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Rewarding cooperators and punishing defectors are effective measures for promoting cooperation in evolutionary game theory. Given that previous models treated rewards as constants, this does not reflect real-world dynamics changes. Therefore, this paper focused on the classical payoff matrix and examined the dynamic variable rewards affected by cooperation and defection strategies, as well as the impact of time delays. First, for the system without a time delay, we analyzed the existence and stability of numerous equilibrium points and explored transcritical bifurcations under various conditions. Second, for the time-delay system, we discussed a series of delayed dynamical behaviors including Hopf bifurcation, period, and the stability and direction of bifurcation. Finally, the changes of cooperation strategy were observed by numerical simulation, and some interesting results were obtained: (ⅰ) Under certain circumstances, even if the reward given to the cooperators reaches the maximum, the proportion of cooperators is still zero, which means that increasing rewards does not always promote cooperation. (ⅱ) The initial state can affect the choice of cooperation strategy and defection strategy. (ⅲ) The increase of the time delay makes the stable equilibrium point disappear and forms a stable limit cycle.

Abstract Background Lipid management based on cardiovascular risk level is the cornerstone of primary prevention of coronary artery disease (CAD), while the accuracy and adherence of traditional cardiovascular risk stratification have been questioned. Prevention strategies based on imaging screening for atherosclerotic plaques are found to be more objective and adherent in recent studies. This trial aims to investigate the role of coronary computed tomography angiography (CCTA) in guiding the primary prevention of CAD in a randomized controlled design. Methods Approximately 3400 middle-aged asymptomatic community participants will be recruited and randomized in a 1:1 ratio to a traditional cardiovascular risk score-guided (usual care group) or CCTA-guided (CCTA group) strategy. Participants with cardiovascular disease, prior lipid-lowering therapy, CCTA contraindication, or serious diseases that affect life span will be excluded. The intervention strategy includes blood pressure, blood glucose, and lipid management and lifestyle modifications. Blood pressure and glucose targets and lifestyle modification recommendations keep the same in both strategies, while lipid management is personalized based on traditional risk level or CCTA results, respectively. The primary outcome is the proportion of participants taking lipid-lowering medication regularly at both 6 and 12 months. The secondary outcomes include the proportion of participants achieving low-density lipoprotein cholesterol lowering targets at 12 months, mean changes in lipid levels from baseline to 12 months, barriers to adherence, adverse reactions related to CCTA examination, and cardiovascular events. Discussion The study is the first randomized clinical trial to examine the effectiveness of a CCTA-guided versus a traditional risk score-guided primary prevention strategy in an asymptomatic community-based population. Trial registration ClinicalTrials.gov NCT05725096. Registered on 2 February 2023.