The cumulative effect of risk compensation on infection preventive measures.

We study several epidemic models (with and without gender structure) that incorporate risk compensation behavior in response to a lower chance of acquiring the infection as a result of preventive measures that are only partially effective. We show that the cumulative risk compensation that occurs between a high risk susceptible and infectious individual may play an important role in whether the implementation of these measures is successful in lowering the epidemic reproductive number. In addition, we show that certain levels of risk compensation may cancel the benefit of the low infection risk practiced by diagnosed infectious individuals when the goal is a reduction of the epidemic reproductive number.

The global stability of coexisting equilibria for three models of mutualism.

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.

Evolution of early male-killing in horizontally transmitted parasites.

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.

Is more better? Higher sterilization of infected hosts need not result in reduced pest population size.

We analyze the effect of sterilization in the infected hosts in several epidemiological models involving infectious diseases that can be transmitted both vertically and horizontally. Sterilizing pathogens can be used as pest control agents by intentionally inoculating the target population, with the goal of reducing or eliminating it completely. Contrary to previous models that did not include vertical transmission we found that the population size at the endemic equilibrium may actually increase with higher levels of sterility. This effect is proved to exist for low to high efficiencies of vertical transmission. On the other hand, if the disease is sexually transmitted and the host reproduction and disease transmission are both consistently mediated by mating, we do not observe such a counter-intuitive effect and the population size in the stable endemic equilibrium is decreasing with higher levels of sterility. We suggest that models of the pest control techniques involving the release of sterilizing pathogens have to carefully consider the routes such pathogens use for transmission.

Fatal or harmless: extreme bistability induced by sterilizing, sexually transmitted pathogens.

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.

Double impact of sterilizing pathogens: added value of increased life expectancy on pest control effectiveness.

Sterilizing pathogens are commonly assumed not to affect longevity of infected individuals, and if they do then negatively. Examples abound, however, of species in which the absence of reproduction actually increases life expectancy. This happens because by decreasing the energy outlay on reproduction individuals with lowered reproduction can live longer. Alternatively, fertile individuals are more susceptible to predators or parasitoids if the latter can capitalize on mating signals of the former. Here we develop and analyze an SI epidemiological model to explore whether and to what extent does such a life expectancy prolongation due to sterilizing pathogens affect host dynamics. In particular, we are interested in an added value of increased life expectancy on the possibility of successful pest control, that is, the effect of increased lifespan and hence increased potential of the infected individuals to spread the disease on pest control effectiveness. We show that although the parameter range in which we observe an effect of increased lifespan of the sterilized individuals is not large, the effect itself can be significant. In particular, the increase in pest control effectiveness can be very dramatic when disease transmission efficiency is close to birth rate, mortality rate of susceptibles is relatively high (i.e., the species is relatively short-lived), and sterilization efficiency is relatively high. Our results thus characterize pathogens that are promising candidates for an effective pest control and that might possibly be engineered if not occurring naturally.

The role of sexually abstained groups in two-sex demographic and epidemic logistic models with non-linear mortality.

We describe several gender structured population models governed by logistic growth with non-linear death rate. We extend these models to include groups of people isolated from sexual activity and individuals exposed to a mild and long-lasting sexually transmitted disease, i.e. without disease-induced mortality and recovery. The transmission of the disease is modeled through formation/separation of heterosexual couples assuming that one infected individual automatically infects his/her partner. We are interested in how the non-reproductive class may change the demographic tendencies in the general population and whether they can curb the growth of the infected group while keeping the healthy one at acceptable levels. A comparison of the equilibrium total population size in the presence and the absence of the isolated class is also provided.

The influence of sexually active non-reproductive groups on persistent sexually transmitted diseases.

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.

The effect of nonreproductive groups on persistent sexually transmitted diseases.

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 groups isolated from sexual contact and analyze their 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.