Vincent A. A. Jansen

Modelling the influence of human behaviour on the spread of infectious diseases: a review

Human behaviour plays an important role in the spread of infectious diseases, and understanding the influence of behaviour on the spread of diseases can be key to improving control efforts. While behavioural responses to the spread of a disease have often been reported anecdotally, there has been relatively little systematic investigation into how behavioural changes can affect disease dynamics. Mathematical models for the spread of infectious diseases are an important tool for investigating and quantifying such effects, not least because the spread of a disease among humans is not amenable to direct experimental study. Here, we review recent efforts to incorporate human behaviour into disease models, and propose that such models can be broadly classified according to the type and source of information which individuals are assumed to base their behaviour on, and according to the assumed effects of such behaviour. We highlight recent advances as well as gaps in our understanding of the interplay between infectious disease dynamics and human behaviour, and suggest what kind of data taking efforts would be helpful in filling these gaps.

The spread of awareness and its impact on epidemic outbreaks

When a disease breaks out in a human population, changes in behavior in response to the outbreak can alter the progression of the infectious agent. In particular, people aware of a disease in their proximity can take measures to reduce their susceptibility. Even if no centralized information is provided about the presence of a disease, such awareness can arise through first-hand observation and word of mouth. To understand the effects this can have on the spread of a disease, we formulate and analyze a mathematical model for the spread of awareness in a host population, and then link this to an epidemiological model by having more informed hosts reduce their susceptibility. We find that, in a well-mixed population, this can result in a lower size of the outbreak, but does not affect the epidemic threshold. If, however, the behavioral response is treated as a local effect arising in the proximity of an outbreak, it can completely stop a disease from spreading, although only if the infection rate is below a threshold. We show that the impact of locally spreading awareness is amplified if the social network of potential infection events and the network over which individuals communicate overlap, especially so if the networks have a high level of clustering. These findings suggest that care needs to be taken both in the interpretation of disease parameters, as well as in the prediction of the fate of future outbreaks.

Altruism through beard chromodynamics

The evolution of altruism, a behaviour that benefits others at ones own fitness expense, poses a darwinian paradox. The paradox is resolved if many interactions are with related individuals so that the benefits of altruism are reaped by copies of the altruistic gene in other individuals, a mechanism called kin selection. However, recognition of altruists could provide an alternative route towards the evolution of altruism. Arguably the simplest recognition system is a conspicuous, heritable tag, such as a green beard. Despite the fact that such genes have been reported, the ‘green beard effect’ has often been dismissed because it is unlikely that a single gene can code for altruism and a recognizable tag. Here we model the green beard effect and find that if recognition and altruism are always inherited together, the dynamics are highly unstable, leading to the loss of altruism. In contrast, if the effect is caused by loosely coupled separate genes, altruism is facilitated through beard chromodynamics in which many beard colours co-occur. This allows altruism to persist even in weakly structured populations and implies that the green beard effect, in the form of a fluid association of altruistic traits with a recognition tag, can be much more prevalent than hitherto assumed.

QUANTIFYING THE KINETIC PARAMETERS OF PRION REPLICATION

The mechanism of protein-only prion replication is controversial. A detailed mathematical model of prion replication by nucleated polymerisation is developed, and its parameters are estimated from published data. PrP-res decay is around two orders of magnitude slower than PrP-sen decay, a plausible ratio of two parameters estimated from very different experiments. By varying the polymer breakage rate, we reveal that systems of short polymers grow the fastest. Drugs which break polymers could therefore accelerate disease progression. Growth in PrP-res seems slower than growth in infectious titre. This can be explained either by a novel hypothesis concerning inoculum clearance from a newly infected brain, or by the faster growth of compartments containing smaller polymers. The existence of compartments can also explain why prion growth sometimes reaches a plateau. Published kinetic data are all compatible with our mathematical model, so the nucleated polymerisation hypothesis cannot be ruled out on dynamic grounds.

Regulation of predator-prey systems through spatial interactions:a possible solution to the paradox of enrichment.

Many natural predator-prey systems oscillate but persist with densities staying well away from zero. Non-spatial predator-prey models predict that in environments where prey on itself can do well, a predator-prey system can oscillate with troughs in which the populations become vanishingly small. This phenomenon has become known as the paradox of enrichment. In this paper the role of space in bounding overall population oscillations is analysed in the simplest version of spatial predator-prey models: a two-patch model for a Lotka-Volterra system and a Rosenzweig-MacArthur system with logistic prey growth and Holling type II functional response of predator to prey density within each patch. It was found that the spatial interactions can bound the fluctuations of the predator-prey system and regulate predator and prey populations, even in the absence of density dependent processes. The spatial dynamics take the form of locally asynchronous fluctuations. Enrichment of the environment in a two-patch model does not necessarily have the paradoxical consequence that the populations reach densities where extinction is likely to occur.

Pharmacokinetic Principles of Bacteriophage Therapy

Use of bacteriophage to control bacterial infections, including antibioticresistant infections, shows increasing therapeutic promise. Effective bacteriophage therapy requires awareness of various novel kinetic phenomena not known in conventional drug treatments. Kinetic theory predicts that timing of treatment could be critical, with the strange possibility that inoculations given too early could be less effective or fail completely. Another paradoxical result is that adjuvant use of an antibiotic can sometimes diminish the efficacy of phage therapy. For a simple kinetic model, mathematical formulae predict the values of critical density thresholds and critical time points, given as functions of independently measurable biological parameters. Understanding such formulae is important for interpreting data and guiding experimental design. Tailoring pharmacokinetic models for specific systems needs to become standard practice in future studies.

Phage therapy: The peculiar kinetics of self‐replicating pharmaceuticals

The specter of antibiotic‐resistant bacteria has provoked renewed interest in the possible use of bacteriophages to control bacterial infections. We argue that clinical application of phage therapy has been held back by a failure to appreciate the extent to which the pharmacokinetics of self‐replicating agents differ from those of normal drugs. For self‐replicating pharmaceutical agents, treatment outcome depends critically on various density‐dependent thresholds, often with apparently paradoxical consequences. An ability to predict these thresholds and associated critical time points is a necessity if phage therapy is to become clinically practicable.

Quantitative models of in vitro bacteriophage-host dynamics and their application to phage therapy.

Phage therapy is the use of bacteriophages as antimicrobial agents for the control of pathogenic and other problem bacteria. It has previously been argued that successful application of phage therapy requires a good understanding of the non-linear kinetics of phage–bacteria interactions. Here we combine experimental and modelling approaches to make a detailed examination of such kinetics for the important food-borne pathogen Campylobacter jejuni and a suitable virulent phage in an in vitro system. Phage-insensitive populations of C. jejuni arise readily, and as far as we are aware this is the first phage therapy study to test, against in vitro data, models for phage–bacteria interactions incorporating phage-insensitive or resistant bacteria. We find that even an apparently simplistic model fits the data surprisingly well, and we confirm that the so-called inundation and proliferation thresholds are likely to be of considerable practical importance to phage therapy. We fit the model to time series data in order to estimate thresholds and rate constants directly. A comparison of the fit for each culture reveals density-dependent features of phage infectivity that are worthy of further investigation. Our results illustrate how insight from empirical studies can be greatly enhanced by the use of kinetic models: such combined studies of in vitro systems are likely to be an essential precursor to building a meaningful picture of the kinetic properties of in vivo phage therapy.

The Evolution of Parasite Virulence, Superinfection, and Host Resistance

We analyze the evolutionary consequences of host resistance (the ability to decrease the probability of being infected by parasites) for the evolution of parasite virulence (the deleterious effect of a parasite on its host). When only single infections occur, host resistance does not affect the evolution of parasite virulence. However, when superinfections occur, resistance tends to decrease the evolutionarily stable (ES) level of parasite virulence. We first study a simple model in which the host does not coevolve with the parasite (i.e., the frequency of resistant hosts is independent of the parasite). We show that a higher proportion of resistant host decreases the ES level of parasite virulence. Higher levels of the efficiency of host resistance, however, do not always decrease the ES parasite virulence. The implications of these results for virulence management (evolutionary consequences of public health policies) are discussed. Second, we analyze the case where host resistance is allowed to coevolve with parasite virulence using the classical gene‐for‐gene (GFG) model of host‐parasite interaction. It is shown that GFG coevolution leads to lower parasite virulence (in comparison with a fully susceptible host population). The model clarifies and relates the different components of the cost of parasitism: infectivity (ability to infect the host) and virulence (deleterious effect) in an evolutionary perspective.

Endemic disease, awareness, and local behavioural response

The spread of a contagious disease is often accompanied by a rise in awareness of those in the social vicinity of infected individuals, and a subsequent change in behaviour. Such reactions can manifest themselves in lower susceptibility as people try to prevent themselves from catching the disease, but also in lower infectivity because of self-imposed quarantine or better hygiene, shorter durations of infectiousness or longer immunity. We here focus on the scenario of an endemic disease of which members of the population can be either aware or unaware, and consider a broad set of possible reactions. We quantify the impact on the endemicity of a disease in a well-mixed population under the variation of different disease parameters as a consequence of growing awareness in the population. Applying a pair-closure scheme allows us to analyse the effect of local correlations if aware individuals tend to occur near infected cases, and to link this to the amount of overlap between the networks underlying the spread of awareness and disease, respectively. Lastly, we study the consequences on the dynamics when the pathogen and awareness spread at different velocities.