Summary Continual effort is needed to reduce the impact of exotic species in the context of increased globalization. Any innovation in this respect would be an asset. We assess the potential of combining two pest control techniques: the well‐established sterile insect technique (SIT) and a novel male‐killing technique (MKT), which comprises inoculation of a pest population with bacteria that kill the infected male embryos. Population models are developed to assess the efficiency of using the MKT for insect pest control, either alone or together with the SIT. We seek for conditions under which the MKT weakens requirements on the SIT. Regarding the SIT, we consider both non‐heritable and inherited sterility. In both cases, the MKT and SIT benefit one another. The MKT may prevent the SIT from failing when not enough sterilized males are released due to high production costs and/or uncertainty on their mating ability following a high irradiation dose. Conversely, with already established SIT, pest eradication can be achieved after introduction of male‐killing bacteria with lower vertical transmission efficiency than if the MKT was applied alone. For tephritid fruit flies with non‐heritable sterility, maximal impact of the SIT is achieved when the released males are fully sterile. Conversely, for lepidopterans with inherited sterility, maximal impact of the SIT is achieved for intermediate irradiation doses. In both cases, increasing vertical transmission efficiency of male‐killing bacteria benefits the SIT; high enough vertical transmission efficiency allows for pest eradication where the SIT is absent or induces only pest suppression when used alone. Synthesis and applications. While both techniques can suppress or eliminate the pest on their own, combined application of the male‐killing technique and the sterile insect technique substantially increases pest control efficiency. If male‐killing bacteria are already established in the pest, any assessment of the sterile insect technique needs to account for their presence; otherwise, management recommendations could be exaggerated and unnecessarily costly.
We analyze the dynamics of three models of mutualism, establishing the global stability of coexisting equilibria by means of Lyapunov's second method. This further establishes the usefulness of certain Lyapunov functionals of an abstract nature introduced in an earlier paper. As a consequence, it is seen that the use of higher order self-limiting terms cures the shortcomings of Lotka-Volterra mutualisms, preventing unbounded growth and promoting global stability.
Early male-killing (MK) bacteria are vertically transmitted reproductive parasites which kill male offspring that inherit them. Whereas their incidence is well documented, characteristics allowing originally non-MK bacteria to gradually evolve MK ability remain unclear. We show that horizontal transmission is a mechanism enabling vertically transmitted bacteria to evolve fully efficient MK under a wide range of host and parasite characteristics, especially when the efficacy of vertical transmission is high. We also show that an almost 100% vertically transmitted and 100% effective male-killer may evolve from a purely horizontally transmitted non-MK ancestor, and that a 100% efficient male-killer can form a stable coexistence only with a non-MK bacterial strain. Our findings are in line with the empirical evidence on current MK bacteria, explain their high efficacy in killing infected male embryos and their variability within and across insect taxa, and suggest that they may have evolved independently in phylogenetically distinct species.
We analyze the global stability of the coexisting equilibria for several models of commensalism, first by devising a procedure to modify several Lyapunov functionals which were introduced earlier for corresponding models of mutualism, further confirming their usefulness. It is seen that commensalism promotes global stability, in connection with higher-order self-limiting terms which prevent unboundedness. We then use the theory of asymptotically autonomous systems to prove global stability results for models of commensalism which are subject to Allee effects, finding that commensalisms of appropriate strength can overcome the influence of strong Allee effects.
We study an epidemic model that incorporates risk-taking behaviour as a response to a perceived low prevalence of infection that follows from the administration of an effective treatment or vaccine. We assume that knowledge about the number of infected, recovered and vaccinated individuals has an effect in the contact rate between susceptible and infectious individuals. We show that, whenever optimism prevails in the risk behaviour response, the fate of an epidemic may change from disease clearance to disease persistence. Moreover, under certain conditions on the parameters, increasing the efficiency of vaccine and/or treatment has the unwanted effect of increasing the epidemic reproductive number, suggesting a wider range of diseases may become endemic due to risk-taking alone. These results indicate that the manner in which treatment/vaccine effectiveness is advertised can have an important influence on how the epidemic unfolds.
We describe several population models exposed to a mild life-long sexually transmitted disease, i.e. without significant increased mortality among infected individuals and providing no immunity/recovery. We then modify these models to include non-reproductive groups consisting of those isolated from sexual contact and those who are sexually active but infertile due to choice, medical or other reasons. We analyse the potential effect on the dynamics of the population. We are interested in how the isolated class may curb the growth of the infected group while keeping the healthy population at acceptable levels. We also analyse the difference between being sexually active and abstained within the non-reproductive class and its impact on the epidemic reproductive number and the nature of the bifurcation around the disease-free equilibrium. We provide a comparison with our models introduced in a previous article, which include only the isolated from sexual contact class.
Models of sexually transmitted infections have become a fixture of mathematical epidemiology. A common attribute of all these models is treating reproduction and mating, and hence pathogen transmission, as uncoupled events. This is fine for humans, for example, where only a tiny fraction of sexual intercourses ends up with having a baby. But it can be a deficiency for animals in which mating and giving birth are tightly coupled, and mating thus mediates both reproduction and pathogen transmission. Here, we model dynamics of sterilizing, sexually transmitted infections in such animals, assuming structural consistency between the processes of reproduction and pathogen transmission. We show that highly sterilizing, sexually transmitted pathogens trigger bistability in the host population. In particular, the host population can end up in two extreme alternative states, disease-free persistence and pathogen-driven extinction, depending on its initial state. Given that sterilizing, sexually transmitted infections that affect animals are abundant, our results might implicate an effective pest control tactic that consists of releasing the corresponding pathogens, possibly after genetically enhancing their sterilization power.
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