Prediction of viral spillover risk based on the mass action principle.

Infectious zoonotic disease emergence, through spillover events, is of global concern and has the potential to cause significant harm to society, as recently demonstrated by COVID-19. More than 70% of the 400 infectious diseases that emerged in the past five decades have a zoonotic origin, including all recent pandemics. There have been several approaches used to predict the risk of spillover through some of the known or suspected infectious disease emergence drivers, largely using correlative approaches. Here, we predict the spatial distribution of spillover risk by approximating general transmission through animal and human interactions. These mass action interactions are approximated through the multiplication of the spatial distribution of zoonotic virus diversity and human population density. Although our results indicate higher risk in regions along the equator and in Southeast Asia where both virus diversity and human population density are high, it should be noted that this is primarily a conceptual exercise. We compared our spillover risk map to key factors, including the model inputs of zoonotic virus diversity estimate map, human population density map, and the spatial distribution of species richness. Despite the limitations of this approach, this viral spillover map is a step towards developing a more comprehensive spillover risk prediction system to inform global monitoring.

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.

A simple influenza model with complicated dynamics.

We propose and analyse a model for the dynamics of a single strain of an influenza-like infection. The model incorporates waning acquired immunity to infection and punctuated antigenic drift of the virus, employing a set of differential equations within a season and a discrete map between seasons. We show that the between-season map displays a variety of qualitatively different dynamics: fixed points, periodic solutions, or more complicated behaviour suggestive of chaos. For some example parameters we demonstrate the existence of two distinct basins of attraction, that is the initial conditions determine the long term dynamics. Our results suggest that there is no reason to expect influenza dynamics to be regular, or to expect past epidemics to give a clear indication of future seasons' behaviour.

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.

The effect of Wolbachia on dengue dynamics in the presence of two serotypes of dengue: symmetric and asymmetric epidemiological characteristics.

An innovative strategy to reduce dengue transmission uses the bacterium Wolbachia. We analysed the effects of Wolbachia on dengue transmission dynamics in the presence of two serotypes of dengue using a mathematical model, allowing for differences in the epidemiological characteristics of the serotypes. We found that Wolbachia has a greater effect on secondary infections than on primary infections across a range of epidemiological characteristics. If one serotype is more transmissible than the other, it will dominate primary infections and Wolbachia will be less effective at reducing secondary infections of either serotype. Differences in the antibody-dependent enhancement of the two serotypes have considerably less effect on the benefits of Wolbachia than differences in transmission probability. Even if the antibody-dependent enhancement rate is high, Wolbachia is still effective in reducing dengue. Our findings suggest that Wolbachia will be effective in the presence of more than one serotype of dengue; however, a better understanding of serotype-specific differences in transmission probability may be needed to optimize delivery of a Wolbachia intervention.

Modelling the transmission dynamics of dengue in the presence of Wolbachia.

Use of the bacterium Wolbachia is an innovative new strategy designed to break the cycle of dengue transmission. There are two main mechanisms by which Wolbachia could achieve this: by reducing the level of dengue virus in the mosquito and/or by shortening the host mosquito's lifespan. However, although Wolbachia shortens the lifespan, it also gives a breeding advantage which results in complex population dynamics. This study focuses on the development of a mathematical model to quantify the effect on human dengue cases of introducing Wolbachia into the mosquito population. The model consists of a compartment-based system of first-order differential equations; seasonal forcing in the mosquito population is introduced through the adult mosquito death rate. The analysis focuses on a single dengue outbreak typical of a region with a strong seasonally-varying mosquito population. We found that a significant reduction in human dengue cases can be obtained provided that Wolbachia-carrying mosquitoes persist when competing with mosquitoes without Wolbachia. Furthermore, using the Wolbachia strain WMel reduces the mosquito lifespan by at most 10% and allows them to persist in competition with non-Wolbachia-carrying mosquitoes. Mosquitoes carrying the WMelPop strain, however, are not likely to persist as it reduces the mosquito lifespan by up to 50%. When all other effects of Wolbachia on the mosquito physiology are ignored, cytoplasmic incompatibility alone results in a reduction in the number of human dengue cases. A sensitivity analysis of the parameters in the model shows that the transmission probability, the biting rate and the average adult mosquito death rate are the most important parameters for the outcome of the cumulative proportion of human individuals infected with dengue.

How population heterogeneity in susceptibility and infectivity influences epidemic dynamics.

An important concern in public health is what population group should be prioritised for vaccination. To this end, we present an epidemic model with arbitrary initial distributions for population susceptibility, and corresponding infectivity distributions. We consider four scenarios: first, a population with heterogeneous susceptibility with a uniform distribution, but homogeneous infectivity; second, a heterogeneously susceptible population with linear heterogeneous infectivity functions, where the most susceptible are either the most or least infectious; third, a bimodal distribution for susceptibility, with all combinations of infectivity functions; finally, we consider the effects of additional pre-epidemic immunity, ostensibly through vaccination, on the epidemic dynamics. For a seasonal influenza-like infectious disease, we find the smallest final size and overall number of deaths due to the epidemic to occur if the most susceptible are vaccinated, corresponding to targeting children.