4.3.1. Influence of Knowledge about VA Use Specification on Farmer's Behavioral Choices

The farmers were randomly distributed in the simulation area at the start of the simulation and then interacted with each other over time. Repeated experiments revealed relatively obvious curve changes when the value of knowledge of VA use specification, *ϕi*1, was set to 1, 2, 3, and 5. Figure 2 reflects the co-variation between knowledge about VA use specification and behavioral choices of pig farmers. As shown in Figure 2, the behavioral choices of farmers appeared to have some regularity under the four different parameter settings of VA use knowledge of farmers—likelihood of good VA use behavior increases with increasing knowledge about VS use specification. When the value of *ϕi*<sup>1</sup> was 1, that is, the farmers generally have a low level of knowledge of VA use specification, there was a high probability of improper VA use, fluctuating between 95% and 100%, in the farmer group, as shown in Figure 2a. The probability of improper VA use decreased gradually when the value of *ϕi*<sup>1</sup> changed from 1 to 2 and 3. When *ϕi*<sup>1</sup> = 3, the probabilities of proper and improper uses fluctuated around 50%. When *ϕi*<sup>1</sup> further increased to 5, the probability of improper VA use was significantly lower than that of proper use. The above findings indicated that the probability of improper VA use decreased with an increase in the farmers' knowledge of VA use specification. This was consistent with the conclusion of Wu [26]. However, the probability of improper VA use was still higher than that of proper use. Only when the level of knowledge was sufficiently high were farmers inclined to use VAs properly. Also, such result echoes to the finding of Pham and colleagues [27] that the farmers seldom know the real and specific purpose of using VA. Therefore, persistent improvement of pig farmers' knowledge about VA use specification plays a fundamental role in promoting proper VA use. Note that in the model, the x-axis represents a parameter of time, but we did not specifically assign a time unit for that parameter. By not specifying time period can extend the flexibility and generalizability of the models and results [24].

**Figure 2.** Simulation results of the changes of farmers' behavioral choices regarding VA use under the variation of their knowledge about VA use specification: (**a**) the value of *ϕi*<sup>1</sup> (the farmers' knowledge of VA use specification) was set to 1; (**b**) the value of *ϕi*<sup>1</sup> was set to 2; (**c**) the value of *ϕi*<sup>1</sup> was set to 3; (**d**) the value of *ϕi*<sup>1</sup> was set to 5.

4.3.2. Influence of Knowledge about the Hazards of VA Residues on Farmer's Behavioral Choices

Figure 3 demonstrates the relationship between farmers' knowledge about the hazards of VA residues on the behavioral choices of them. As can be seen from Figure 3a (*ϕi*<sup>2</sup> = 1), when farmers

had no knowledge about the hazards of VA residues, there was a high probability of improper VA use, fluctuating around 90%, in the farmer group. This result was consistent with the survey finding that respondents with improper VA use had a poor knowledge about the hazards of VA residues. Moreover, the probability of proper VA use increased significantly when the whole group's knowledge about the hazards of VA residues increased to a certain level, as shown in Figure 3b. When *ϕi*<sup>2</sup> = 3, the probabilities of improper and proper VA use fluctuated between 40% and 60%. A comparison of Figure 3b (*ϕi*<sup>2</sup> = 3) and 3c (*ϕi*<sup>2</sup> = 4) indicated that the probability of improper VA use did not significantly decrease with the further increase in knowledge about the hazards of VA residues. One possible reason is the difficulties in government regulation due to decentralized farming. Moreover, the economic benefits from improper VA use in pig farming are attractive enough for most farmers due to the general absence of strict supervision and punishment by the government [26]. Therefore, it is necessary to educate farmers about the hazards of improper VA use, and at the same time impose financial penalties for improper VA use to reduce willful misconduct.

**Figure 3.** Simulation results of the changes of farmers' behavioral choices regarding VA use under the variation of their knowledge about hazards of VA residues: (**a**) the value of *ϕi*<sup>2</sup> (knowledge of hazards of VA residues) was set to 1; (**b**) the value of *ϕi*<sup>2</sup> was set to 3; (**c**) the value of *ϕi*<sup>2</sup> was set to 4.
