Evolutionary simulation of governments' pandemic control strategies in presence of infection probability

doi:10.16265/j.cnki.issn1003-3033.2023.03.0835

Abstract

Abstract:

In order to effectively curb the rapid spread of major public health emergencies, taking COVID-19 as an example, firstly, a government-public evolutionary game model considering the probability of infection was constructed to depict the game relationship between the government and the public. Then, the key factors affecting the evolution of the government and public behavior were analyzed through the model solution. Finally, MATLAB simulation analysis was carried out based on the actual situation of the evolution of the epidemic in Wuhan to verify the validity and feasibility of the model and conclusions. Results indicate that infection probability plays an indispensable role in the selection of strategies of the government and the public. When the probability of infection is small, and the cost of government is greater than the benefit, the system eventually evolves into a stable state in which the government responds passively and the public does not exercise self-discipline. When the infection probability reaches a fixed value and the revenue of the government is less than cost, the increase of punishment on the public would slow down the response time of government and the public. However, in terms of the same situation, the increase of punishment on the government is useful to upgrade their response efficiency. In addition, it is conducive to enhancing the probability of the selection of self-discipline strategies for the public, which can promote the development of the epidemic in a better direction.

Key words: infection probability, epidemic prevention control, evolutionary game, major public health emergency, punishment mechanism

LI Xiaoli, CAO Cejun, LIU Weihua, ZHANG Fanshun. Evolutionary simulation of governments' pandemic control strategies in presence of infection probability[J]. China Safety Science Journal, 2023, 33(3): 42-50.

Figures/Tables 16

Tab.1

Game payment between the public and the government

公众	政府部门
公众	积极管控y	消极应对(1-y)
自律x	$P - C, R g - C g$	$P - C$ , 0
不自律 (1-x)	$(1 - β) P - D - β S - C 1, R g - C g$	$(1 - α) P - α S, - α M$

Tab.1

Tab.2

Local stability analysis of case 1

约束条件	$D < C - C 1 - β (P + S)$			$D > C - C 1 - β (P + S)$
平衡点	trJ	detJ	局部稳定性	trJ	detJ	局部稳定性
F₁(0,0)	-	+	稳定点	-	+	稳定点
F₂(0,1)	±	-	鞍点	+	+	不稳定点
F₃(1,0)	±	-	鞍点	±	-	鞍点
F₄(1,1)	+	+	不稳定点	±	-	鞍点
K (x^, y^)	0	±	鞍点	0	±	鞍点

Tab.2

Tab.3

Tab.4

Local stability analysis of case 3

约束条件	$D < C - C 1 - β (P + S)$			$D > C - C 1 - β (P + S)$
平衡点	trJ	detJ	局部稳定性	trJ	detJ	局部稳定性
F₁(0,0)	±	-	鞍点	±	-	鞍点
F₂(0,1)	±	-	鞍点	+	+	不稳定点
F₃(1,0)	-	+	稳定点	-	+	稳定点
F₄(1,1)	+	+	不稳定点	±	-	鞍点
K (x^, y^)	0	±	鞍点	0	±	鞍点

Tab.4

Tab.5

Tab.6

Local stability analysis of case 5

约束条件	$α < C P + S$			$α > C P + S$
平衡点	trJ	detJ	局部稳定性	trJ	detJ	局部稳定性
F₁(0,0)	±	-	鞍点	+	+	不稳定点
F₂(0,1)	-	+	稳定点	-	+	稳定点
F₃(1,0)	+	+	不稳定点	±	-	鞍点
F₄(1,1)	±	-	鞍点	±	-	鞍点
K (x^, y^)	0	±	鞍点	0	±	鞍点

Tab.6

Tab.7

Local stability analysis of case 6

约束条件	$α > C P + S$			$α < C P + S$
平衡点	trJ	detJ	局部稳定性	trJ	detJ	局部稳定性
F₁(0,0)	+	+	不稳定点	±	-	鞍点
F₂(0,1)	±	-	鞍点	±	-	鞍点
F₃(1,0)	±	-	鞍点	+	+	不稳定点
F₄(1,1)	-	+	稳定点	-	+	稳定点
K (x^, y^)	0	±	鞍点	0	±	鞍点

Tab.7

Tab.8

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

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发展阶段	时间	阶段特征
初期阶段	2019-12-12— 2020-01-22	武汉发现不明原因肺炎,但由于对疫情认识不足,政府部门并未正式发布“人传人”的相关信息,且未采取任何防控措施,公众也并未意识到病毒的高传染性,仍正常流动
快速发展与爆发期阶段	2020-01-23— 2020-02-22	传染病学专家钟南山院士确认了新型冠状病毒肺炎“人传人”的特征,政府通过官方渠道发布此重要信息,并积极采取交通管制、社区管控等措施。然而,由于疫情具有较高的不确定性,政府暂不能完全准确的把握疫情的演变趋势,公众的危机意识有待进一步加强,政府的各项管控措施、法律法规仍在建设与完善中
减缓期阶段	2020-02-22— 2020-03-23	疫情经过一定时间的发展,在全国引起普遍重视,武汉公众的危机意识已全面建立起来。并且,由于中央的高度重视与积极干预,不惜人力、财力、物力,对湖北省各级地方政府进行补贴,减轻了地方政府的财政压力
平稳期阶段	2020-03-24— 2022-12-03	尽管武汉疫情很快得到控制,但由于国外疫情的迅速蔓延,使武汉仍然面临一定程度的境外及省外输入风险