Effects of gastrointestinal tissue structure on computed dipole vectors

Background  

Digestive diseases are difficult to assess without using invasive measurements. Non-invasive measurements of body surface electrical and magnetic activity resulting from underlying gastro-intestinal activity are not widely used, in large due to their difficulty in interpretation. Mathematical modelling of the underlying processes may help provide additional information. When modelling myoelectrical activity, it is common for the electrical field to be represented by equivalent dipole sources. The gastrointestinal system is comprised of alternating layers of smooth muscle (SM) cells and Interstitial Cells of Cajal (ICC). In addition the small intestine has regions of high curvature as the intestine bends back upon itself. To eventually use modelling diagnostically, we must improve our understanding of the effect that intestinal structure has on dipole vector behaviour.     

Quantifying HTLV-I dynamics

Despite significant advances in our understanding of the immune response to persistent viruses like human T-cell lymphotropic virus type I (HTLV-I), many important questions remain unanswered. Mathematical modelling enables us to interpret and synthesise diverse experimental data in new ways and thus can contribute to our understanding. Here, we review recent advances in mathematical modelling of HTLV-I infection and illustrate how mathematics has enabled us to identify factors that determine an individual's viral burden and risk of developing HTLV-I-associated diseases.     

A research agenda for helminth diseases of humans: modelling for control and elimination

Mathematical modelling of helminth infections has the potential to inform policy and guide research for the control and elimination of human helminthiases. However, this potential, unlike in other parasitic and infectious diseases, has yet to be realised. To place contemporary efforts in a historical context, a summary of the development of mathematical models for helminthiases is presented. These efforts are discussed according to the role that models can play in furthering our understanding of parasite population biology and transmission dynamics, and the effect on such dynamics of control interventions, as well as in enabling estimation of directly unobservable parameters, exploration of transmission breakpoints, and investigation of evolutionary outcomes of control. The Disease Reference Group on Helminth Infections (DRG4), established in 2009 by the Special Programme for Research and Training in Tropical Diseases (TDR), was given the mandate to review helminthiases research and identify research priorities and gaps. A research and development agenda for helminthiasis modelling is proposed based on identified gaps that need to be addressed for models to become useful decision tools that can support research and control operations effectively. This agenda includes the use of models to estimate the impact of large-scale interventions on infection incidence; the design of sampling protocols for the monitoring and evaluation of integrated control programmes; the modelling of co-infections; the investigation of the dynamical relationship between infection and morbidity indicators; the improvement of analytical methods for the quantification of anthelmintic efficacy and resistance; the determination of programme endpoints; the linking of dynamical helminth models with helminth geostatistical mapping; and the investigation of the impact of climate change on human helminthiases. It is concluded that modelling should be embedded in helminth research, and in the planning, evaluation, and surveillance of interventions from the outset. Modellers should be essential members of interdisciplinary teams, propitiating a continuous dialogue with end users and stakeholders to reflect public health needs in the terrain, discuss the scope and limitations of models, and update biological assumptions and model outputs regularly. It is highlighted that to reach these goals, a collaborative framework must be developed for the collation, annotation, and sharing of databases from large-scale anthelmintic control programmes, and that helminth modellers should join efforts to tackle key questions in helminth epidemiology and control through the sharing of such databases, and by using diverse, yet complementary, modelling approaches.     

Using Hawkes Processes to model imported and local malaria cases in near-elimination settings

Developing new methods for modelling infectious diseases outbreaks is important for monitoring transmission and developing policy. In this paper we propose using semi-mechanistic Hawkes Processes for modelling malaria transmission in near-elimination settings. Hawkes Processes are well founded mathematical methods that enable us to combine the benefits of both statistical and mechanistic models to recreate and forecast disease transmission beyond just malaria outbreak scenarios. These methods have been successfully used in numerous applications such as social media and earthquake modelling, but are not yet widespread in epidemiology. By using domain-specific knowledge, we can both recreate transmission curves for malaria in China and Eswatini and disentangle the proportion of cases which are imported from those that are community based.     

Is endemic stability of tick-borne disease in cattle a useful concept?

Endemic stability is a widely used term in the epidemiology of ticks and tick-borne diseases. It is generally accepted to refer to a state of a host-tick-pathogen interaction in which there is a high level of challenge of calves by infected ticks, absence of clinical disease in calves despite infection, and a high level of immunity in adult cattle with consequent low incidence of clinical disease. Although endemic stability is a valid epidemiological concept, the modelling studies that underpinned subsequent studies on the epidemiology of tick-borne diseases were specific to a single host-tick-pathogen system, and values derived from these models should not be applied in other regions or host-tick-pathogen systems.     

Strengthening data collection for neglected tropical diseases: What data are needed for models to better inform tailored intervention programmes?

Locally tailored interventions for neglected tropical diseases (NTDs) are becoming increasingly important for ensuring that the World Health Organization (WHO) goals for control and elimination are reached. Mathematical models, such as those developed by the NTD Modelling Consortium, are able to offer recommendations on interventions but remain constrained by the data currently available. Data collection for NTDs needs to be strengthened as better data are required to indirectly inform transmission in an area. Addressing specific data needs will improve our modelling recommendations, enabling more accurate tailoring of interventions and assessment of their progress. In this collection, we discuss the data needs for several NTDs, specifically gambiense human African trypanosomiasis, lymphatic filariasis, onchocerciasis, schistosomiasis, soil-transmitted helminths (STH), trachoma, and visceral leishmaniasis. Similarities in the data needs for these NTDs highlight the potential for integration across these diseases and where possible, a wider spectrum of diseases.     

Spatial and temporal modelling for parasite transmission studies and risk assessment

Spatial and temporal modelling of parasite transmission and risk assessment require relevant spatial information at appropriate spatial and temporal scales. There is now a large literature that demonstrates the utility of satellite remote sensing and spatial modelling within geographical information systems (GIS) and firmly establishes these technologies as the key tools for spatial epidemiology. This review outlines the strength of satellite remotely sensed data for spatial mapping of landscape characteristics in relation to disease reservoirs, host distributions and human disease. It is suggested that current satellite technology can fulfill the spatial mapping needs of disease transmission and risk modelling, but that temporal resolution, which is a function of the satellite data acquisition characteristics, may be a limitating factor for applications requiring information about landscape or ecosystem dynamics. The potential of the Modis sensor for spatial epidemiology is illustrated with reference to mapping spatial and temporal vegetation dynamics and small mammal parasite hosts on the Tibetan plateau. Future research directions and priorities for landscape epidemiology are considered.     

Advances in satellite remote sensing of pheno-climatic features for epidemiological applications

Geographical Information Systems (GIS) and Remote Sensing (RS) technologies are being used increasingly to study the spatial and temporal patterns of diseases. They can be used to complement conventional ecological monitoring and modelling techniques, and provide a means to portray complex relationships in the ecology of diseases with strong environmental determinants. In particular, satellite technology has been extraordinarily improved during recent years, providing new parameters useful to understand the epidemiology of parasites, such as vegetation indices, land surface temperatures, soil moisture and rainfall indices. In the present review, Normalized Difference Vegetation Index (NDVI) is primarily considered, since it is the index characterizing vegetation that is most used in epidemiological studies. Multi-temporal study of RS data allows collection of bio-climatic information about risk area distribution, along with predictive studies and anticipatory models of diseases, at different geographic scales ranging from global to local. The main physical and technological basis of a mathematical model, effective at different scales, for identification of landscape pheno-climatic features is described in the current paper.     

How to make predictions about future infectious disease risks

Formal, quantitative approaches are now widely used to make predictions about the likelihood of an infectious disease outbreak, how the disease will spread, and how to control it. Several well-established methodologies are available, including risk factor analysis, risk modelling and dynamic modelling. Even so, predictive modelling is very much the 'art of the possible', which tends to drive research effort towards some areas and away from others which may be at least as important. Building on the undoubted success of quantitative modelling of the epidemiology and control of human and animal diseases such as AIDS, influenza, foot-and-mouth disease and BSE, attention needs to be paid to developing a more holistic framework that captures the role of the underlying drivers of disease risks, from demography and behaviour to land use and climate change. At the same time, there is still considerable room for improvement in how quantitative analyses and their outputs are communicated to policy makers and other stakeholders. A starting point would be generally accepted guidelines for 'good practice' for the development and the use of predictive models.     

TheX → Y → Z scheme after 23 years

Mathematical modelling of the course of the immune response is undoubtedly one of the most progressive and most promising areas of modern immunology. Mathematical models (along with computer programs) can be taken as "the only means of thoroughly testing and examining a large and intricate theory" (Partridge et al. 1984). The first phase of construction of mathematical models is the formulation of assumptions based on the knowledge of the facts to be modelled (manifested usually in a scheme of the presumed course of the modelled process). The first mathematical models of immune response were based on the hypothesis of a two-stage differentiation of cells participating in the humoral response, published in Prague 23 years ago (Sercarz and Coons 1962; Sterzl 1962) and illustrated by the X----Y----Z scheme. Many contemporary mathematical models still stem from this scheme which undoubtedly fits the fundamental data concerning the immune system.     

Estimation of the transmission dynamics of Theileria equi and Babesia caballi in horses

For the evaluation of the epidemiology of Theileria equi and Babesia caballi in a herd of 510 horses in SW Mongolia, several mathematical models of the transmission dynamics were constructed. Because the field data contain information on the presence of the parasite (determined by PCR) and the presence of antibodies (determined by IFAT), the models cater for maternal protection with antibodies, susceptible animals, infected animals and animals which have eliminated the parasite and also allow for age-dependent infection in susceptible animals. Maximum likelihood estimation procedures were used to estimate the model parameters and a Monte Carlo approach was applied to select the best fitting model. Overall, the results are in line with previous experimental work, and add evidence that the epidemiology of T. equi differs from that of Babesia spp. The presented modelling approach provides a useful tool for the investigation of some vector-borne diseases and the applied model selection procedure avoids asymptotical assumptions that may not be adequate for the analysis of epidemiological field data.     

Investigation of the Shelf Ecological System on the Basis of Modeling and Field Work

Mathematical modelling of the ecosystem of the North-West shelf of the Black Sea is based on the method of aggregation and averaging with the subsequent hierarchic decomposition (BELYAEV , 1987; BELYAEV and KONDUFOROVA , 1989). This approach includes the step-by-step comparison of the modelling results with field observations. The observations have been performed during the integrated oceanographic expedition of the research vessel “Professor Kolesnikov” (1987), for the first time specially organized to verify the modelling results. The comparison of the results of modelling and observation demonstrated that their agreement is satisfactory quantitatively and qualitatively. The efficiency of using models of optical fields for verification is also shown.     

Canard-induced complex oscillations in an excitatory network

Journal of Mathematical Biology - In Neuroscience, mathematical modelling involving multiple spatial and temporal scales can unveil complex oscillatory activity such as excitable responses to an...     

Geographical Information System (GIS) as a Tool in Surveillance and Monitoring of Animal Diseases

In the veterinary epidemiology, the advantage of mapping the locations of farms and other facilities with animals is obvious. In an outbreak of a disease it could make the management of the situation easier, and it could also provide a tool to evaluate different strategies to prevent the spread of infectious diseases. This paper aims to describe and give an overview of the possibilities and potential uses of a Geographical Information System (GIS) in the field of surveillance and monitoring of animal diseases. The following areas in which GIS and special GIS-functions could be incorporated are presented: recording and reporting information, epidemic emergency, cluster analysis, modelling disease spread, and planning control strategies. Different sources of data; geographical data, farm locations and disease information, used in the development of the GIS at the National Veterinary Institute in Norway are thoroughly described in the paper. Further, it presents a few examples where the GIS has been applied to studies of epidemiology and surveillance of animal diseases in Norway, which shows the significant value of GIS in these areas. At the same time, the incorporation of GIS in this field shows the scarcity of the data available, which should encourage improvement in the data recording and the quality of the registries.     

Mathematical modelling of intra-aortic balloon pump

Background: Ischemic heart diseases now afflict thousands of Iranians and are the major cause of death in many industrialised countries. Mathematical modelling of an intra-aortic balloon pump (IABP) could provide a better understanding of its performance and help to represent blood flow and pressure in systemic arteries before and after inserting the pump.

Methods: A mathematical modelling of the whole cardiovascular system was formulated using MATLAB software. The block diagram of the model consists of 43 compartments. All the anatomical data was extracted from the physiological references. In the next stage, myocardial infarction (MI) was induced in the model by decreasing the contractility of the left ventricle. The IABP was mathematically modelled and inserted in the model in the thoracic aorta I artery just before the descending aorta. The effects of IABP on MI were studied using the mathematical model.

Results: The normal operation of the cardiovascular system was studied firstly. The pressure–time graphs of the ventricles, atriums, aorta, pulmonary system, capillaries and arterioles were obtained. The volume–time curve of the left ventricle was also presented. The pressure–time curves of the left ventricle and thoracic aorta I were obtained for normal, MI, and inserted IABP conditions. Model verification was performed by comparing the simulation results with the clinical observations reported in the literature.

Conclusions: IABP can be described by a theoretical model. Our model representing the cardiovascular system is capable of showing the effects of different pathologies such as MI and we have shown that MI effects can be reduced using IABP in accordance with the modelling results. The mathematical model should serve as a useful tool to simulate and better understand cardiovascular operation in normal and pathological conditions.     

Mathematical and computational approaches can complement experimental studies of host–pathogen interactions

In addition to traditional and novel experimental approaches to study host–pathogen interactions, mathematical and computer modelling have recently been applied to address open questions in this area. These modelling tools not only offer an additional avenue for exploring disease dynamics at multiple biological scales, but also complement and extend knowledge gained via experimental tools. In this review, we outline four examples where modelling has complemented current experimental techniques in a way that can or has already pushed our knowledge of host–pathogen dynamics forward. Two of the modelling approaches presented go hand in hand with articles in this issue exploring fluorescence resonance energy transfer and two-photon intravital microscopy. Two others explore virtual or ' in silico ' deletion and depletion as well as a new method to understand and guide studies in genetic epidemiology. In each of these examples, the complementary nature of modelling and experiment is discussed. We further note that multi-scale modelling may allow us to integrate information across length (molecular, cellular, tissue, organism, population) and time (e.g. seconds to lifetimes). In sum, when combined, these compatible approaches offer new opportunities for understanding host–pathogen interactions.     

Petri net modelling of biological networks

Mathematical modelling is increasingly used to get insights into the functioning of complex biological networks. In this context, Petri nets (PNs) have recently emerged as a promising tool among the various methods employed for the modelling and analysis of molecular networks. PNs come with a series of extensions, which allow different abstraction levels, from purely qualitative to more complex quantitative models. Noteworthily, each of these models preserves the underlying graph, which depicts the interactions between the biological components. This article intends to present the basics of the approach and to foster the potential role PNs could play in the development of the computational systems biology.     

Environmental Variation Generates Environmental Opportunist Pathogen Outbreaks

Many socio-economically important pathogens persist and grow in the outside host environment and opportunistically invade host individuals. The environmental growth and opportunistic nature of these pathogens has received only little attention in epidemiology. Environmental reservoirs are, however, an important source of novel diseases. Thus, attempts to control these diseases require different approaches than in traditional epidemiology focusing on obligatory parasites. Conditions in the outside-host environment are prone to fluctuate over time. This variation is a potentially important driver of epidemiological dynamics and affect the evolution of novel diseases. Using a modelling approach combining the traditional SIRS models to environmental opportunist pathogens and environmental variability, we show that epidemiological dynamics of opportunist diseases are profoundly driven by the quality of environmental variability, such as the long-term predictability and magnitude of fluctuations. When comparing periodic and stochastic environmental factors, for a given variance, stochastic variation is more likely to cause outbreaks than periodic variation. This is due to the extreme values being further away from the mean. Moreover, the effects of variability depend on the underlying biology of the epidemiological system, and which part of the system is being affected. Variation in host susceptibility leads to more severe pathogen outbreaks than variation in pathogen growth rate in the environment. Positive correlation in variation on both targets can cancel the effect of variation altogether. Moreover, the severity of outbreaks is significantly reduced by increase in the duration of immunity. Uncovering these issues helps in understanding and controlling diseases caused by environmental pathogens.