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The abuse of opioids is harmful to the national economy and health. The U.S. government has spent a lot of time, energy and money to deal with this phenomenon. Based on the topic background and team discussion, we deeply excavated the data and information provided in the topic, determined the current use of opioids, and constructed an improved SIR model to determine the source of drug abuse, the mechanism of drug abuse diffusion and the origin of each state through reverse derivation, which provided guidance for the government in the context of opioid abuse.Based on the above results, we simulated and analyzed the improved SIR model and determined the accuracy and stability of the model in the data set.

Despite tendencies toward convergence, differences between individuals and groups continue to exist in beliefs, attitudes, and behavior. An agent-based adaptive model reveals the effects of a mechanism of convergent social influence. The actors are placed at fixed sites. The basic premise is that the more similar an actor is to a neighbor, the more likely that that actor will adopt one of the neighbor's traits. Unlike previous models of social influence or cultural change that treat features one at a time, the proposed model takes into account the interaction between different features. The model illustrates how local convergence can generate global polarization. Simulations show that the number of stable homogeneous regions decreases with the number of features, increases with the number of alternative traits per feature, decreases with the range of interaction, and (most surprisingly) decreases when the geographic territory grows beyond a certain size.

With the wide applications of the communication networks, the topic of information networks security is getting more and more attention from governments and individuals. This paper is devoted to investigating a malware propagation model with carrier compartment and delay to describe the process of malware propagation in mobile wireless sensor networks. Based on matrix theory for characteristic values, the local stability criterion of equilibrium points is established. Applying the linear approximation method of nonlinear systems, we study the existence of Hopf bifurcation at the equilibrium points. At the same time, we identify some sensitive parameters in the process of malware propagation. Finally, numerical simulations are performed to illustrate the theoretical results.

We connect three characteristics of political candidates: their preferences, their platforms, and their valence. To do so, we define and study three types of elite polarization: preference polarization, valence polarization, and platform polarization. In our model, policy is represented as a position in a unidimensional space; candidates are policy motivated; valence is represented as a dimension orthogonal to policy; and candidates can increase their valence by paying a cost. We find that candidates will in general not converge to one another in the policy dimension or in the valence dimension. A candidate's preferences are positively, but not perfectly, correlated with her platform. Strikingly, under some circumstances, candidates' platforms will diverge when their preferences converge. And there is an unfortunate trade-off regarding candidates' attributes: they will display high valence or low polarization, but not both. One of our empirical predictions is a positive correlation between campaign spending and platform polarization. Adapted from the source document.

Michael Wallace reports a very pronounced curvilinear relationship between a new measure of the polarization of the state system and warfare during 1815-1964. He suggests considerable caution when interpreting the results and urges replication. This is a replication. Given the original cautions, the additional ones made here, and the results of a reanalysis, the conclusion is clear. There is no relationship—linear, monotonic, or nonmonotonic—between polarization and the number, severity, or magnitude of international wars during the period 1815-1976.

We offer a theory of polarization as an optimal response to ambiguity. Suppose individual A's beliefs first-order stochastically dominate individual B's. They observe a common signal. They exhibit polarization if A's posterior dominates her prior and B's prior dominates her posterior. Given agreement on conditional signal likelihoods, we show that polarization is impossible under Bayesian updating or after observing extreme signals. However, we also show that polarization can arise after intermediate signals as ambiguity averse individuals implement their optimal prediction strategies. We explore when this polarization will occur and the logic underlying it. (JEL D81, D82, D83)