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This work aims mainly to study the controllability of pertussis infection in the presence of waning and natural booster of pertussis immunity and to study their impact on the overall dynamics and disease outcomes. Therefore, an SIVRWS (Susceptible-Infected-Vaccinated-Recovered-Waned-Susceptible) model for pertussis infection spread in a demographically stationary, homogeneous, and fully symmetric mixing population is introduced. The model has been mathematically analyzed, where both equilibrium and stability analyses have been established, and uniform persistence of the model has been shown. The conditions on model parameters that ensure effective control of the infection have been derived. The effects of the interplay between waning and boosting pertussis immunity by re-exposure to Bordetella pertussis and vaccination on the dynamics have been investigated. The analytical results have been numerically confirmed and explained. The analysis reveals that ignoring the natural booster of immunity overestimates the endemic prevalence of the infection. Moreover, ignoring the differential susceptibility between secondary and primary susceptible individuals overestimates the critical vaccination coverage required to eliminate the infection. Moreover, the shorter the period of immunity acquired by either vaccination or experiencing natural infection, the higher the reproduction number and the endemic prevalence of infection, and therefore, the higher the effort needed to eliminate the infection. 

Low-lying coastal cities across the world are vulnerable to the combined impact of rainfall and storm tide. However, existing approaches lack the ability to model the combined effect of these flood mechanisms, especially under climate change and sea level rise (SLR). Thus, to increase flood resilience of coastal cities, modeling techniques to improve the understanding and prediction of the combined effect of these flood hazards are critical. To address this need, this study presents a modeling system for assessing the combined flood impact on coastal cities under selected future climate scenarios that leverages ocean modeling with land surface modeling capable of resolving urban drainage infrastructure within the city. The modeling approach is demonstrated in quantifying the impact of possible future climate scenarios on transportation infrastructure within Norfolk, Virginia, USA. A series of combined storm events are modeled for current (2020) and projected future (2070) climate scenarios. The results show that pluvial flooding causes a larger interruption to the transportation network compared to tidal flooding under current climate conditions. By 2070, however, tidal flooding will be the dominant flooding mechanism with even nuisance flooding expected to happen daily due to SLR. In 2070, nuisance flooding is expected to cause a 4.6% total link close time (TLC), which is more than two times that of a 50-year storm surge (1.8% TLC) in 2020. The coupled flood model was compared with a widely used but physically simplistic bathtub method to assess the difference resulting from the more complex modeling presented in this study. The results show that the bathtub method overestimated the flooded area near the shoreline by 9.5% and 3.1% for a 10-year storm surge event in 2020 and 2070, respectively, but underestimated the flooded area in the inland region by 9.0% and 4.0% for the same events. The findings demonstrate the benefit of sophisticated modeling methods compared to more simplistic bathtub approaches, in climate adaptive planning and policy in coastal communities. 

We have previously suggested that a shift from bee to hummingbird pollination, in concert with floral architecture modifications, occurred at the crown of Salvia subgenus Calosphace in North America ca. 20 mya (Kriebel et al. 2020 and references therein). Sazatornil et al. (2022), using a hidden states model, challenged these assertions, arguing that bees were the ancestral pollinator of subg. Calosphace and claiming that hummingbirds could not have been the ancestral pollinator of subg. Calosphace because hummingbirds were not contemporaneous with crown subg. Calosphace in North America. Here, using a variety of models, we demonstrate that most analyses support hummingbirds as ancestral pollinators of subg. Calosphace and show that Sazatornil et al. (2022) erroneously concluded that hummingbirds were absent from North America ca. 20 mya. We contend that “biological realism” – based on timing and placement of hummingbirds in Mexico ca. 20 mya and the correlative evolution of hummingbird associated floral traits – must be considered when comparing models based on fit and complexity, including hidden states models.