms to evolve and to subsequently remain stable over time, is essential to fully understand patterns of global biodiversity and for evidence based conservation policy. Theoretically, spatial heterogeneity of mutualists, through increased likelihood of fidelity between cooperative partners in structured populations, and 'self-restraint' of symbionts, due to selection against high levels of virulence leading to short-term host overexploitation, will result in either a positive correlation between the reproductive success of both mutualists prior to the total exploitation of any host resource or no correlation after any host resource has been fully exploited. A quantitative review by meta-analysis on the results of 96 studies from 35 papers, showed no evidence of a significant fitness correlation between mutualists across a range of systems that captured much taxonomic diversity. However, when the data were split according to four categories of host: 1) cnidarian corals, 2) woody plants, 3) herbaceous plants, and 4) insects, a significantly positive effect in corals was revealed. The trends for the remaining three categories did not significantly differ to zero. Our results suggest that stability in mutualisms requires alternative processes, or mechanisms in addition to, spatial heterogeneity of hosts and/or 'self-restraint' of symbionts.

Non-quantitative adjustment of offspring sex ratios in pollinating fig wasps.

Fig wasp is one of the most well known model systems in examining whether or not the parents could adjust their offspring sex ratio to maximize their gene frequency transmission in next generations. Our manipulative experiments showed that, in all of the five pollinator wasps of figs (Agaonidae) that have different averages of foundress numbers per syconium, almost the same proportions of male offspring are produced in the experiment that foundresses deposit one hour then are killed with ether (66.1%-70.1%) and over the lifespan of each foundress (14.0%-21.0%). The foundresses tend to deposit their male eggs prior to female eggs. The observed increase in the proportion of male offspring as a function of foundress number results from density-dependent interference competition among the foundresses. These results showed that the selection of gene frequency transmission through the behavioral adjustment in the evolution of sex ratio does not exist in these five fig wasps. The results here implied that genetic adjustment mechanisms of the sex ratio of fig wasps can only be triggered to be on or off and that the foundresses can not quantitatively adjust their sex ratio according to increased environmental selection pressure.

Asymmetric interaction paired with a super-rational strategy might resolve the tragedy of the commons without requiring recognition or negotiation.

Avoiding the tragedy of the commons requires that one or more individuals in a group or partnership "volunteer", benefiting the group at a cost to themselves. Recognition and negotiation with social partners can maintain cooperation, but are often not possible. If recognition and negotiation are not always the mechanism by which cooperative partnerships avoid collective tragedies, what might explain the diverse social cooperation observed in nature? Assuming that individuals interact asymmetrically and that both "weak" and "strong" players employ a super-rational strategy, we find that tragedy of the commons can be avoided without requiring either recognition or negotiation. Whereas in the volunteer's dilemma game a rational "strong" player is less likely to volunteer to provide a common good in larger groups, we show that under a wide range of conditions a super-rational "strong" player is more likely to provide a common good. These results imply that the integration of super-rationality and asymmetric interaction might have the potential to resolve the tragedy of the commons. By illuminating the conditions under which players are likely to volunteer, we shed light on the patterns of volunteerism observed in variety of well-studied cooperative social systems, and explore how societies might avert social tragedies.

Evolutionary stability in the asymmetric volunteer's dilemma.

It is often assumed that in public goods games, contributors are either strong or weak players and each individual has an equal probability of exhibiting cooperation. It is difficult to explain why the public good is produced by strong individuals in some cooperation systems, and by weak individuals in others. Viewing the asymmetric volunteer's dilemma game as an evolutionary game, we find that whether the strong or the weak players produce the public good depends on the initial condition (i.e., phenotype or initial strategy of individuals). These different evolutionarily stable strategies (ESS) associated with different initial conditions, can be interpreted as the production modes of public goods of different cooperation systems. A further analysis revealed that the strong player adopts a pure strategy but mixed strategies for the weak players to produce the public good, and that the probability of volunteering by weak players decreases with increasing group size or decreasing cost-benefit ratio. Our model shows that the defection probability of a "strong" player is greater than the "weak" players in the model of Diekmann (1993). This contradicts Selten's (1980) model that public goods can only be produced by a strong player, is not an evolutionarily stable strategy, and will therefore disappear over evolutionary time. Our public good model with ESS has thus extended previous interpretations that the public good can only be produced by strong players in an asymmetric game.