Daniel Maxin

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.

A two-sex demographic model with single-dependent divorce rate

Divorce appears to be one of the least studied demographic processes, both empirically and in two-sex demographic models. In this paper, we study mathematical as well as biological implications of the assumption that the divorce rate is positively affected by the amount of single (i.e., unmarried/unpaired) individuals in the population. We do that by modifying the classical exponential two-sex model accounting for pair formation and separation. We model the divorce rate as an increasing function of the single population size and show that the single population pressure on the established couples alters the exponential behavior of the classical model in which the divorce rate is assumed constant. In particular, the total population size becomes bounded and a unique positive equilibrium exists. In addition, a Hopf bifurcation analysis around the positive equilibrium shows that the modified model may exhibit sustained oscillations.

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 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 Lyapunovs 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.

Why have parasites promoting mating success been observed so rarely

Host manipulation by sexually transmitted parasites which increases host mating rate and thus parasite transmission rate has long been viewed as a plausible parasite adaptation. However, empirical evidence for it is rare. Here, using an adaptive dynamics approach to evolution, we explore conditions under which such disease-induced mating enhancement is (or is not) likely to occur. We find that increased mating success is less likely to evolve if the host reproduction rate, or the baseline disease transmission rate, is reduced, and the parasite affects just one sex, compared to when it affects both. We also find that it is less likely to evolve if the virulence-transmission trade-off curve is stronger, since we assume that enhanced disease transmission can only be achieved at the cost of increased virulence and as this trade-off is concave. In addition, we demonstrate that if disease-induced mating enhancement is equally acting in both sexes the mating system has no effect on evolutionary outcomes. On the contrary, if disease-induced mating enhancement is acting in just one sex, the potential for its evolution increases with the degree of polygyny in the host population. To study the examined phenomenon in greater detail we encourage further empirical research on this apparently less explored impact of sexually transmitted parasites on host fitness.

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.

A generalized two-sex logistic model

We provide a generalization of the logistic two-sex model with ephemeral pair-bonds and with stable couples without assuming any specific mathematical form for fertility, mortality and the mating function. In particular, we establish a necessary and sufficient condition on the fertility/mortality density-dependent ratio that ensures the existence of the logistic behaviour. Several differences and similarities between the two models are also provided.

The impact of sexually abstaining groups on persistence of sexually transmitted infections in populations with ephemeral pair bonds

Individuals often stop reproducing some time before they die. In this paper we compose and analyze a logistic two-sex population model in which individuals form pairs just to mate (i.e. pair bonds are ephemeral) and later move on to sexually abstaining groups. Using this model, we study the impact of sexually abstaining groups on persistence of a benign sexually transmitted infection (STI) in populations with such ephemeral pair bonds. We observe that the presence of sexually abstaining groups cannot prevent an STI from invasion or eliminate it when already present if the transition rates to the sexually abstaining groups are independent of the infection status of individuals (susceptible or infected). On the other hand, if they depend on that status, the presence of sexually abstaining groups can prevent an STI from invasion or eliminate it when present. Specifically, in the simple case of sex-independent vital parameters, this happens if the transition rate of the infected individuals to the sexually abstaining group is higher than the transition rate of the susceptible ones. These results contrast the earlier results based on assuming long-term, stable pair bonds, in which case one is capable of preventing or eliminating the disease with the same isolation rate for the susceptible and infected individuals.

Global stability results for models of commensalism

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.

The Effect of Risk-taking Behaviour in Epidemic Models

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.