Extinction times in the subcritical stochastic SIS logistic epidemic

Many real epidemics of an infectious disease are not straightforwardly super- or sub-critical, and the understanding of epidemic models that exhibit such complexity has been identified as a priority for theoretical work. We provide insights into the near-critical regime by considering the stochastic SIS logistic epidemic, a well-known birth-and-death chain used to model the spread of an epidemic within a population of a given size $N$. We study the behaviour of the process as the population size $N$ tends to infinity. Our results cover the entire subcritical regime, including the "barely subcritical" regime, where the recovery rate exceeds the infection rate by an amount that tends to 0 as $N \to \infty$ but more slowly than $N^{-1/2}$. We derive precise asymptotics for the distribution of the extinction time and the total number of cases throughout the subcritical regime, give a detailed description of the course of the epidemic, and compare to numerical results for a range of parameter values. We hypothesise that features of the course of the epidemic will be seen in a wide class of other epidemic models, and we use real data to provide some tentative and preliminary support for this theory.Comment: Revised; 34 pages; 6 figure

Bacterial killing by complement requires membrane attack complex formation via surface-bound C5 convertases

The immune system kills bacteria by the formation of lytic membrane attack complexes (MACs), triggered when complement enzymes cleave C5. At present, it is not understood how the MAC perturbs the composite cell envelope of Gram-negative bacteria. Here, we show that the role of C5 convertase enzymes in MAC assembly extends beyond the cleavage of C5 into the MAC precursor C5b. Although purified MAC complexes generated from preassembled C5b6 perforate artificial lipid membranes and mammalian cells, these components lack bactericidal activity. In order to permeabilize both the bacterial outer and inner membrane and thus kill a bacterium, MACs need to be assembled locally by the C5 convertase enzymes. Our data indicate that C5b6 rapidly loses the capacity to form bactericidal pores; therefore, bacterial killing requires both in situ conversion of C5 and immediate insertion of C5b67 into the membrane. Using flow cytometry and atomic force microscopy, we show that local assembly of C5b6 at the bacterial surface is required for the efficient insertion of MAC pores into bacterial membranes. These studies provide basic molecular insights into MAC assembly and bacterial killing by the immune system

Self-Interest versus Group-Interest in Antiviral Control

Antiviral agents have been hailed to hold considerable promise for the treatment and prevention of emerging viral diseases like H5N1 avian influenza and SARS. However, antiviral drugs are not completely harmless, and the conditions under which individuals are willing to participate in a large-scale antiviral drug treatment program are as yet unknown. We provide population dynamical and game theoretical analyses of large-scale prophylactic antiviral treatment programs. Throughout we compare the antiviral control strategy that is optimal from the public health perspective with the control strategy that would evolve if individuals make their own, rational decisions. To this end we investigate the conditions under which a large-scale antiviral control program can prevent an epidemic, and we analyze at what point in an unfolding epidemic the risk of infection starts to outweigh the cost of antiviral treatment. This enables investigation of how the optimal control strategy is moulded by the efficacy of antiviral drugs, the risk of mortality by antiviral prophylaxis, and the transmissibility of the pathogen. Our analyses show that there can be a strong incentive for an individual to take less antiviral drugs than is optimal from the public health perspective. In particular, when public health asks for early and aggressive control to prevent or curb an emerging pathogen, for the individual antiviral drug treatment is attractive only when the risk of infection has become non-negligible. It is even possible that from a public health perspective a situation in which everybody takes antiviral drugs is optimal, while the process of individual choice leads to a situation where nobody is willing to take antiviral drugs

Effects of infection-induced migration delays on the epidemiology of avian influenza in wild mallard populations

Wild waterfowl populations form a natural reservoir of Avian Influenza (AI) virus, and fears exist that these birds may contribute to an AI pandemic by spreading the virus along their migratory flyways. Observational studies suggest that individuals infected with AI virus may delay departure from migratory staging sites. Here, we explore the epidemiological dynamics of avian influenza virus in a migrating mallard (Anas platyrhynchos) population with a specific view to understanding the role of infection-induced migration delays on the spread of virus strains of differing transmissibility. We develop a host-pathogen model that combines the transmission dynamics of influenza with the migration, reproduction and mortality of the host bird species. Our modeling predicts that delayed migration of individuals influences both the timing and size of outbreaks of AI virus. We find that (1) delayed migration leads to a lower total number of cases of infection each year than in the absence of migration delay, (2) when the transmission rate of a strain is high, the outbreak starts at the staging sites at which birds arrive in the early part of the fall migration, (3) when the transmission rate is low, infection predominantly occurs later in the season, which is further delayed when there is a migration delay. As such, the rise of more virulent AI strains in waterfowl could lead to a higher prevalence of infection later in the year, which could change the exposure risk for farmed poultry. A sensitivity analysis shows the importance of generation time and loss of immunity for the effect of migration delays. Thus, we demonstrate, in contrast to many current transmission risk models solely using empirical information on bird movements to assess the potential for transmission, that a consideration of infection-induced delays is critical to understanding the dynamics of AI infection along the entire flyway.<br /

Man Bites Mosquito: Understanding the Contribution of Human Movement to Vector-Borne Disease Dynamics

In metropolitan areas people travel frequently and extensively but often in highly structured commuting patterns. We investigate the role of this type of human movement in the epidemiology of vector-borne pathogens such as dengue. Analysis is based on a metapopulation model where mobile humans connect static mosquito subpopulations. We find that, due to frequency dependent biting, infection incidence in the human and mosquito populations is almost independent of the duration of contact. If the mosquito population is not uniformly distributed between patches the transmission potential of the pathogen at the metapopulation level, as summarized by the basic reproductive number, is determined by the size of the largest subpopulation and reduced by stronger connectivity. Global extinction of the pathogen is less likely when increased human movement enhances the rescue effect but, in contrast to classical theory, it is not minimized at an intermediate level of connectivity. We conclude that hubs and reservoirs of infection can be places people visit frequently but briefly and the relative importance of human and mosquito populations in maintaining the pathogen depends on the distribution of the mosquito population and the variability in human travel patterns. These results offer an insight in to the paradoxical observation of resurgent urban vector-borne disease despite increased investment in vector control and suggest that successful public health intervention may require a dual approach. Prospective studies can be used to identify areas with large mosquito populations that are also visited by a large fraction of the human population. Retrospective studies can be used to map recent movements of infected people, pinpointing the mosquito subpopulation from which they acquired the infection and others to which they may have transmitted it

Single-molecule kinetics of pore assembly by the membrane attack complex

The membrane attack complex (MAC) is a hetero-oligomeric protein assembly that kills pathogens by perforating their cell envelopes. The MAC is formed by sequential assembly of soluble complement proteins C5b, C6, C7, C8 and C9, but little is known about the rate-limiting steps in this process. Here, we use rapid atomic force microscopy (AFM) imaging to show that MAC proteins oligomerize within the membrane, unlike structurally homologous bacterial pore-forming toxins. C5b-7 interacts with the lipid bilayer prior to recruiting C8. We discover that incorporation of the first C9 is the kinetic bottleneck of MAC formation, after which rapid C9 oligomerization completes the pore. This defines the kinetic basis for MAC assembly and provides insight into how human cells are protected from bystander damage by the cell surface receptor CD59, which is offered a maximum temporal window to halt the assembly at the point of C9 insertion