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.     

Mapping Risk of Malaria Transmission in Mainland Portugal Using a Mathematical Modelling Approach

Malaria is currently one of the world´s major health problems. About a half-million deaths are recorded every year. In Portugal, malaria cases were significantly high until the end of the 1950s but the disease was considered eliminated in 1973. In the past few years, endemic malaria cases have been recorded in some European countries. With the increasing human mobility from countries with endemic malaria to Portugal, there is concern about the resurgence of this disease in the country. Here, we model and map the risk of malaria transmission for mainland Portugal, considering 3 different scenarios of existing imported infections. This risk assessment resulted from entomological studies on An. atroparvus, the only known mosquito capable of transmitting malaria in the study area. We used the malariogenic potential (determined by receptivity, infectivity and vulnerability) applied over geospatial data sets to estimate spatial variation in malaria risk. The results suggest that the risk exists, and the hotspots are concentrated in the northeast region of the country and in the upper and lower Alentejo regions.     

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]     

Mathematical Modelling of Enzymatic Butanolysis of Vegetable Oils

Lipozyme catalysed alcoholysis of castor or coconut oils by n-butanol has been mathematically modelled. In addition to the butyl esters of the fatty acids, the reaction produces diglycerides which further get converted to monoglycerides. The model considers the competitive binding of the triglycerides and the diglycerides to the enzyme. The Michaelis-Menten constants for both steps were estimated from the experimental data. Increasing n-butanol concentration inhibited the rate of the process.     

Mathematical Modelling of the Transmission Dynamics of Contagious Bovine Pleuropneumonia Reveals Minimal Target Profiles for Improved Vaccines and Diagnostic Assays

Contagious bovine pleuropneumonia (CBPP) is a cattle disease that has hampered the development of the livestock sector in sub-Saharan Africa. Currently, vaccination with a live vaccine strain is its recommended control measure although unofficial antimicrobial use is widely practiced. Here, modelling techniques are used to assess the potential impact of early elimination of infected cattle via accurate diagnosis on CBPP dynamics. A herd-level stochastic epidemiological model explicitly incorporating test sensitivity and specificity is developed. Interventions by annual vaccination, annual testing and elimination and a combination of both are implemented in a stepwise manner and their effectiveness compared by running 1000 simulations per intervention over ten years. The model predicts that among the simulated interventions, the ones likely to eliminate the disease from an isolated herd all involved annual vaccination of more than 75% of the animals with a vaccine that protects for at least 18 months combined with annual testing (and elimination of positive reactors) of 75% of the animals every six months after vaccination. The highest probability of disease elimination was 97.5% and this could occur within a median of 2.3 years. Generally, our model predicts that regular testing and elimination of positive reactors using improved tests will play a significant role in minimizing CBPP burden especially in the current situation where improved vaccines are yet to be developed.     

The Origin of Species by Means of Mathematical Modelling

Darwin described biological species as groups of morphologically similar individuals. These groups of individuals can split into several subgroups due to natural selection, resulting in the emergence of new species. Some species can stay stable without the appearance of a new species, some others can disappear or evolve. Some of these evolutionary patterns were described in our previous works independently of each other. In this work we have developed a single model which allows us to reproduce the principal patterns in Darwin’s diagram. Some more complex evolutionary patterns are also observed. The relation between Darwin’s definition of species, stated above, and Mayr’s definition of species (group of individuals that can reproduce) is also discussed.     

Mathematical Modelling of a Class of Paleontological Evolution Processes

The time-dependent behaviour of number of genera in taxa replacing one another phylogenetically is studied with the help of a simple differential equation model with time-dependent or state-dependent coefficients.     

Mathematical Modelling of Toxicity Associated with Intracellular Chromium Reduction

Chromium is a known allergen and carcinogen, but the mechanisms by which damage is caused are not clearly understood. Based on experimental literature, we devise a conceptual model examining the intracellular reduction of chromium through reductants such as glutathione and ascorbic acid. From this, we build a mathematical model describing these events in detail and we use this to clarify the key steps in the process of chromium reduction within cells. In particular, we consider the free radicals which are generated as a result of chromium reduction and that are likely to cause most harm to the cell. To explore the practical implications of the model predication, we investigate what the effects of a single eight hours of exposure and multiple eight hour exposures over the course of 3 days with increasing extracellular chromium concentration are. The dependence on initial chromium concentration is of particular significance with the proportions of the various chromium states changing as well as free radical generation increasing with greater chromium exposure.     

三十年前他与雪豹数次相遇

“一只肚子圆鼓鼓的雪豹突然出现在我们眼前．朝着我们呲牙裂嘴．低声怒吼．但是它却一动不动．我感到很奇怪……”     

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.     

Mathematical Modelling of Aerosolised Skin Grafts Incorporating Keratinocyte Clonal Subtypes

Severe burns can be very traumatic for the patient, and while burns caused by industrial or domestic accidents are common, there are also increasing numbers of burns associated with terrorism. A novel technique to assist in the healing process is to spray skin cells, keratinocytes, that are cultured from the patient’s own tissue, directly onto the burn site. This process involves taking some undamaged skin from the patient, allowing the skin cells to proliferate rapidly in the laboratory over a period of 5–10 days, harvesting and separating the cells and then spraying them onto the burn. This paper deals with keratinocytes that have been cultured in vitro for a short period of time (early passage cultured cells). The spraying process has yet to be optimised with respect to the seeding density required for fastest re-epithelisation and thus there is a need for this process to be modelled. In this paper, we review some of the skin biology and develop a mathematical model of the growth patterns of cell colonies after they have been applied using a aerosolised technique. The model allows us to predict coverage over time and can be used as a decision support tool for clinicians. PACS: 92B05     

Transmission Networks and Population Turnover of Echovirus 30

Globally, echovirus 30 (E30) is one of the most frequently identified enteroviruses and a major cause of meningitis. Despite its wide distribution, little is known about its transmission networks or the dynamics of its recombination and geographical spread. To address this, we have conducted an extensive molecular epidemiology and evolutionary study of E30 isolates collected over 8 years from a geographically wide sample base (11 European countries, Asia, and Australia). 3Dpol sequences fell into several distinct phylogenetic groups, interspersed with other species B serotypes, enabling E30 isolates to be classified into 38 recombinant forms (RFs). Substitutions in VP1 and 3Dpol regions occurred predominantly at synonymous sites (ratio of nonsynonymous to synonymous substitutions, 0.05) with VP1 showing a rapid substitution rate of 8.3 × 10⁻³ substitutions per site per year. Recombination frequency was tightly correlated with VP1 divergence; viruses differing by evolutionary distances of >0.1 (or 6 years divergent evolution) almost invariably (>97%) had different 3Dpol groups. Frequencies of shared 3Dpol groups additionally correlated with geographical distances, with Europe and South Asia showing turnover of entirely distinct virus populations. Population turnover of E30 was characterized by repeated cycles of emergence, dominance, and disappearance of individual RFs over periods of 3 to 5 years, although the existence and nature of evolutionary selection underlying these population replacements remain unclear. The occurrence of frequent “sporadic” recombinants embedded within VP1 groupings of other RFs and the much greater number of 3Dpol groups than separately identifiable VP1 lineages suggest frequent recombination with an external diverse reservoir of non-E30 viruses.The genus Enterovirus in the family Picornaviridae is a group of nonenveloped RNA viruses that cause a wide range of diseases in humans and other mammals. Enteroviruses contain a positive-sense RNA genome of approximately 7,500 nucleotides encoding a polyprotein that after cleavage yields structural (capsid proteins VP1 to VP4) and nonstructural (2A to 3D) proteins. Primary infection with an enterovirus leads to viral replication in the tissue around the gastrointestinal tract, followed by a transient viremia and sometimes migration into other tissues (6, 44). Although infection in immunocompetent individuals is often asymptomatic or causes mild febrile illness, enteroviruses are a common etiological agent in aseptic meningitis, encephalitis, and paralysis in individuals of all ages, with persistent and/or widely disseminated systemic infection in immunosuppressed individuals and neonates (12, 19, 23).Enteroviruses were originally classified as polioviruses, coxsackie virus type A or B viruses, or echoviruses (enteric cytopathic human orphan viruses), depending upon the infectious properties of the virus such as pathogenicity in mice (reviewed in reference 22). From the 1960s onwards, enteroviruses within these groups were further differentiated into serotypes originally by using panels of specific neutralizing antisera and, more recently, by sequence comparisons of structural gene regions such as VP1 (9, 34, 38, 43). There are currently over 100 recognized human enterovirus serotypes that fall into four main species (designated A to D) using phylogenetic analysis (54). The Enterovirus genus additionally contains several other species infecting primates, cattle, and pigs and has recently been expanded to include the genetically related human rhinovirus A and B (54).The species B serotype, echovirus 30 (E30), is a major cause of meningitis in both children and adults. Among the many serotypes associated with this disease presentation, E30 is generally the most commonly isolated in Europe (8, 31, 49), the United States (10, 37), Asia (1, 60), and South America (33). E30 infections typically occur as a series of outbreaks every 3 to 5 years, frequently over large geographical areas. For example, high frequencies of E30 detection in meningitis cases and surveillance programs were reported for 2000 to 2001 throughout Europe, including Denmark (58), Belgium (57), Cyprus (45), Germany (46), and France (3, 5), and again in 2005 to 2006 (8). Similarly, in the United States, long-term surveillance by the Centers for Disease Control and Prevention revealed peaks of E30 isolation in 1981, 1991 to 1993, 1997, and 2003 (10, 37). The underlying basis for this periodicity in E30 infections and the possible association of different genetic variants of E30 with outbreaks are currently poorly understood.At any one time point, a range of different species B enterovirus serotypes circulate in human populations. The evolution of enteroviruses occurs through genetic drift and, over much longer periods, antigenic diversification in the structural gene region encoding the virus capsid (7, 14, 25, 30, 51, 55); it may also occur by recombination between the capsid and nonstructural coding parts of the genome and the 5′ untranslated region (2, 13, 16, 20, 26, 28, 29, 35, 39, 41, 47, 48, 53). To date, almost all documented examples of recombination have been limited to members of the same species (e.g., between species B serotypes), with the exception of the 5′ untranslated region, where only a single genetic group can be identified within human species A and B and a second with species C and D (48).In this study, we have carried out an extensive investigation of VP1 sequence divergence and recombination through sequencing the 3Dpol region of E30 isolates and samples collected from several European countries, Southeast Asia, and Australia over a combined 8-year observation period. Using this geographically diverse sample collection, our aims were to document the time span and geographical extent of different E30 variants as they emerged and spread during the observation period. The identification of individual recombinants of E30 provides the means to document in detail the dynamics of E30 population turnover, geographical ranges of enterovirus transmission networks, and, ultimately, the relationship between the emergence of new variants of E30 and longer-term changes in disease associations and pathogenicity.     

A Mathematical Model of Anthrax Transmission in Animal Populations

A general mathematical model of anthrax (caused by Bacillus anthracis) transmission is formulated that includes live animals, infected carcasses and spores in the environment. The basic reproduction number \(\mathcal {R}_0\) is calculated, and existence of a unique endemic equilibrium is established for \(\mathcal {R}_0\) above the threshold value 1. Using data from the literature, elasticity indices for \(\mathcal {R}_0\) and type reproduction numbers are computed to quantify anthrax control measures. Including only herbivorous animals, anthrax is eradicated if \(\mathcal {R}_0 < 1\). For these animals, oscillatory solutions arising from Hopf bifurcations are numerically shown to exist for certain parameter values with \(\mathcal {R}_0>1\) and to have periodicity as observed from anthrax data. Including carnivores and assuming no disease-related death, anthrax again goes extinct below the threshold. Local stability of the endemic equilibrium is established above the threshold; thus, periodic solutions are not possible for these populations. It is shown numerically that oscillations in spore growth may drive oscillations in animal populations; however, the total number of infected animals remains about the same as with constant spore growth.