Monotonicity properties arising in a simple model of Wolbachia invasion for wild mosquito populations.

In this paper, we propose a simplified bidimensional Wolbachia infestation model in a population of Aedes aegypti mosquitoes, preserving the main features associated with the biology of this species that can be found in higher-dimensional models. Namely, our model represents the maternal transmission of the Wolbachia symbiont, expresses the reproductive phenotype of cytoplasmic incompatibility, accounts for different fecundities and mortalities of infected and wild insects, and exhibits the bistable nature leading to the so-called principle of competitive exclusion. Using tools borrowed from monotone dynamical system theory, in the proposed model, we prove the existence of an invariant threshold manifold that allows us to provide practical recommendations for performing single and periodic releases of Wolbachia-carrying mosquitoes, seeking the eventual elimination of wild insects that are capable of transmitting infections to humans. We illustrate these findings with numerical simulations using parameter values corresponding to the wMelPop strain of Wolbachia that is considered the best virus blocker but induces fitness loss in its carriers. In these tests, we considered multiple scenarios contrasting a periodic release strategy against a strategy with a single inundative release, comparing their effectiveness. Our study is presented as an expository and mathematically accessible tool to study the use of Wolbachia-based biocontrol versus more complex models.

Comparison of performance in an anaerobic digestion process: one-reactor vs two-reactor configurations.

The present work compares two types of configurations for a two-reaction (acidogenesis and methanogenesis) anaerobic digestion model. These configurations are as follows: (i) a single bioreactor, where the acidogenesis and methanogenesis reactions occur inside and, (ii) two bioreactors connected sequentially, where each reaction occurs separately in each reactor. The mathematical models that describe the mentioned configurations are analyzed at steady state, comparing the following criteria: the stability of the processes (stability properties of desired equilibria) and soluble organic matter removal performance (substrate levels at steady states), concluding that separation of the reactions in two bioreactors does not improve the stability of the process nor the soluble organic matter removal capacity, unless the improvement of the growth functions of both microorganism populations is considerably important at the moment of separating them into two reactors.