Synthesising 30 Years of Mathematical Modelling of Echinococcus Transmission

Background

Echinococcosis is a complex zoonosis that has domestic and sylvatic lifecycles, and a range of different intermediate and definitive host species. The complexities of its transmission and the sparse evidence on the effectiveness of control strategies in diverse settings provide significant challenges for the design of effective public health policy against this disease. Mathematical modelling is a useful tool for simulating control packages under locally specific transmission conditions to inform optimal timing and frequency of phased interventions for cost-effective control of echinococcosis. The aims of this review of 30 years of Echinococcus modelling were to discern the epidemiological mechanisms underpinning models of Echinococcus granulosus and E. multilocularis transmission and to establish the need to include a human transmission component in such models.

Methodology/Principal Findings

A search was conducted of all relevant articles published up until July 2012, identified from the PubMED, Web of Knowledge and Medline databases and review of bibliographies of selected papers. Papers eligible for inclusion were those describing the design of a new model, or modification of an existing mathematical model of E. granulosus or E. multilocularis transmission. A total of 13 eligible papers were identified, five of which described mathematical models of E. granulosus and eight that described E. multilocularis transmission. These models varied primarily on the basis of six key mechanisms that all have the capacity to modulate model dynamics, qualitatively affecting projections. These are: 1) the inclusion of a ‘latent’ class and/or time delay from host exposure to infectiousness; 2) an age structure for animal hosts; 3) the presence of density-dependent constraints; 4) accounting for seasonality; 5) stochastic parameters; and 6) inclusion of spatial and risk structures.

Conclusions/Significance

This review discusses the conditions under which these mechanisms may be important for inclusion in models of Echinococcus transmission and proposes recommendations for the design of dynamic human models of transmission. Accounting for the dynamic behaviour of the Echinococcus parasites in humans will be key to predicting changes in the disease burden over time and to simulate control strategies that optimise public health impact.     

Transmission and Control of Plasmodium knowlesi: A Mathematical Modelling Study

Introduction

Plasmodium knowlesi is now recognised as a leading cause of malaria in Malaysia. As humans come into increasing contact with the reservoir host (long-tailed macaques) as a consequence of deforestation, assessing the potential for a shift from zoonotic to sustained P. knowlesi transmission between humans is critical.

Methods

A multi-host, multi-site transmission model was developed, taking into account the three areas (forest, farm, and village) where transmission is thought to occur. Latin hypercube sampling of model parameters was used to identify parameter sets consistent with possible prevalence in macaques and humans inferred from observed data. We then explore the consequences of increasing human-macaque contact in the farm, the likely impact of rapid treatment, and the use of long-lasting insecticide-treated nets (LLINs) in preventing wider spread of this emerging infection.

Results

Identified model parameters were consistent with transmission being sustained by the macaques with spill over infections into the human population and with high overall basic reproduction numbers (up to 2267). The extent to which macaques forage in the farms had a non-linear relationship with human infection prevalence, the highest prevalence occurring when macaques forage in the farms but return frequently to the forest where they experience higher contact with vectors and hence sustain transmission. Only one of 1,046 parameter sets was consistent with sustained human-to-human transmission in the absence of macaques, although with a low human reproduction number (R_0H = 1.04). Simulations showed LLINs and rapid treatment provide personal protection to humans with maximal estimated reductions in human prevalence of 42% and 95%, respectively.

Conclusion

This model simulates conditions where P. knowlesi transmission may occur and the potential impact of control measures. Predictions suggest that conventional control measures are sufficient at reducing the risk of infection in humans, but they must be actively implemented if P. knowlesi is to be controlled.     

Identifying Malaria Transmission Foci for Elimination Using Human Mobility Data

Humans move frequently and tend to carry parasites among areas with endemic malaria and into areas where local transmission is unsustainable. Human-mediated parasite mobility can thus sustain parasite populations in areas where they would otherwise be absent. Data describing human mobility and malaria epidemiology can help classify landscapes into parasite demographic sources and sinks, ecological concepts that have parallels in malaria control discussions of transmission foci. By linking transmission to parasite flow, it is possible to stratify landscapes for malaria control and elimination, as sources are disproportionately important to the regional persistence of malaria parasites. Here, we identify putative malaria sources and sinks for pre-elimination Namibia using malaria parasite rate (PR) maps and call data records from mobile phones, using a steady-state analysis of a malaria transmission model to infer where infections most likely occurred. We also examined how the landscape of transmission and burden changed from the pre-elimination setting by comparing the location and extent of predicted pre-elimination transmission foci with modeled incidence for 2009. This comparison suggests that while transmission was spatially focal pre-elimination, the spatial distribution of cases changed as burden declined. The changing spatial distribution of burden could be due to importation, with cases focused around importation hotspots, or due to heterogeneous application of elimination effort. While this framework is an important step towards understanding progressive changes in malaria distribution and the role of subnational transmission dynamics in a policy-relevant way, future work should account for international parasite movement, utilize real time surveillance data, and relax the steady state assumption required by the presented model.     

Defining the In Vivo Phenotype of Artemisinin-Resistant Falciparum Malaria: A Modelling Approach

BackgroundArtemisinin-resistant falciparum malaria has emerged in Southeast Asia, posing a major threat to malaria control. It is characterised by delayed asexual-stage parasite clearance, which is the reference comparator for the molecular marker ‘Kelch 13’ and in vitro sensitivity tests. However, current cut-off values denoting slow clearance based on the proportion of individuals remaining parasitaemic on the third day of treatment (''day-3''), or on peripheral blood parasite half-life, are not well supported. We here explore the parasite clearance distributions in an area of artemisinin resistance with the aim refining the in vivo phenotypic definitions.ConclusionsCharacterisation of overlapping distributions of parasite half-lives provides quantitative insight into the relationship between parasite clearance and artemisinin resistance, as well as the predictive value of the 10% cut-off in ''day-3'' parasitaemia. The findings are important for the interpretation of in vitro sensitivity tests and molecular markers for artemisinin resistance and for contextualising the ‘day 3’ threshold to account for initial parasitaemia and sample size.     

Mathematical Modelling of the MAP Kinase Pathway Using Proteomic Datasets

The advances in proteomics technologies offer an unprecedented opportunity and valuable resources to understand how living organisms execute necessary functions at systems levels. However, little work has been done up to date to utilize the highly accurate spatio-temporal dynamic proteome data generated by phosphoprotemics for mathematical modeling of complex cell signaling pathways. This work proposed a novel computational framework to develop mathematical models based on proteomic datasets. Using the MAP kinase pathway as the test system, we developed a mathematical model including the cytosolic and nuclear subsystems; and applied the genetic algorithm to infer unknown model parameters. Robustness property of the mathematical model was used as a criterion to select the appropriate rate constants from the estimated candidates. Quantitative information regarding the absolute protein concentrations was used to refine the mathematical model. We have demonstrated that the incorporation of more experimental data could significantly enhance both the simulation accuracy and robustness property of the proposed model. In addition, we used the MAP kinase pathway inhibited by phosphatases with different concentrations to predict the signal output influenced by different cellular conditions. Our predictions are in good agreement with the experimental observations when the MAP kinase pathway was inhibited by phosphatase PP2A and MKP3. The successful application of the proposed modeling framework to the MAP kinase pathway suggests that our method is very promising for developing accurate mathematical models and yielding insights into the regulatory mechanisms of complex cell signaling pathways.     

Controlling Malaria Using Livestock-Based Interventions: A One Health Approach

Where malaria is transmitted by zoophilic vectors, two types of malaria control strategies have been proposed based on animals: using livestock to divert vector biting from people (zooprophylaxis) or as baits to attract vectors to insecticide sources (insecticide-treated livestock). Opposing findings have been obtained on malaria zooprophylaxis, and despite the success of an insecticide-treated livestock trial in Pakistan, where malaria vectors are highly zoophilic, its effectiveness is yet to be formally tested in Africa where vectors are more anthropophilic. This study aims to clarify the different effects of livestock on malaria and to understand under what circumstances livestock-based interventions could play a role in malaria control programmes. This was explored by developing a mathematical model and combining it with data from Pakistan and Ethiopia. Consistent with previous work, a zooprophylactic effect of untreated livestock is predicted in two situations: if vector population density does not increase with livestock introduction, or if livestock numbers and availability to vectors are sufficiently high such that the increase in vector density is counteracted by the diversion of bites from humans to animals. Although, as expected, insecticide-treatment of livestock is predicted to be more beneficial in settings with highly zoophilic vectors, like South Asia, we find that the intervention could also considerably decrease malaria transmission in regions with more anthropophilic vectors, like Anopheles arabiensis in Africa, under specific circumstances: high treatment coverage of the livestock population, using a product with stronger or longer lasting insecticidal effect than in the Pakistan trial, and with small (ideally null) repellency effect, or if increasing the attractiveness of treated livestock to malaria vectors. The results suggest these are the most appropriate conditions for field testing insecticide-treated livestock in an Africa region with moderately zoophilic vectors, where this intervention could contribute to the integrated control of malaria and livestock diseases.     

QTL形态标记定位的一种数学方法

根据家蚕中位于Z染色体上的伴性遗传的双形态标记和假定与其有连锁关系的一个具有一对主基因差异的数量性状在测交世代中,所作的理论分布,本文建立了QTL形态标记定位的数学方法,即频数分布面积法,并给出了相应的检测一对主基因在测交世代中的同分离比例及其与形态标记是否有连锁关系的X2统计量．这种定位方法亦适应于非伴性遗传方式的QTL形态标记定位．与单标记定位的极大似然方法相比,我们的方法所作的双标记定位能显示QTL与形态标记发生重组的交叉干步作用,并且定位结果不受作用于数量性状的环境效应所影响．     

Investigating the Contribution of Peri-domestic Transmission to Risk of Zoonotic Malaria Infection in Humans

BackgroundIn recent years, the primate malaria Plasmodium knowlesi has emerged in human populations throughout South East Asia, with the largest hotspot being in Sabah, Malaysian Borneo. Control efforts are hindered by limited knowledge of where and when people get exposed to mosquito vectors. It is assumed that exposure occurs primarily when people are working in forest areas, but the role of other potential exposure routes (including domestic or peri-domestic transmission) has not been thoroughly investigated.Conclusions/SignificanceThis study shows there is a possibility that humans can be exposed to P. knowlesi infection around their homes. The vector is highly exophagic and few were caught indoors indicating interventions using bednets inside households may have relatively little impact.     

Mapping Risk of Nipah Virus Transmission from Bats to Humans in Thailand

Nipah virus (NiV) is a zoonotic virus that can pose a serious threat to human and livestock health. Old-world fruit bats (Pteropus spp.) are the natural reservoir hosts for NiV, and Pteropus lylei, Lyle’s flying fox, is an important host of NiV in mainland Southeast Asia. NiV can be transmitted from bats to humans directly via bat-contaminated foods (i.e., date palm sap or fruit) or indirectly via livestock or other intermediate animal hosts. Here we construct risk maps for NiV spillover and transmission by combining ecological niche models for the P. lylei bat reservoir with other spatial data related to direct or indirect NiV transmission (livestock density, foodborne sources including fruit production, and human population). We predict the current and future (2050 and 2070) distribution of P. lylei across Thailand, Cambodia, and Vietnam. Our best-fit model predicted that central and western regions of Thailand and small areas in Cambodia are currently the most suitable habitats for P. lylei. However, due to climate change, the species range is predicted to expand to include lower northern, northeastern, eastern, and upper southern Thailand and almost all of Cambodia and lower southern Vietnam. This expansion will create additional risk areas for human infection from P. lylei in Thailand. Our combined predictive risk maps showed that central Thailand, inhabited by 2.3 million people, is considered highly suitable for the zoonotic transmission of NiV from P. lylei. These current and future NiV transmission risk maps can be used to prioritize sites for active virus surveillance and developing awareness and prevention programs to reduce the risk of NiV spillover and spread in Thailand.

     

Analysis of a Vector-Bias Model on Malaria Transmission

We incorporate a vector-bias term into a malaria-transmission model to account for the greater attractiveness of infectious humans to mosquitoes in terms of differing probabilities that a mosquito arriving at a human at random picks that human depending on whether he is infectious or susceptible. We prove that transcritical bifurcation occurs at the basic reproductive ratio equalling 1 by projecting the flow onto the extended centre manifold. We next study the dynamics of the system when incubation time of malaria parasites in mosquitoes is included, and find that the longer incubation time reduces the prevalence of malaria. Also, we incorporate a random movement of mosquitoes as a diffusion term and a chemically directed movement of mosquitoes to humans expressed in terms of sweat and body odour as a chemotaxis term to study the propagation of infected population to uninfected population. We find that a travelling wave occurs; its speed is calculated numerically and estimated for the lower bound analytically.     

Seasonally Dependent Relationships between Indicators of Malaria Transmission and Disease Provided by Mathematical Model Simulations

Evaluating the effectiveness of malaria control interventions on the basis of their impact on transmission as well as impact on morbidity and mortality is becoming increasingly important as countries consider pre-elimination and elimination as well as disease control. Data on prevalence and transmission are traditionally obtained through resource-intensive epidemiological and entomological surveys that become difficult as transmission decreases. This work employs mathematical modeling to examine the relationships between malaria indicators allowing more easily measured data, such as routine health systems data on case incidence, to be translated into measures of transmission and other malaria indicators. Simulations of scenarios with different levels of malaria transmission, patterns of seasonality and access to treatment were run with an ensemble of models of malaria epidemiology and within-host dynamics, as part of the OpenMalaria modeling platform. For a given seasonality profile, regression analysis mapped simulation results of malaria indicators, such as annual average entomological inoculation rate, prevalence, incidence of uncomplicated and severe episodes, and mortality, to an expected range of values of any of the other indicators. Results were validated by comparing simulated relationships between indicators with previously published data on these same indicators as observed in malaria endemic areas. These results allow for direct comparisons of malaria transmission intensity estimates made using data collected with different methods on different indicators. They also address key concerns with traditional methods of quantifying transmission in areas of differing transmission intensity and sparse data. Although seasonality of transmission is often ignored in data compilations, the models suggest it can be critically important in determining the relationship between transmission and disease. Application of these models could help public health officials detect changes of disease dynamics in a population and plan and assess the impact of malaria control interventions.     

Localization of Canine Brachycephaly Using an Across Breed Mapping Approach

The domestic dog, Canis familiaris, exhibits profound phenotypic diversity and is an ideal model organism for the genetic dissection of simple and complex traits. However, some of the most interesting phenotypes are fixed in particular breeds and are therefore less tractable to genetic analysis using classical segregation-based mapping approaches. We implemented an across breed mapping approach using a moderately dense SNP array, a low number of animals and breeds carefully selected for the phenotypes of interest to identify genetic variants responsible for breed-defining characteristics. Using a modest number of affected (10–30) and control (20–60) samples from multiple breeds, the correct chromosomal assignment was identified in a proof of concept experiment using three previously defined loci; hyperuricosuria, white spotting and chondrodysplasia. Genome-wide association was performed in a similar manner for one of the most striking morphological traits in dogs: brachycephalic head type. Although candidate gene approaches based on comparable phenotypes in mice and humans have been utilized for this trait, the causative gene has remained elusive using this method. Samples from nine affected breeds and thirteen control breeds identified strong genome-wide associations for brachycephalic head type on Cfa 1. Two independent datasets identified the same genomic region. Levels of relative heterozygosity in the associated region indicate that it has been subjected to a selective sweep, consistent with it being a breed defining morphological characteristic. Genotyping additional dogs in the region confirmed the association. To date, the genetic structure of dog breeds has primarily been exploited for genome wide association for segregating traits. These results demonstrate that non-segregating traits under strong selection are equally tractable to genetic analysis using small sample numbers.     

Mapping Biological Transmission: An Empirical,Dynamical, and Evolutionary Approach

The current debate over extending inheritance and its evolutionary impact has focused on adding new categories of non-genetic factors to the classical transmission of DNA, and on trying to redefine inheritance. Transmitted factors have been mainly characterized by their directions of transmission (vertical, horizontal, or both) and the way they store variations. In this paper, we leave aside the issue of defining inheritance. We rather try to build an evolutionary conceptual framework that allows for tracing most, if not all forms of transmission and makes sense of their different tempos and modes. We discuss three key distinctions that should in particular be the targets of theoretical and empirical investigation, and try to assess the interplay among them and evolutionary dynamics. We distinguish two channels of transmission (channel 1 and channel 2), two measurements of the temporal dynamics of transmission, respectively across and within generations (durability and residency), and two types of transmitted factors according to their evolutionary relevance (selectively relevant and neutral stable factors). By implementing these three distinctions we can then map different forms of transmission over a continuous space describing the combination of their varying dynamical features. While our aim is not to provide yet another model of inheritance, putting together these distinctions and crossing them, we manage to offer an inclusive conceptual framework of transmission, grounded in empirical observation, and coherent with evolutionary theory. This interestingly opens possibilities for qualitative and quantitative analyses, and is a necessary step, we argue, in order to question the interplay between the dynamics of evolution and the dynamics of multiple forms of transmission.     

Impact of Vaccination on 14 High-Risk HPV Type Infections: A Mathematical Modelling Approach

The development of high-risk human papillomavirus (hrHPV) infection to cervical cancer is a complicated process. We considered solely hrHPV infections, thus avoiding the confounding effects of disease progression, screening, and treatments. To analyse hrHPV epidemiology and to estimate the overall impact of vaccination against infections with hrHPVs, we developed a dynamic compartmental transmission model for single and multiple infections with 14 hrHPV types. The infection-related parameters were estimated using population-based sexual behaviour and hrHPV prevalence data from Finland. The analysis disclosed the important role of persistent infections in hrHPV epidemiology, provided further evidence for a significant natural immunity, and demonstrated the dependence of transmission probability estimates on the model structure. The model predicted that vaccinating girls at 80% coverage will result in a 55% reduction in the overall hrHPV prevalence and a higher 65% reduction in the prevalence of persistent hrHPV infections in females. In males, the reduction will be 42% in the hrHPV prevalence solely by the herd effect from the 80% coverage in girls. If such high coverage among girls is not reached, it is still possible to reduce the female hrHPV prevalence indirectly by the herd effect if also boys are included in the vaccination program. On the other hand, any herd effects in older unvaccinated cohorts were minor. Limiting the epidemiological model to infection yielded improved understanding of the hrHPV epidemiology and of mechanisms with which vaccination impacts on hrHPV infections.     

Parameters for the Mathematical Modelling of Clostridium difficile Acquisition and Transmission: A Systematic Review

Introduction

Mathematical modelling of Clostridium difficile infection dynamics could contribute to the optimisation of strategies for its prevention and control. The objective of this systematic review was to summarise the available literature specifically identifying the quantitative parameters required for a compartmental mathematical model of Clostridium difficile transmission.

Methods

Six electronic healthcare databases were searched and all screening, data extraction and study quality assessments were undertaken in duplicate. Results were synthesised using a narrative approach.

Results

Fifty-four studies met the inclusion criteria. Reproduction numbers for hospital based epidemics were described in two studies with a range from 0.55 to 7. Two studies provided consistent data on incubation periods. For 62% of cases, symptoms occurred in less than 4 weeks (3-28 days) after infection. Evidence on contact patterns was identified in four studies but with limited data reported for populating a mathematical model. Two studies, including one without clinically apparent donor-recipient pairs, provided information on serial intervals for household or ward contacts, showing transmission intervals of <1 week in ward based contacts compared to up to 2 months for household contacts. Eight studies reported recovery rates of between 75% - 100% for patients who had been treated with either metronidazole or vancomycin. Forty-nine studies gave recurrence rates of between 3% and 49% but were limited by varying definitions of recurrence. No study was found which specifically reported force of infection or net reproduction numbers.

Conclusions

There is currently scant literature overtly citing estimates of the parameters required to inform the quantitative modelling of Clostridium difficile transmission. Further high quality studies to investigate transmission parameters are required, including through review of published epidemiological studies where these quantitative estimates may not have been explicitly estimated, but that nonetheless contain the relevant data to allow their calculation. [Systematic review reference: CRD42012003081]