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We investigate the impact of differential vaccine effectiveness, waning immunity, and natural cross-immunity on the capacity for vaccine-induced strain replacement in two-strain models of infectious disease spread. We focus specifically on the case where the first strain is more transmissible but the second strain is more immune-resistant. We consider two cases on vaccine-induced immunity: (1) a monovalent model where the second strain has immune escape with respect to vaccination; and (2) a bivalent model where the vaccine remains equally effective against both strains. Our analysis reaffirms the capacity for vaccine-induced strain replacement under a variety of circumstances; surprisingly, however, we find that which strain is preferred depends sensitively on the degree of differential vaccine effectiveness. In general, the monovalent model favors the more immune-resistant strain at high vaccination levels while the bivalent model favors the more transmissible strain at high vaccination levels. To further investigate this phenomenon, we parametrize the bifurcation space between the monovalent and bivalent model. 

The basic reproduction number R0 is a concept which originated in population dynamics, mathematical epidemiology, and ecology and is closely related to the mean number of children in branching processes (reflecting the fact that the phenomena of interest are well approximated via branching processes, at their inception). Despite the very extensive literature around R0 for deterministic epidemic models, we believe there are still aspects which are not fully understood. Foremost is the fact that R0 is not a function of the original ODE model, unless we also include in it a certain (F,V) gradient decomposition, which is not unique. This is related to the specification of the “infected compartments”, which is also not unique. A second interesting question is whether the extinction probabilities of the natural continuous time Markovian chain approximation of an ODE model around boundary points (disease-free equilibrium and invasion points) are also related to the (F,V) gradient decomposition. We offer below several new contributions to the literature: (1) A universal algorithmic definition of a (F,V) gradient decomposition (and hence of the resulting R0). (2) A fixed point equation for the extinction probabilities of a stochastic model associated to a deterministic ODE model, which may be expressed in terms of the (F,V) decomposition. Last but not least, we offer Mathematica scripts and implement them for a large variety of examples, which illustrate that our recipe offers always reasonable results, but that sometimes other reasonable (F,V) decompositions are available as well. 

We introduce a two-strain model with asymmetric temporary immunity periods and partial cross-immunity. We derive explicit conditions for competitive exclusion and coexistence of the strains depending on the strain-specific basic reproduction numbers, temporary immunity periods, and degree of cross-immunity. The results of our bifurcation analysis suggest that, even when two strains share similar basic reproduction numbers and other epidemiological parameters, a disparity in temporary immunity periods and partial or complete cross-immunity can provide a significant competitive advantage. To analyze the dynamics, we introduce a quasi-steady state reduced model which assumes the original strain remains at its endemic steady state. We completely analyze the resulting reduced planar hybrid switching system using linear stability analysis, planar phase-plane analysis, and the Bendixson-Dulac criterion. We validate both the full and reduced models with COVID-19 incidence data, focusing on the Delta (B.1.617.2), Omicron (B.1.1.529), and Kraken (XBB.1.5) variants. These numerical studies suggest that, while early novel strains of COVID-19 had a tendency toward dramatic takeovers and extinction of ancestral strains, more recent strains have the capacity for co-existence. 

Abstract Understanding the connectivity of reef organisms is important to assist in the conservation of biological diversity and to facilitate sustainable fisheries in these ecosystems. Common methods to assess reef connectivity include both population genetics and biophysical modelling. Individually, these techniques can offer insight into population structure; however, the information acquired by any singular analysis is often subject to limitations, underscoring the need for a multi-faceted approach. To assess the connectivity dynamics of the red grouper (Epinephelus morio), an economically important reef fish species found throughout the Gulf of Mexico and USA western Atlantic, we utilized two sets of genetic markers (12 microsatellite loci and 632 single nucleotide polymorphisms) to resolve this species’ population genetic structure, along with biophysical modelling to deliver a spatial forecast of potential larval “sources” and “sinks” across these same regions and spatial scale. Our genetic survey indicates little, if any, evidence of population genetic structure and modelling efforts indicate the potential for ecological connectivity between sampled regions over multiple generations. We offer that using a dual empirical and theoretical approach lessens the error associated with the use of any single method and provides an important step towards the validation of either of these methodologies.