A stochastic mathematical model of methicillin resistant Staphylococcus aureus transmission in an intensive care unit: predicting the impact of interventions

OBJECTIVES: To estimate the transmission rate of MRSA in an intensive care unit (ICU) in an 800 bed Australian teaching hospital and predict the impact of infection control interventions. METHODS: A mathematical model was developed which consisted of four compartments: colonised and uncolonised patients and contaminated and uncontaminated health-care workers (HCWs). Patient movements, MRSA acquisition and daily prevalence data were collected from an ICU over 939 days. Hand hygiene compliance and the probability of MRSA transmission from patient to HCW per discordant contact were measured during the study. Attack rate and reproduction ratio were estimated using Bayesian methods. The impact of a number of interventions on attack rate was estimated using both stochastic and deterministic versions of the model. RESULTS: The mean number of secondary cases arising from the ICU admission of colonised patients, also called the ward reproduction ratio, R(w), was estimated to be 0.50 (95% CI 0.39-0.62). The attack rate was one MRSA transmission per 160 (95% CI 130-210) uncolonised-patient days. Results were not sensitive to uncertainty in measured model parameters (hand hygiene rate and transmission probability per contact). Hand hygiene was predicted to be the most effective intervention. Decolonisation was predicted to be relatively ineffective. Increasing HCW numbers was predicted to increase MRSA transmission, in the absence of patient cohorting. The predictions of the stochastic model differed from those of the deterministic model, with lower levels of colonisation predicted by the stochastic model. CONCLUSIONS: The number of secondary cases of MRSA colonisation within the ICU in this study was below unity. Transmission of MRSA was sustained through admission of colonised patients. Stochastic model simulations give more realistic predictions in hospital ward settings than deterministic models. Increasing staff does not necessarily lead to reduced transmission of nosocomial pathogens.     

Parasite transmission modes and the evolution of virulence

A mathematical model is presented that explores the relationship between transmission patterns and the evolution of virulence for horizontally transmitted parasites when only a single parasite strain can infect each host. The model is constructed by decomposing parasite transmission into two processes, the rate of contact between hosts and the probability of transmission per contact. These transmission rate components, as well as the total parasite mortality rate, are allowed to vary over the course of an infection. A general evolutionarily stable condition is presented that partitions the effects of virulence on parasite fitness into three components: fecundity benefits, mortality costs, and morbidity costs. This extension of previous theory allows us to explore the evolutionary consequences of a variety of transmission patterns. I then focus attention on a special case in which the parasite density remains approximately constant during an infection, and I demonstrate two important ways in which transmission modes can affect virulence evolution: by imposing different morbidity costs on the parasite and by altering the scheduling of parasite reproduction during an infection. Both are illustrated with examples, including one that examines the hypothesis that vector-borne parasites should be more virulent than non-vector-borne parasites (Ewald 1994). The validity of this hypothesis depends upon the way in which these two effects interact, and it need not hold in general.     

Towards a comprehensive simulation model of malaria epidemiology and control

Planning of the control of Plasmodium falciparum malaria leads to a need for models of malaria epidemiology that provide realistic quantitative prediction of likely epidemiological outcomes of a wide range of control strategies. Predictions of the effects of control often ignore medium- and long-term dynamics. The complexities of the Plasmodium life-cycle, and of within-host dynamics, limit the applicability of conventional deterministic malaria models. We use individual-based stochastic simulations of malaria epidemiology to predict the impacts of interventions on infection, morbidity, mortality, health services use and costs. Individual infections are simulated by stochastic series of parasite densities, and naturally acquired immunity acts by reducing densities. Morbidity and mortality risks, and infectiousness to vectors, depend on parasite densities. The simulated infections are nested within simulations of individuals in human populations, and linked to models of interventions and health systems. We use numerous field datasets to optimise parameter estimates. By using a volunteer computing system we obtain the enormous computational power required for model fitting, sensitivity analysis, and exploration of many different intervention strategies. The project thus provides a general platform for comparing, fitting, and evaluating different model structures, and for quantitative prediction of effects of different interventions and integrated control programmes.     

Modelling the effect of urbanization on the transmission of an infectious disease

This paper models the impact of urbanization on infectious disease transmission by integrating a CA land use development model, population projection matrix model and CA epidemic model in S-Plus. The innovative feature of this model lies in both its explicit treatment of spatial land use development, demographic changes, infectious disease transmission and their combination in a dynamic, stochastic model. Heuristically-defined transition rules in cellular automata (CA) were used to capture the processes of both land use development with urban sprawl and infectious disease transmission. A population surface model and dwelling distribution surface were used to bridge the gap between urbanization and infectious disease transmission. A case study is presented involving modelling influenza transmission in Southampton, a dynamically evolving city in the UK. The simulation results for Southampton over a 30-year period show that the pattern of the average number of infection cases per day can depend on land use and demographic changes. The modelling framework presents a useful tool that may be of use in planning applications.     

Interactions between frequency-dependent and vertical transmission in host-parasite systems.

We investigate host-pathogen dynamics and conditions for coexistence in two models incorporating frequency-dependent horizontal transmission in conjunction with vertical transmission. The first model combines frequency-dependent and uniparental vertical transmission, while the second addresses parasites transmitted vertically via both parents. For the first model, we ask how the addition of vertical transmission changes the coexistence criteria for parasites transmitted by a frequency-dependent horizontal route, and show that vertical transmission significantly broadens the conditions for parasite invasion. Host-parasite coexistence is further affected by the form of density-dependent host regulation. Numerical analyses demonstrate that within a host population, a parasite strain with horizontal frequency-dependent transmission can be driven to extinction by a parasite strain that is additionally transmitted vertically for a wide range of parameters. Although models of asexual host populations predict that vertical transmission alone cannot maintain a parasite over time, analysis of our second model shows that vertical transmission via both male and female parents can maintain a parasite at a stable equilibrium. These results correspond with the frequent co-occurrence of vertical with sexual transmission in nature and suggest that these transmission modes can lead to host-pathogen coexistence for a wide range of systems involving hosts with high reproductive rates.     

Inference and dynamic simulation of malaria using a simple climate-driven entomological model of malaria transmission

Given the crucial role of climate in malaria transmission, many mechanistic models of malaria represent vector biology and the parasite lifecycle as functions of climate variables in order to accurately capture malaria transmission dynamics. Lower dimension mechanistic models that utilize implicit vector dynamics have relied on indirect climate modulation of transmission processes, which compromises investigation of the ecological role played by climate in malaria transmission. In this study, we develop an implicit process-based malaria model with direct climate-mediated modulation of transmission pressure borne through the Entomological Inoculation Rate (EIR). The EIR, a measure of the number of infectious bites per person per unit time, includes the effects of vector dynamics, resulting from mosquito development, survivorship, feeding activity and parasite development, all of which are moderated by climate. We combine this EIR-model framework, which is driven by rainfall and temperature, with Bayesian inference methods, and evaluate the model’s ability to simulate local transmission across 42 regions in Rwanda over four years. Our findings indicate that the biologically-motivated, EIR-model framework is capable of accurately simulating seasonal malaria dynamics and capturing of some of the inter-annual variation in malaria incidence. However, the model unsurprisingly failed to reproduce large declines in malaria transmission during 2018 and 2019 due to elevated anti-malaria measures, which were not accounted for in the model structure. The climate-driven transmission model also captured regional variation in malaria incidence across Rwanda’s diverse climate, while identifying key entomological and epidemiological parameters important to seasonal malaria dynamics. In general, this new model construct advances the capabilities of implicitly-forced lower dimension dynamical malaria models by leveraging climate drivers of malaria ecology and transmission.     

Disease-driven reduction in human mobility influences human-mosquito contacts and dengue transmission dynamics

Heterogeneous exposure to mosquitoes determines an individual’s contribution to vector-borne pathogen transmission. Particularly for dengue virus (DENV), there is a major difficulty in quantifying human-vector contacts due to the unknown coupled effect of key heterogeneities. To test the hypothesis that the reduction of human out-of-home mobility due to dengue illness will significantly influence population-level dynamics and the structure of DENV transmission chains, we extended an existing modeling framework to include social structure, disease-driven mobility reductions, and heterogeneous transmissibility from different infectious groups. Compared to a baseline model, naïve to human pre-symptomatic infectiousness and disease-driven mobility changes, a model including both parameters predicted an increase of 37% in the probability of a DENV outbreak occurring; a model including mobility change alone predicted a 15.5% increase compared to the baseline model. At the individual level, models including mobility change led to a reduction of the importance of out-of-home onward transmission (R, the fraction of secondary cases predicted to be generated by an individual) by symptomatic individuals (up to -62%) at the expense of an increase in the relevance of their home (up to +40%). An individual’s positive contribution to R could be predicted by a GAM including a non-linear interaction between an individual’s biting suitability and the number of mosquitoes in their home (>10 mosquitoes and 0.6 individual attractiveness significantly increased R). We conclude that the complex fabric of social relationships and differential behavioral response to dengue illness cause the fraction of symptomatic DENV infections to concentrate transmission in specific locations, whereas asymptomatic carriers (including individuals in their pre-symptomatic period) move the virus throughout the landscape. Our findings point to the difficulty of focusing vector control interventions reactively on the home of symptomatic individuals, as this approach will fail to contain virus propagation by visitors to their house and asymptomatic carriers.     

Elucidating relationships between P.falciparum prevalence and measures of genetic diversity with a combined genetic-epidemiological model of malaria

There is an abundance of malaria genetic data being collected from the field, yet using these data to understand the drivers of regional epidemiology remains a challenge. A key issue is the lack of models that relate parasite genetic diversity to epidemiological parameters. Classical models in population genetics characterize changes in genetic diversity in relation to demographic parameters, but fail to account for the unique features of the malaria life cycle. In contrast, epidemiological models, such as the Ross-Macdonald model, capture malaria transmission dynamics but do not consider genetics. Here, we have developed an integrated model encompassing both parasite evolution and regional epidemiology. We achieve this by combining the Ross-Macdonald model with an intra-host continuous-time Moran model, thus explicitly representing the evolution of individual parasite genomes in a traditional epidemiological framework. Implemented as a stochastic simulation, we use the model to explore relationships between measures of parasite genetic diversity and parasite prevalence, a widely-used metric of transmission intensity. First, we explore how varying parasite prevalence influences genetic diversity at equilibrium. We find that multiple genetic diversity statistics are correlated with prevalence, but the strength of the relationships depends on whether variation in prevalence is driven by host- or vector-related factors. Next, we assess the responsiveness of a variety of statistics to malaria control interventions, finding that those related to mixed infections respond quickly (∼months) whereas other statistics, such as nucleotide diversity, may take decades to respond. These findings provide insights into the opportunities and challenges associated with using genetic data to monitor malaria epidemiology.     

The transmission dynamics of gonorrhoea: modelling the reported behaviour of infected patients from Newark, New Jersey.

A survey of the sexual behaviour of gonorrhoea patients in Newark was undertaken to evaluate parameters within a model of gonorrhoea transmission. Modelling work aimed to explain observed epidemiological patterns and to explore the potential impact of interventions. Reported behaviours, along with values derived from the literature, were used within a standard deterministic model of gonorrhoea transmission, where the population was stratified according to sex and rates of sex-partner change. The behaviours reported, particularly among women, are insufficient by themselves to explain the continued existence of gonorrhoea within the population. The majority of symptomatic patients seek treatment within a few days, and report that they do not have unprotected sex while symptomatic. The proportion of patients with low numbers of sex partners suggests that sexual mixing between people categorized according to sexual behaviour is near random. To explain the persistence of gonorrhoea, there must be some patients who, when infected, do not seek care in public clinics. In addition, gonorrhoea incidence in the model is sensitive to change, such that very small reductions in risk behaviour could lead to its elimination. This does not accord with the observed failure of many interventions to eliminate infection, suggesting that the modelled infection is too sensitive to change. The model, which has been influential in gonorrhoea epidemiology, is not consistent with the observed epidemiology of gonorrhoea in populations. Alternative models need to explore the observed stability of gonorrhoea before robust modelling conclusions can be drawn on how best to control infection. However, the current results do highlight the potential importance of asymptomatic infections and infections in those who are diseased and do not attend public health services. Screening and contact-tracing to identify asymptomatic infections in both men and women will be more effective in reaching those who maintain the infection within the community rather than simply treating symptomatic cases.     

Age-related infection and transmission patterns of human cysticercosis

Neurocysticercosis is recognised as an important but neglected cause of epilepsy in developing countries where the parasite occurs. Data on the transmission dynamics of the parasite in endemic areas are scarce. Individuals living in these areas are likely to be highly exposed to the parasite, but relatively few of them develop active infections. The present study aimed to describe and gain insights into changes in antibody responses and infection patterns related to age and/or gender in a south Ecuadorian rural population by combining antibody and antigen serological data with demographic characteristics. In 25% of the population, antibodies to Taenia solium cysticerci were detected whilst 2.9% had circulating parasite antigens. The proportion of antibody-positive individuals increased significantly until the age of 40 years to become stable in older individuals. A rule-based simulation model was developed to explain these variations and to reflect the dynamics of exposure to, and transmission of, the parasite. In contrast, the proportion of people presenting circulating parasite antigens, reflecting an active infection, was significantly higher in people older than 60 years. Immunosenescence could explain such an observation since a weaker immune system in the elderly would facilitate the establishment and maintenance of viable cysticerci compared with fully immunocompetent younger individuals. This work points out the role of the immune system in the development of cysticercosis within an exposed population and highlights new essential issues in understanding the transmission dynamics of the parasite, its incidence and the resulting immunological response at a population level.     

Malaria transmission blocking immunity and sexual stage vaccines for interrupting malaria transmission in Latin America

Malaria is a vector-borne disease that is considered to be one of the most serious public health problems due to its high global mortality and morbidity rates. Although multiple strategies for controlling malaria have been used, many have had limited impact due to the appearance and rapid dissemination of mosquito resistance to insecticides, parasite resistance to multiple antimalarial drug, and the lack of sustainability. Individuals in endemic areas that have been permanently exposed to the parasite develop specific immune responses capable of diminishing parasite burden and the clinical manifestations of the disease, including blocking of parasite transmission to the mosquito vector. This is referred to as transmission blocking (TB) immunity (TBI) and is mediated by specific antibodies and other factors ingested during the blood meal that inhibit parasite development in the mosquito. These antibodies recognize proteins expressed on either gametocytes or parasite stages that develop in the mosquito midgut and are considered to be potential malaria vaccine candidates. Although these candidates, collectively called TB vaccines (TBV), would not directly stop malaria from infecting individuals, but would stop transmission from infected person to non-infected person. Here, we review the progress that has been achieved in TBI studies and the development of TBV and we highlight their potential usefulness in areas of low endemicity such as Latin America.     

Malaria transmission and morbidity

Stable malaria endemicity is maintained over a wide range of transmission intensities in sub-Saharan Africa. This paper considers variations in the clinical manifestations and their consequences with differences in transmission intensity. Epidemiological approaches to malarial disease have concentrated on two clinical syndromes, severe malarial anaemia and cerebral malaria. Within an area the mean age of children with severe malarial anaemia is always lower than that of those with cerebral malaria. In areas of higher malaria transmission children, on average, encounter malaria at a younger age and the mean age of clinical cases is lower. Malarial anaemia tends therefore to be relatively more important under high transmission settings and cerebral malaria tends to gain in importance under lower transmission settings. In a number of studies the total load of malaria morbidity, whether measured as none severe malaria in the community or as severe malaria admitted to hospital, is low under stable low transmission conditions but is at its highest under moderate intensities of transmission. Thereafter it reaches a plateau, or even falls, at the highest transmission intensities. It is not known whether the same is true for mortality in communities living under different transmission settings. Possible implications for changes in patterns of morbidity and mortality following interventions which lower malaria transmission are discussed. It is concluded that such interventions should play an important role in integrated malaria control programmes but that these should involve concomitant introduction of other interventions, in order to minimise the possible risks of a reduced effect as the immune response of the population re-equilibrates in the face of reduced challenge.     

Modelling the Impact of Artemisinin Combination Therapy and Long-Acting Treatments on Malaria Transmission Intensity

Background

Artemisinin derivatives used in recently introduced combination therapies (ACTs) for Plasmodium falciparum malaria significantly lower patient infectiousness and have the potential to reduce population-level transmission of the parasite. With the increased interest in malaria elimination, understanding the impact on transmission of ACT and other antimalarial drugs with different pharmacodynamics becomes a key issue. This study estimates the reduction in transmission that may be achieved by introducing different types of treatment for symptomatic P. falciparum malaria in endemic areas.

Methods and Findings

We developed a mathematical model to predict the potential impact on transmission outcomes of introducing ACT as first-line treatment for uncomplicated malaria in six areas of varying transmission intensity in Tanzania. We also estimated the impact that could be achieved by antimalarials with different efficacy, prophylactic time, and gametocytocidal effects. Rates of treatment, asymptomatic infection, and symptomatic infection in the six study areas were estimated using the model together with data from a cross-sectional survey of 5,667 individuals conducted prior to policy change from sulfadoxine-pyrimethamine to ACT. The effects of ACT and other drug types on gametocytaemia and infectiousness to mosquitoes were independently estimated from clinical trial data. Predicted percentage reductions in prevalence of infection and incidence of clinical episodes achieved by ACT were highest in the areas with low initial transmission. A 53% reduction in prevalence of infection was seen if 100% of current treatment was switched to ACT in the area where baseline slide-prevalence of parasitaemia was lowest (3.7%), compared to an 11% reduction in the highest-transmission setting (baseline slide prevalence = 57.1%). Estimated percentage reductions in incidence of clinical episodes were similar. The absolute size of the public health impact, however, was greater in the highest-transmission area, with 54 clinical episodes per 100 persons per year averted compared to five per 100 persons per year in the lowest-transmission area. High coverage was important. Reducing presumptive treatment through improved diagnosis substantially reduced the number of treatment courses required per clinical episode averted in the lower-transmission settings although there was some loss of overall impact on transmission. An efficacious antimalarial regimen with no specific gametocytocidal properties but a long prophylactic time was estimated to be more effective at reducing transmission than a short-acting ACT in the highest-transmission setting.

Conclusions

Our results suggest that ACTs have the potential for transmission reductions approaching those achieved by insecticide-treated nets in lower-transmission settings. ACT partner drugs and nonartemisinin regimens with longer prophylactic times could result in a larger impact in higher-transmission settings, although their long term benefit must be evaluated in relation to the risk of development of parasite resistance.     

Determination of the processes driving the acquisition of immunity to malaria using a mathematical transmission model

Acquisition of partially protective immunity is a dominant feature of the epidemiology of malaria among exposed individuals. The processes that determine the acquisition of immunity to clinical disease and to asymptomatic carriage of malaria parasites are poorly understood, in part because of a lack of validated immunological markers of protection. Using mathematical models, we seek to better understand the processes that determine observed epidemiological patterns. We have developed an age-structured mathematical model of malaria transmission in which acquired immunity can act in three ways (“immunity functions”): reducing the probability of clinical disease, speeding the clearance of parasites, and increasing tolerance to subpatent infections. Each immunity function was allowed to vary in efficacy depending on both age and malaria transmission intensity. The results were compared to age patterns of parasite prevalence and clinical disease in endemic settings in northeastern Tanzania and The Gambia. Two types of immune function were required to reproduce the epidemiological age-prevalence curves seen in the empirical data; a form of clinical immunity that reduces susceptibility to clinical disease and develops with age and exposure (with half-life of the order of five years or more) and a form of anti-parasite immunity which results in more rapid clearance of parasitaemia, is acquired later in life and is longer lasting (half-life of >20 y). The development of anti-parasite immunity better reproduced observed epidemiological patterns if it was dominated by age-dependent physiological processes rather than by the magnitude of exposure (provided some exposure occurs). Tolerance to subpatent infections was not required to explain the empirical data. The model comprising immunity to clinical disease which develops early in life and is exposure-dependent, and anti-parasite immunity which develops later in life and is not dependent on the magnitude of exposure, appears to best reproduce the pattern of parasite prevalence and clinical disease by age in different malaria transmission settings. Understanding the effector mechanisms underlying these two immune functions will assist in the design of transmission-reducing interventions against malaria.     

Simulating transmission and control of Taenia solium infections using a Reed-Frost stochastic model

The transmission dynamics of the human-pig zoonotic cestode Taenia solium are explored with both deterministic and stochastic versions of a modified Reed-Frost model. This model, originally developed for microparasitic infections (i.e. bacteria, viruses and protozoa), assumes that random contacts occur between hosts and that hosts can be either susceptible, infected or 'recovered and presumed immune'. Transmission between humans and pigs is modelled as susceptible roaming pigs scavenging on human faeces infected with T. solium eggs. Transmission from pigs to humans is modelled as susceptible humans eating under-cooked pork meat harbouring T. solium metacestodes. Deterministic models of each scenario were first run, followed by stochastic versions of the models to assess the likelihood of infection elimination in the small population modelled. The effects of three groups of interventions were investigated using the model: (i) interventions affecting the transmission parameters such as use of latrines, meat inspection, and cooking habits; (ii) routine interventions including rapid detection and treatment of human carriers or pig vaccination; and (iii) treatment interventions of either humans or pigs. It is concluded that mass-treatment can result in a short term dramatic reduction in prevalence, whereas interventions targeting interruption of the life cycle lead to long-term reduction in prevalence.     

A climate-based distribution model of malaria transmission in sub-Saharan Africa.

Malaria remains the single largest threat to child survival in sub-Saharan Africa and warrants long-term investment for control. Previous malaria distribution maps have been vague and arbitrary. Marlies Craig, Bob Snow and David le Sueur here describe a simple numerical approach to defining distribution of malaria transmission, based upon biological constraints of climate on parasite and vector development. The model compared well with contemporary field data and historical 'expert opinion' maps, excepting small-scale ecological anomalies. The model provides a numerical basis for further refinement and prediction of the impact of climate change on transmission. Together with population, morbidity and mortality data, the model provides a fundamental tool for strategic control of malaria.     

Social foraging: individual learning and cultural transmission of innovations

We present two stochastic models of individual and social learningthat count the number of individuals exhibiting a learned, resource-producingtrait in a group of social foragers. The novelty of our modelingresults from incorporating the empirically based assumptionthat rates of both individual and social learning should dependon the frequency of the learned trait within the group. Whenresources occur as clumps shared by group members, a naive individual'sacquisition of the skill required for clump discovery/productionshould involve opposing processes of frequency dependence. Theopportunity to learn via cultural transmission should increasewith the trait's frequency, but the opportunity for learningindividually should decrease as the trait's frequency increases.The results of the model suggest that the evolution of the capacityfor cultural transmission may be promoted in environments wherescrounging at resource clumps inhibits rates of individual learning.     

Mathematical models of Neospora caninum infection in dairy cattle: transmission and options for control

The transmission and control of Neospora caninum infection in dairy cattle was examined using deterministic and stochastic models. Parameter estimates were derived from recent studies conducted in the UK and from the published literature. Three routes of transmission were considered: maternal vertical transmission with a high probability (0.95), horizontal transmission from infected cattle within the herd, and horizontal transmission from an independent external source. Putative infection via pooled colostrum was used as an example of within-herd horizontal transmission, and the recent finding that the dog is a definitive host of N. caninum supported the inclusion of an external independent source of infection. The predicted amount of horizontal transmission required to maintain infection at levels commonly observed in field studies in the UK and elsewhere, was consistent with that observed in studies of post-natal seroconversion (0.85-9.0 per 100 cow-years). A stochastic version of the model was used to simulate the spread of infection in herds of 100 cattle, with a mean infection prevalence similar to that observed in UK studies (around 20%). The distributions of infected and uninfected cattle corresponded closely to Normal distributions, with S.D.s of 6.3 and 7.0, respectively. Control measures were considered by altering birth, death and horizontal transmission parameters. A policy of annual culling of infected cattle very rapidly reduced the prevalence of infection, and was shown to be the most effective method of control in the short term. Not breeding replacements from infected cattle was also effective in the short term, particularly in herds with a higher turnover of cattle. However, the long-term effectiveness of these measures depended on the amount and source of horizontal infection. If the level of within-herd transmission was above a critical threshold, then a combination of reducing within-herd, and blocking external sources of transmission was required to permanently eliminate infection.     

Host-parasite population dynamics under combined frequency- and density-dependent transmission

Many host‐parasite models assume that transmission increases linearly with host population density (‘density‐dependent transmission’), but various alternative transmission functions have been proposed in an effort to capture the complexity of real biological systems. The most common alternative (usually applied to sexually transmitted parasites) assumes instead that the rate at which hosts contact one another is independent of population density, leading to ‘frequency‐dependent’ transmission. This straight‐forward distinction generates fundamentally different dynamics (e.g. deterministic, parasite‐driven extinction with frequency‐ but not density‐dependence). Here, we consider the situation where transmission occurs through two different types of contact, one of which is density‐dependent (e.g. social contacts), the other density‐independent (e.g. sexual contacts). Drawing on a range of biological examples, we propose that this type of contact structure may be widespread in natural populations. When our model is characterized mainly by density‐dependent transmission, we find that allowing even small amounts of transmission to occur through density‐independent contacts leads to the possibility of deterministic, parasite‐driven extinction (and lowers the threshold for parasite persistence). Contrastingly, allowing some density‐dependent transmission to occur in a model characterized mainly by density‐independent contacts (i.e. by frequency‐dependent transmission) does not affect the extinction threshold, but does increase the likelihood of parasite persistence. The idea that directly transmitted parasites exploit different types of host contact is not new, but here we show that the impact on dynamics can be fundamental even in the simplest cases. For example, in systems where density‐dependent transmission is normally assumed de facto, we show that parasite‐driven extinction can occur if a small amount of transmission occurs through density‐independent contacts. Many empirical studies are still guided by the traditional density/frequency dichotomy, but our combined transmission function may provide a better model for systems in which both types of transmission occur.     

Modelling Parasite Transmission in a Grazing System: The Importance of Host Behaviour and Immunity

Parasitic helminths present one of the most pervasive challenges to grazing herbivores. Many macro-parasite transmission models focus on host physiological defence strategies, omitting more complex interactions between hosts and their environments. This work represents the first model that integrates both the behavioural and physiological elements of gastro-intestinal nematode transmission dynamics in a managed grazing system. A spatially explicit, individual-based, stochastic model is developed, that incorporates both the hosts’ immunological responses to parasitism, and key grazing behaviours including faecal avoidance. The results demonstrate that grazing behaviour affects both the timing and intensity of parasite outbreaks, through generating spatial heterogeneity in parasite risk and nutritional resources, and changing the timing of exposure to the parasites’ free-living stages. The influence of grazing behaviour varies with the host-parasite combination, dependent on the development times of different parasite species and variations in host immune response. Our outputs include the counterintuitive finding that under certain conditions perceived parasite avoidance behaviours (faecal avoidance) can increase parasite risk, for certain host-parasite combinations. Through incorporating the two-way interaction between infection dynamics and grazing behaviour, the potential benefits of parasite-induced anorexia are also demonstrated. Hosts with phenotypic plasticity in grazing behaviour, that make grazing decisions dependent on current parasite burden, can reduce infection with minimal loss of intake over the grazing season. This paper explores how both host behaviours and immunity influence macro-parasite transmission in a spatially and temporally heterogeneous environment. The magnitude and timing of parasite outbreaks is influenced by host immunity and behaviour, and the interactions between them; the incorporation of both regulatory processes is required to fully understand transmission dynamics. Understanding of both physiological and behavioural defence strategies will aid the development of novel approaches for control.