Vaccination, if available, is the best preventive measure against infectious diseases. It is, however, needed to prudently design vaccination strategies to successfully mitigate the disease spreading, especially in a time when vaccine scarcity is inevitable. Here we investigate a vaccination strategy on a scale-free network where susceptible individuals, who have social connections with infected people, are being detected and given vaccination before having any physical contact with the infected one. Nevertheless, detecting susceptible (also infected ones) may not be perfect due to the lack of information. Also, vaccines do not confer perfect immunity in reality. We incorporate these pragmatic hindrances in our analysis. We find that if vaccines are highly efficacious, and the detecting error is low, then it is possible to confine the disease spreading—by administering a less amount of vaccination—within a short period. In a situation where tracing susceptible seems difficult, then expanding the range for vaccination targets can be socially advantageous only if vaccines are effective enough. Our analysis further reveals that a more frequent screening for vaccination can reduce the effect of detecting errors. In the end, we present a link percolation-based analytic method to approximate the results of our simulation.
Imitation and aspiration learning rules are frequently observed in humans and animals. The former is an act of copying other’s action, whereas the latter is characterized by the self-evaluation. Here we study the coexistence of these learning mechanisms in structured populations. Both rules have been combined focusing on two different scenarios: (I) adoption of either update rule with a certain probability, and (II) grouping the entire population according to the update rules. We present two pair approximation models, illustrating both scenarios, which yield a nice agreement—under weak selection—with that of agent-based simulations. For weak selection and large population size, we find that the condition for cooperation to dominate defection is similar in both heterogeneous and homogeneous update rules. We examine several variants of the mixed model such as time-evolving aspirations alongside strategies and the coevolution of strategies and update rules. In the former case, our simulation reveals that Prisoner’s dilemma and, in some cases, Stag-hunt experience overall less aspiration levels compared to other games such as Chicken or Trivial. The coevolution of strategies and update rules demonstrates a better cooperation, in contrast to the fixed update rule case, exhibiting the possibility of asymptotic coexistence of both learning mechanisms.
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