ABSTRACT
In the present work, we study the introduction of a latent interaction index, examining its impact on the formation and development of complex networks. This index takes into account both observed and unobserved heterogeneity per node in order to overcome the limitations of traditional compositional similarity indices, particularly when dealing with large networks comprising numerous nodes. In this way, it effectively captures specific information about participating nodes while mitigating estimation problems based on network structures. Furthermore, we develop a Shannon-type entropy function to characterize the density of networks and establish optimal bounds for this estimation by leveraging the network topology. Additionally, we demonstrate some asymptotic properties of pointwise estimation using this function. Through this approach, we analyze the compositional structural dynamics, providing valuable insights into the complex interactions within the network. Our proposed method offers a promising tool for studying and understanding the intricate relationships within complex networks and their implications under parameter specification. We perform simulations and comparisons with the formation of Erdös-Rényi and Barabási-Alber-type networks and Erdös-Rényi and Shannon-type entropy. Finally, we apply our models to the detection of microbial communities.
ABSTRACT
The dilution and amplification effects are important concepts in the field of zoonotic diseases. While the dilution effect predicts that pathogen prevalence is negatively correlated with increased species diversity, the opposite trend is observed when the amplification effect occurs. Understanding how interspecific interactions such as predation and competition within a community influence disease transmission is highly relevant. We explore the conditions under which the dilution and amplification effects arise, using compartmental models that integrate ecological and epidemiological interactions. We formulate an intraguild predation model where each species is divided into two compartments: susceptible and infected individuals. We obtained that increasing predation increases the disease transmission potential of the predator and the density of infected individuals, but decreases the disease transmission potential of the prey, as well as their density. Also, we found that interspecific competition always helps to decrease the number of infected individuals in the population of the two species. Therefore, dilution and amplification effects can be observed simultaneously but depending on different types of cological interactions.
