The public health technology R&D alliance is an innovative platform focused on public health events, driven by the imperative to safeguard people's lives and wellbeing. It is led by the government, with participation from pharmaceutical enterprises, and coordination from academic and research institutes (26). The government guides the establishment and operation of the public health technology R&D alliance through policy tools. By organizing interdisciplinary teams for scientific and technological cooperation and coordinating science and technology with clinical prevention and control efforts, as well as closely aligning the science and technology governance system with government, industry, academia, research, and application sectors, this aims to promote project research and development, technology transformation, and application of achievements. Therefore, the public health technology R&D alliance embodies typical characteristics of being government-driven. The interaction mechanism among public health subjects can be deconstructed from three dimensions: subject structure, policy mechanism, and factor input and effect (as shown in Figure 1).

In terms of the subject structure, the main body of the public health technology R&D alliance includes the government, pharmaceutical enterprises, and academic and research institutions. This reflects an innovative relationship where the government leads, pharmaceutical enterprises participate, and academic and research institutions cooperate. In response to major public health emergencies, the state quickly mobilizes superior scientific and technological resources from various sectors such as pharmaceutical enterprises and academic and research institutions. This forms a public health technology R&D alliance that swiftly invests in emergency research projects. The organization of the technology R&D alliance reflects typical characteristics of the government's use of a policy mix to drive collaboration among multiple public health stakeholders (27).

In terms of policy mechanisms, the government builds and guides the operation and evolution of public health technology R&D alliances through a multi-level and systematic combination of policy tools. According to the policy classification model of Rothwell and Zegved (12), policy tools in the field of public health can be divided into three categories: supply side, demand side, and environmental side. They work in synergy to form the core mechanism that drives alliance construction, resource integration, and efficiency output. Supply-side policy tools focus on financial support, technological support, and talent development. The government directly addresses key element gaps in the R&D cycle of the alliance by setting up special research funds, building public experimental platforms, sharing data resources, and organizing cross-disciplinary research teams, thereby reducing innovation risks and accelerating technological breakthroughs. Demand-side policy tools, centered on government procurement, provide clear market access and technology transfer pathways for alliance members through centralized procurement of medical supplies, testing equipment, and scientific and technological research services, directly encouraging enterprises and academic research institutions to engage in emergency R&D and production. Meanwhile, as a key user, the government guides the R&D direction to closely align with actual demands by establishing technical standards and performance requirements. Environmental-side policy tools focus on institutional incentives and ecological development. By implementing preferential policies such as additional deductions for R&D expenses, tax reductions and exemptions, and expedited approval processes for pharmaceutical enterprises and academic institutions, a policy environment conducive to long-term collaboration and continuous innovation is created (28). These three types of policy tools, driven by the government, jointly shape the evolution of the alliance from emergency response to long-term development, promoting the continuous optimization of the science and technology governance system featuring the deep integration of “government, industry, academia, research, and application”.

In terms of factor input, government policy support is the key resource input for the public health technology R&D alliance. The government has played a leading role in the rapid response mechanism for emergency science and technology research, including capital investment in infrastructure construction, coordinated deployment of project personnel, and platform development for information resource collection. Academic and research institutions provide intellectual support such as talent, technology, patents, and essential experimental instruments and equipment for drug vaccine research and development. They also offer technical solutions for sudden public health events. Pharmaceutical enterprises leverage the supply capacity of the industrial chain to quickly bring drug vaccine products to market based on technological R&D results from academic and research institutions. Hospitals and related clinical rescue institutions use these drug vaccines to promptly treat patients during public health emergencies (29). In terms of revenue effect, rapid response and timely processing of public health emergencies can ensure regional social stability while improving social welfare and governance performance. By participating in the public health technology R&D alliance, academic and research institutions can enhance the quality of personnel training as well as the efficiency of scientific and technological achievement transformation. Pharmaceutical enterprises are able to convert scientific and technological innovation into products while enhancing overall value through improvements in the industrial chain (30).

Based on the analysis of the operational mechanism of the public health technology R&D alliance, it is evident that the successful operation of the public health technology R&D alliance requires active participation from various stakeholders, including the government, pharmaceutical enterprises, academic and research institutions, and other relevant entities. Each stakeholder has its own intrinsic motivations and resistance toward promoting the establishment of a technology R&D alliance due to their resource dependence on one another. Motivations are primarily driven by anticipated benefits, while resistance stems from expected costs. The decision to promote the construction of a public health technology R&D alliance should be based on a comprehensive consideration of both benefits and costs. Therefore, this paper focuses on analyzing the government, pharmaceutical enterprises, and academic and research institutions to construct an evolutionary game model for the public health technology R&D alliance. Based on this analysis, we propose the following hypothesis.

According to the hypothesis, it is concluded that the evolutionary game income matrix of the three parties under the strategy set of (positive incentive, negative incentive), (active participation, negative participation), and (active participation, negative participation) is shown in Table 1. Analysis of the evolutionary stability strategy of public health subjects.

According to the evolutionary game matrix and evolutionary game tree regarding whether the government actively promotes the formation of technology R&D alliances, the expected returns corresponding to different government strategic choices are calculated. Subsequently, the replication dynamic equation of the government's evolutionary game is constructed. The expected return and average expected return are as follows: U₁₁, U₁₂ obtained by the government's active promotion or negative and non-active promotion of the technology R&D alliance formation strategy, and the average expected returns U1¯.

According to evolutionary game theory, the replication dynamic equation and the first-order partial derivative of the government's promotion of technology R&D alliance behavior can be expressed as follows:

Suppose μ(y) = k₁y−W₁−B₁+zk₂+py+pz+ryW₂+ryW₃−yzp. According to the stability theorem of differential equations, the probability that the government actively promotes emergency science and technology research should be satisfied in a stable state: F(x) = 0 and F′(x) <0 due to∂μ(y)∂y>0. That is, μ(y) is an increasing function with respect to y. Therefore, wheny=y*=W1+B1-zk2-pz-λzW3k1+p+λW2-zP, μ(y) = 0. The government's stability strategy cannot be determined. When y<y^*, μ(y) <0, so dF(x)dx|x=1<0. At this time, x = 1 is the stable strategy point. To further analyze the important factors that affect the government's incentive strategy, the first-order partial derivatives of each variable y^* are obtained, respectively, ∂y*∂W1>0,∂y*∂B1>0, ∂y*∂W3<0,∂y*∂k2<0, ∂y*∂p<0, ∂y*∂k1<0, ∂y*∂W2<0. Therefore, the smaller the values of k₁, k₂, p, W₂, W₃, or the larger the values of B₁, W₁, the greater the y^*, making it easier to meet the conditions. The government tends to actively use policies to promote public health entities to conduct scientific and technological research. Based on the above analysis, the following inference can be made.

Corollary 1: The likelihood of the government promoting active participation in public health technology R&D alliances is inversely related to the government's input costs and procurement from pharmaceutical enterprises and academic and research institutions for economic gains through collaborative R&D. It is also negatively associated with the loss of credibility in adverse situations, the opportunity cost of prevention and control, and positively linked to enhancing government credibility.

According to the evolutionary game matrix and evolutionary game tree regarding whether enterprises actively participate in public health technology R&D alliances, the expected returns corresponding to different strategic choices of enterprises are calculated, and then the replication dynamic equation of the enterprise evolutionary game is constructed. Therefore, the expected returnsU₂₁ and U₂₂ obtained by enterprises actively or passively participating in the technology R&D alliance, and the average expected returns U2¯ are

According to evolutionary game theory, the replication dynamic equation and the first derivative of the behavior of enterprises promoting the public health technology R&D alliance are

Suppose φ(z) = c_b2−B₂−W₂−xk₁−px−rW₂x+xzp−λpxz. According to the stability theorem of differential equation, the probability of pharmaceutical enterprises actively participating in collaborative emergency science and technology research must be satisfied in a stable state. F(y) = 0 and F′(y) <0. Since φ(z)∂z>0, that is, φ(z)is an increasing function with respect to z. When z=z*=B2-cb2+W2+xk1+px+rW2xpx(1-λ), φ(z) = 0. The stability strategy of pharmaceutical enterprises cannot be determined. When z<z^*, dF(y)dy|y=0<0, y = 0 is the stable strategy point. To further explore the influencing factors that may affect the probability of pharmaceutical enterprises actively participating in public health technology R&D alliance, the first-order partial derivatives of each variable in z^* are calculated and can be obtained as ∂z*∂cb2<0,∂z*∂B2>0,∂z*∂W2>0,∂z*∂p>0,∂z*∂k1>0, and ∂z*∂λ>0. Therefore, when B₂, W₂, k₁, p, and λ are larger, c_b2 is smaller, z^* is larger, the condition of z<z^* is easier to be established, and pharmaceutical enterprises are more inclined to actively participate in scientific and technological research alliance.

Corollary 2: The probability of pharmaceutical enterprises actively participating in public health technology R&D alliances is positively correlated with economic benefits, financial support funds, additional benefits provided by the government, and the proportion of reputation, opportunity cost loss, and market income under negative participation. It is negatively correlated with production costs such as communication, equipment, and personnel expenses incurred under active participation.

According to the evolutionary game matrix and evolutionary game tree regarding whether academic and research institutions are actively involved in public health technology R&D alliances, the expected benefits corresponding to different strategic choices of these institutions are calculated, and the replication dynamic equation of the evolutionary game for academic and research institutions is constructed.

The expected benefits obtained from the active or negative participation of research institutions in the public health technology R&D alliance are U₃₁, U₃₂, and the average expected returns U3¯:

According to evolutionary game theory, the replication dynamic equation and the first-order partial derivative of the behavior of research institutions promoting the public health technology R&D alliance are formulated.

Suppose 𝔐(y) = c_b3−B₃−W₃−xk₂−px−rW₃x+λpxy. According to the stability theorem of differential equation, the probability that the research institution chooses to actively participate in the public health technology R&D alliance must be satisfied in a stable state: F(z) = 0 and F′(z) <0. Since ∂𝔐(y)∂y>0, 𝔐(y) is an increasing function with respect to y. At that time, y=y**=B3-cb3+W3+xk2+px+rxW3λpx,𝔐(y) = 0 It is impossible to determine the stability strategy of academic and research institutions. When y>y^**, 𝔐(y)>0, dF(z)dz|z=0<0, z = 0is the stable strategy point. Wheny<y^**, 𝔐(y) <0, dF(z)dz|z=1<0, z = 1 is the stable strategy point. To further explore the influencing factors that may affect the probability of academic and research institutions actively participating in public health technology R&D alliance, the first-order partial derivatives of each variable are obtained ∂y**∂B3>0, ∂y**∂cb3<0, ∂y**∂W3>0, ∂y**∂k2>0, ∂y**∂p>0, ∂y**∂λ<0. Therefore, when B₃, W₃, k₂, and p are larger, c_b3 and λ are smaller, y^* is smaller, the condition of y<y^** is easier to be established, and the research institutions are more inclined to actively participate in the public health technology R&D alliance.

Corollary 3: The probability of academic and research institutions actively participating in public health technology R&D alliances is positively correlated with economic benefits, financial support funds, additional benefits from government purchases, reputation, and opportunity cost losses from negative participation. It is negatively correlated with the production costs incurred during active participation and the market income ratio of pharmaceutical enterprises in government procurement.

Based on the above analysis, it is found that there is an interactive relationship among the probability of the government actively guiding and purchasing public health products x, the probability of pharmaceutical enterprises actively participating in the public health technology R&D alliance and providing technical support y, and the probability of academic and research institutions actively participating in the public health technology R&D alliance and providing intellectual support z. Let F(x) = 0, F(y) = 0, F(z) = 0 hold at the same time, eight local equilibrium points of system D can be obtained: H₁(0, 0, 0), H₂(1, 0, 0), H₃(0, 1, 0), H₄(0, 0, 1), H₅(1, 1, 0), H₆(1, 0, 1), H₇(0, 1, 1), H₈(1, 1, 1).

Referring to the evolutionary game analysis method proposed by Friedman, the local stability analysis of the Jacobian matrix of the replication dynamic system can further obtain the ESS of the system (32). According to the previous analysis, the dynamic equations for the government, pharmaceutical enterprises, and academic and research institutions can be obtained, along with the Jacobian matrix J of system D:

Of which:

According to the Lyapunov stability criterion and Reinhard's point of view (38), the equilibrium point is considered an evolutionary stable point of the system when all eigenvalues of the Jacobian matrix are negative real numbers, while the equilibrium point is unstable when at least one eigenvalue is a positive real number. Therefore, the eight local equilibrium points are substituted into the Jacobian matrix, and the eigenvalues corresponding to each equilibrium point can be obtained. The results are shown in Table 2.

According to the analysis of the eigenvalues of the Jacobian matrix in Table 2, the possible equilibrium state of the game system composed of the government, pharmaceutical enterprises, and academic and research institutions is analyzed in depth, as follows:

Case 1: When k₂+B₃+p+W₃+rW₃−λp<c_b3, the cost of active participation of research institutions in the alliance is greater than the benefits obtained, H₅ (1,1,0) is the evolutionary stable point. At this time, the government actively uses policy tools, pharmaceutical enterprises actively participate, and academic and research institutions participate negatively.

Case 2: When W₁+B₁<k₂+k₁+p+rW₂+rW₃, the cost of the government's active promotion of public health technology R&D alliance exceeds the sum of the benefits in its positive state and the losses in its negative state, H₇ (0, 1, 1) is the evolutionary stable point. At this point, the government passively promotes the public health technology R&D alliance, while pharmaceutical enterprises and academic and research institutions actively participate. Due to the complexity, variability, and diffusivity of sudden public health events, substantial funding and resource inputs are necessary. As the institution and implementer of public policy, the government must assume a leading role. In addition, while the government's policy tools can effectively encourage the active participation of pharmaceutical enterprises and academic and research institutions, it is crucial to remain vigilant against the risks of excessive government involvement, which can impose a financial burden that negatively impacts the continuity and stability of policy implementation.

Case 3: When k₁+k₂−B₁+p+rW₂+rW₃<W₁, the cost of the government's policy tools for actively promoting the public health technology R&D alliance is lower than its total revenue, H₈ (1,1,1) is the stable point. At this time, the government actively uses policy tools to promote and guide stakeholders in carrying out technology R&D. Academic and research institutions actively engage in drug and vaccine research and development projects, while pharmaceutical enterprises focus on producing vaccines, drugs, and incubating scientific research initiatives. The active participation of multiple public health entities in technology R&D is the most effective measure for addressing sudden public health events and represents the ideal state. In this system, the “two-wheel drive” of the government and the market positively influences the active involvement of pharmaceutical enterprises and academic and research institutions in the construction of the public health technology R&D alliance, while the government also benefits from reasonable public return income.

Based on the stability analysis of the aforementioned equilibrium point, the ideal evolutionary stable equilibrium should be one where all the entities actively participate, that is, H8 (1, 1, 1), which condition k₁+k₂−B₁+p+rW₂+rW₃<W₁ is met, the system evolution path is shown in Figure 2. The final strategies of the government, pharmaceutical enterprises, and academic and research institutions converge to (1,1,1); that is, the government chooses active incentives, pharmaceutical enterprises choose active participation, and academic and research institutions choose active R&D. This result also verifies the derivation result of situation 3. It can be observed from Figure 2 that pharmaceutical enterprises tend to participate actively at the fastest speed, indicating that these enterprises have the best feedback effect on the market. Next is the government, indicating that it is an important driver of the public health technology R&D alliance. Following this, academic and research institutions indicate that policy-driven approaches are an important direction for optimizing their participation.

The public health technology R&D alliance is focused on sudden public health events. Its key characteristics of short research and development time and high trial and error costs impose greater requirements for the effectiveness of government policy tool combinations. Therefore, from the perspective of government policy tool integration, and based on evolutionary game theory, this paper considers the government, pharmaceutical enterprises, and academic and research institutions as the main players in the game. It constructs an evolutionary game model of the public health technology R&D alliance, analyzes the evolutionary game under different policy incentives, and verifies the findings through numerical simulation. The results show that first, there is a balanced and stable strategy that aligns with the interests of the government, pharmaceutical enterprises, and academic and research institutions. The combination of effective policy tools can promote the establishment of a stable state of emergency science and technology research that is actively supported by the government and enthusiastically participated in by pharmaceutical enterprises and academic and research institutions. Second, different policy tools have varying stimulating effects on the game players. The demand-side product purchase policy can enhance the willingness of multiple players to engage in the public health technology R&D alliance, followed by supply-side financial incentives and environmental-side tax incentives, with enterprises being more sensitive to the feedback from policy tools. Third, the strength of policy tools must be controlled within the scope of science. While the public health technology R&D alliance should leverage the core guidance of the government, it should also activate the contributions of social entities such as pharmaceutical enterprises and academic and research institutions. On the one hand, it should maximize the collaborative efforts of multiple stakeholders, and on the other hand, it should avoid the ‘too little' effect caused by overburdening the government.

Establish a symbiotic and coordinated technology R&D alliance. The formation of a technology R&D alliance is a crucial means to effectively address sudden public health events. It requires the government to actively encourage collaboration, engage in top-level design, and integrate public health resources to build an emergency science and technology research platform. Additionally, developing a normalized public health technology R&D system is essential for gradually improving the efficiency and systematization of emergency science and technology research. Policy tools such as financial incentives, product purchases, and tax incentives should be used to guide emergency management departments, leading pharmaceutical enterprises, key research laboratories, and other related entities to form a public health technology R&D alliance. In the event of a sudden public health crisis, this alliance can quickly mobilize to conduct emergency science and technology research and achieve a rapid response mechanism.

Improve the scientific and efficient interest coordination mechanism. In the face of sudden public health incidents, exploring the common interests of the government, pharmaceutical enterprises, and academic and research institutions is important for the rapid response to emergency science and technology. First, the government should establish reasonable intervals and values according to the specific conditions of each public health issue, combined with quantitative simulation tools. It should adopt appropriate incentive models and safeguard policies for public health entities to improve their initiative to participate in emergency science and technology research. Second, to address the difficulties and interest demands encountered during public health technology R&D, as well as the additional costs associated with major science and technology projects, a corresponding interest compensation mechanism should be implemented to improve the efficiency of technological innovation and the transformation of achievements among public health entities. In addition, further consideration should be given to the impact of opportunity costs on the strategic choices of stakeholders. It is necessary to adjust subsidy measures appropriately to promote the enthusiasm and sense of responsibility of pharmaceutical enterprises and academic and research institutions in drug research and development and key technology research through reputation incentives.

Leverage the combined synergy of policy tools. Due to the differences in the characteristics of multi-alliance subjects and the effects of different policy tools, the combined effects of these tools should be explored in practice. First, the government should exercise reasonable control over the implementation of policy tools, enhance the guiding and stimulating functions of social capital, and avoid the cost burden and crowding-out effect caused by excessive participation. Second, for pharmaceutical enterprises and research institutions, the initial focus should be on strengthening the stimulating effects of policy tools on economic outcomes, while later efforts should shift toward utilizing tax incentives to promote the formation of a positive ecosystem in which multiple stakeholders actively engage in the public health technology R&D alliance.