How immune dynamics shape multi-season epidemics: a continuous-discrete model in one dimensional antigenic space

We extend a previously published model for the dynamics of a single strain of an influenza-like infection. The model incorporates a waning acquired immunity to infection and punctuated antigenic drift of the virus, employing a set of coupled integral equations within a season and a discrete map between seasons. The long term behaviour of the model is demonstrated by examples where immunity to infection depends on the time since a host was last infected, and where immunity depends on the number of times that a host has been infected. The first scenario leads to complicated dynamics in some regions of parameter space, and to regions of parameter space with more than one attractor. The second scenario leads to a stable fixed point, corresponding to an identical epidemic each season. We also examine the model with both paradigms in combination, almost always but not exclusively observing a stable fixed point or periodic solution. Adding stochastic perturbations to the between season map fails to destroy the model's qualitative dynamics. Our results suggest that if the level of host immunity depends on the elapsed time since the last infection then the epidemiological dynamics may be unpredictable.

A model for malaria treatment evaluation in the presence of multiple species

Plasmodium falciparum and P. vivax are the two most common causes of malaria. While the majority of deaths and severe morbidity are due to P. falciparum, P. vivax poses a greater challenge to eliminating malaria outside of Africa due to its ability to form latent liver stage parasites (hypnozoites), which can cause relapsing episodes within an individual patient. In areas where P. falciparum and P. vivax are co-endemic, individuals can carry parasites of both species simultaneously. These mixed infections complicate dynamics in several ways: treatment of mixed infections will simultaneously affect both species, P. falciparum can mask the detection of P. vivax, and it has been hypothesised that clearing P. falciparum may trigger a relapse of dormant P. vivax. When mixed infections are treated for only blood-stage parasites, patients are at risk of relapse infections due to P. vivax hypnozoites. We present a stochastic mathematical model that captures interactions between P. falciparum and P. vivax, and incorporates both standard schizonticidal treatment (which targets blood-stage parasites) and radical cure treatment (which additionally targets liver-stage parasites). We apply this model via a hypothetical simulation study to assess the implications of different treatment coverages of radical cure for mixed and P. vivax infections and a "unified radical cure" treatment strategy where P. falciparum, P. vivax, and mixed infections all receive radical cure after screening glucose-6-phosphate dehydrogenase (G6PD) normal. In addition, we investigated the impact of mass drug administration (MDA) of blood-stage treatment. We find that a unified radical cure strategy leads to a substantially lower incidence of malaria cases and deaths overall. MDA with schizonticidal treatment was found to decrease P. falciparum with little effect on P. vivax. We perform a univariate sensitivity analysis to highlight important model parameters.

SAfE transport: wearing face masks significantly reduces the spread of COVID-19 on trains

COVID-19 has had a substantial impact globally. It spreads readily, particularly in enclosed and crowded spaces, such as public transport carriages, yet there are limited studies on how this risk can be reduced. We developed a tool for exploring the potential impacts of mitigation strategies on public transport networks, called the Systems Analytics for Epidemiology in Transport (SAfE Transport). SAfE Transport combines an agent-based transit assignment model, a community-wide transmission model, and a transit disease spread model to support strategic and operational decision-making. For this simulated COVID-19 case study, the transit disease spread model incorporates both direct (person-to-person) and fomite (person-to-surface-to-person) transmission modes. We determine the probable impact of wearing face masks on trains over a seven day simulation horizon, showing substantial and statistically significant reductions in new cases when passenger mask wearing proportions are greater than 80%. The higher the level of mask coverage, the greater the reduction in the number of new infections. Also, the higher levels of mask coverage result in an earlier reduction in disease spread risk. These results can be used by decision makers to guide policy on face mask use for public transport networks.

The effect of Wolbachia on dengue outbreaks when dengue is repeatedly introduced

Use of the Wolbachia bacterium is a proposed new strategy to reduce dengue transmission, which results in around 390 million individuals infected annually. In places with strong variations in climatic conditions such as temperature and rainfall, dengue epidemics generally occur only at a certain time of the year. Where dengue is not endemic, the time of year in which imported cases enter the population plays a crucial role in determining the likelihood of outbreak occurrence. We use a mathematical model to study the effects of Wolbachia on dengue transmission dynamics and dengue seasonality. We focus in regions where dengue is not endemic but can spread due to the presence of a dengue vector and the arrival of people with dengue on a regular basis. Our results show that the time-window in which outbreaks can occur is reduced in the presence of Wolbachia-carrying Aedes aegypti mosquitoes by up to six weeks each year. We find that Wolbachia reduces overall case numbers by up to 80%. The strongest effect is obtained when the amplitude of the seasonal forcing is low (0.02-0.30). The benefits of Wolbachia also depend on the transmission rate, with the bacteria most effective at moderate transmission rates ranging between 0.08-0.12. Such rates are consistent with fitted estimates for Cairns, Australia.