Modeling Tick-Borne Disease: A Metapopulation Model

Recent increases in reported outbreaks of tick-borne diseases have led to increased interest in understanding and controlling epidemics involving these transmission vectors. Mathematical disease models typically assume constant population size and spatial homogeneity. For tick-borne diseases, these assumptions are not always valid. The disease model presented here incorporates non-constant population sizes and spatial heterogeneity utilizing a system of differential equations that may be applied to a variety of spatial patches. We present analytical results for the one patch version and find parameter restrictions under which the populations and infected densities reach equilibrium. We then numerically explore disease dynamics when parameters are allowed to vary spatially and temporally and consider the effectiveness of various tick-control strategies.     

Probability of a Disease Outbreak in Stochastic Multipatch Epidemic Models

Environmental heterogeneity, spatial connectivity, and movement of individuals play important roles in the spread of infectious diseases. To account for environmental differences that impact disease transmission, the spatial region is divided into patches according to risk of infection. A system of ordinary differential equations modeling spatial spread of disease among multiple patches is used to formulate two new stochastic models, a continuous-time Markov chain, and a system of stochastic differential equations. An estimate for the probability of disease extinction is computed by approximating the Markov chain model with a multitype branching process. Numerical examples illustrate some differences between the stochastic models and the deterministic model, important for prevention of disease outbreaks that depend on the location of infectious individuals, the risk of infection, and the movement of individuals.     

Probability of Disease Extinction or Outbreak in a Stochastic Epidemic Model for West Nile Virus Dynamics in Birds

Acta Biotheoretica - Thresholds for disease extinction provide essential information for the prevention and control of diseases. In this paper, a stochastic epidemic model, a continuous-time Markov...     

Adaptations of the Tick-Borne Pathogen, Anaplasma marginale, for Survival in Cattle and Ticks

The tick-borne cattle pathogen Anaplasma marginale (Rickettsiales: Anaplasmataceae) multiplies within membrane-bound inclusions in host cell cytoplasm. Many geographic isolates of A. marginale occur that vary in genotype, antigenic composition, morphology and infectivity for ticks. A tick cell culture system for propagation of A. marginale proved to be a good model for study of tick-pathogen interactions. Six major surface proteins (MSPs) identified on A. marginale from bovine erythrocytes were conserved on A. marginale derived from tick cells. MSP1a and MSP1b were adhesins for bovine erythrocytes, while only MSP1a was found to be an adhesin for tick cells. The tandemly repeated portion of MSP1a was found to be necessary and sufficient for adhesion to both tick cells and bovine erythrocytes. Infectivity of A. marginale isolates for ticks was dependent on the adhesive capacity of the isolate MSP1a, which was found to involve both the adhesive properties and sequence of the repeated peptides. Cattle immunized with A. marginale derived from bovine erythrocytes or tick cells demonstrated a differential antibody response to MSP1a and MSP1b that resulted from the differential expression of these proteins in cattle and ticks cells. MSP2, derived from a multi-gene family, was found to undergo antigenic variation in cattle and ticks and may contribute to establishment of persistent A. marginale infections. MSP1a has been used as a stable genetic marker for geographic isolates because the molecular weight varies due to differing numbers of the tandem repeats. However, phylogenetic studies of A. marginale isolates from North America using MSP1a and MSP4 demonstrated that MSP4 was a good biogeographic marker, while MSP1a varied greatly among and within geographic areas. Infection and development of A. marginale in cattle and tick cells appears to differ and to be mediated by several surface proteins encoded from the small genome. This revised version was published online in July 2006 with corrections to the Cover Date.     

A Stochastic Version of the Eigen Model

We exhibit a stochastic discrete time model that produces the Eigen model (Naturwissenschaften 58:465–523, 1971) in the deterministic and continuous time limits. The model is based on the competition among individuals differing in terms of fecundity but with the same viability. We explicitly write down the Markov matrix of the discrete time stochastic model in the two species case and compute the master sequence concentration numerically for various values of the total population. We also obtain the master equation of the model and perform a Van Kampen expansion. The results obtained in the two species case are compared with those coming from the Eigen model. Finally, we comment on the range of applicability of the various approaches described, when the number of species is larger than two.     

Adaptability and Persistence of the Emerging Pathogen Bordetella petrii

The first described, environmentally isolated, Bordetella petrii was shown to undergo massive genomic rearrangements in vitro. More recently, B. petrii was isolated from clinical samples associated with jaw, ear bone, cystic fibrosis and chronic pulmonary disease. However, the in vivo consequences of B. petrii genome plasticity and its pathogenicity remain obscure. B. petrii was identified from four sequential respiratory samples and a post-mortem spleen sample of a woman presenting with bronchiectasis and cavitary lung disease associated with nontuberculous mycobacterial infection. Strains were compared genetically, phenotypically and by antibody recognition from the patient and from inoculated mice. The successive B. petrii strains exhibited differences in growth, antibiotic susceptibility and recognition by the patient’s antibodies. Antibodies from mice inoculated with these strains recapitulated the specificity and strain dependent response that was seen with the patient’s serum. Finally, we characterize one strain that was poorly recognized by the patient’s antibodies, due to a defect in the lipopolysaccharide O-antigen, and identify a mutation associated with this phenotype. We propose that B. petrii is remarkably adaptable in vivo, providing a possible connection between immune response and bacterial evasion and supporting infection persistence.     

Exploring the Unique N-Glycome of the Opportunistic Human Pathogen Acanthamoeba

Glycans play key roles in host-pathogen interactions; thus, knowing the N-glycomic repertoire of a pathogen can be helpful in deciphering its methods of establishing and sustaining a disease. Therefore, we sought to elucidate the glycomic potential of the facultative amoebal parasite Acanthamoeba. This is the first study of its asparagine-linked glycans, for which we applied biochemical tools and various approaches of mass spectrometry. An initial glycomic screen of eight strains from five genotypes of this human pathogen suggested, in addition to the common eukaryotic oligomannose structures, the presence of pentose and deoxyhexose residues on their N-glycans. A more detailed analysis was performed on the N-glycans of a genotype T11 strain (4RE); fractionation by HPLC and tandem mass spectrometric analyses indicated the presence of a novel mannosylfucosyl modification of the reducing terminal core as well as phosphorylation of mannose residues, methylation of hexose and various forms of pentosylation. The largest N-glycan in the 4RE strain contained two N-acetylhexosamine, thirteen hexose, one fucose, one methyl, and two pentose residues; however, in this and most other strains analyzed, glycans with compositions of Hex_8–9HexNAc₂Pnt_0–1 tended to dominate in terms of abundance. Although no correlation between pathogenicity and N-glycan structure can be proposed, highly unusual structures in this facultative parasite can be found which are potential virulence factors or therapeutic targets.     

A Mathematical Model of the Inflammatory Response to Pathogen Challenge

The human body’s immune response to bacterial challenge, even when successful in controlling the infection, can result in negative consequences for the host, including reduced functionality of associated tissues. We present and analyze a low-dimensional mathematical model of this immune response to pathogen invasion, incorporating the coordinated actions of active immune cells, and both pro- and anti-inflammatory cytokines. The model simulates both the positive (pathogen reduction) and negative (local tissue dysfunction) effects of the immune response and includes the important role of immunologic memory in the process of a return to stasis. This differential equation-based model is sufficiently general to be applicable to a wide range of human tissues and organs.     

A Stochastic Model of the Repetitive Activity of Neurons

A recurrent model of the repetitive firing of neurons responding to stimuli of long duration is given. The model assumes a deterministic threshold potential and a membrane potential which is composed of both deterministic and random components. The model accurately reproduces interval statistics obtained from different neurons discharging repetitively over a wide range of discharge rates. It is shown that the model has three important parameters; the time course of threshold recovery following a discharge, the variance of the random component, and the level of excitatory drive. The model is extended, by the use of hyperpolarizing afterpotentials, to include negative correlation between successive interspike intervals.     

A Stochastic Model for Surname Evolution

Surnames are inherited in much the same way as biological traits like alleles of one locus. Assuming the heritability of surnames, a simple stochastic model for X, the total number of occurrences of a surname, the Consul distribution defined by the probability mass function: for x = 1, 2, 3,… and zero otherwise and where either (i) m is a positive integer when 0 ≤ θ ≤ 1 such that θ ≦ mθ ≦ 1, or (ii) m≤0, θ ≤0 such that mθ 1, can be arrived at by considering the branching process mechanism. Some applications of the model to real data are also considered.     

Influence of the Biotope on the Tick Infestation of Cattle and on the Tick-Borne Pathogen Repertoire of Cattle Ticks in Ethiopia

Background

The majority of vector-borne infections occur in the tropics, including Africa, but molecular eco-epidemiological studies are seldom reported from these regions. In particular, most previously published data on ticks in Ethiopia focus on species distribution, and only a few molecular studies on the occurrence of tick-borne pathogens or on ecological factors influencing these. The present study was undertaken to evaluate, if ticks collected from cattle in different Ethiopian biotopes harbour (had access to) different pathogens.

Methods

In South-Western Ethiopia 1032 hard ticks were removed from cattle grazing in three kinds of tick biotopes. DNA was individually extracted from one specimen of both sexes of each tick species per cattle. These samples were molecularly analysed for the presence of tick-borne pathogens.

Results

Amblyomma variegatum was significantly more abundant on mid highland, than on moist highland. Rhipicephalus decoloratus was absent from savannah lowland, where virtually only A. cohaerens was found. In the ticks Coxiella burnetii had the highest prevalence on savannah lowland. PCR positivity to Theileria spp. did not appear to depend on the biotope, but some genotypes were unique to certain tick species. Significantly more A. variegatum specimens were rickettsia-positive, than those of other tick species. The presence of rickettsiae (R. africae) appeared to be associated with mid highland in case of A. variegatum and A. cohaerens. The low level of haemoplasma positivity seemed to be equally distributed among the tick species, but was restricted to one biotope type.

Conclusions

The tick biotope, in which cattle are grazed, will influence not only the tick burden of these hosts, but also the spectrum of pathogens in their ticks. Thus, the presence of pathogens with alternative (non-tick-borne) transmission routes, with transstadial or with transovarial transmission by ticks appeared to be associated with the biotope type, with the tick species, or both, respectively.     

Establishment Probability in Fluctuating Environments: A Branching Process Model

We study the establishment probability of invaders in stochastically fluctuating environments and the related issue of extinction probability of small populations in such environments, by means of an inhomogeneous branching process model. In the model it is assumed that individuals reproduce asexually during discrete reproduction periods. Within each period, individuals have (independent) Poisson distributed numbers of offspring. The expected numbers of offspring per individual are independently identically distributed over the periods. It is shown that the establishment probability of an invader varies over the reproduction periods according to a stable distribution. We give a method for simulating the establishment probabilities and approximations for the expected establishment probability. Furthermore, we show that, due to the stochasticity of the establishment success over different periods, the expected success of sequential invasions is larger then that of simultaneous invasions and we study the effects of environmental fluctuations on the extinction probability of small populations and metapopulations. The results can easily be generalized to other offspring distributions than the Poisson.     

A Stochastic Model of DNA Fragments Rejoining

When cells are exposed to ionizing radiation, DNA damages in the form of single strand breaks (SSBs), double strand breaks (DSBs), base damage or their combinations are frequent events. It is known that the complexity and severity of DNA damage depends on the quality of radiation, and the microscopic dose deposited in small segments of DNA, which is often related to the linear transfer energy (LET) of the radiation. Experimental studies have suggested that under the same dose, high LET radiation induces more small DNA fragments than low-LET radiation, which affects Ku efficiently binding with DNA end and might be a main reason for high-LET radiation induced RBE [1] since DNA DSB is a major cause for radiation-induced cell death. In this work, we proposed a mathematical model of DNA fragments rejoining according to non-homologous end joining (NHEJ) mechanism. By conducting Gillespie''s stochastic simulation, we found several factors that impact the efficiency of DNA fragments rejoining. Our results demonstrated that aberrant DNA damage repair can result predominantly from the occurrence of a spatial distribution of DSBs leading to short DNA fragments. Because of the low efficiency that short DNA fragments recruit repair protein and release the protein residue after fragments rejoining, Ku-dependent NHEJ is significantly interfered with short fragments. Overall, our work suggests that inhibiting the Ku-dependent NHEJ may significantly contribute to the increased efficiency for cell death and mutation observed for high LET radiation.     

Multiple Transmission Pathways and Disease Dynamics in a Waterborne Pathogen Model

Multiple transmission pathways exist for many waterborne diseases, including cholera, Giardia, Cryptosporidium, and Campylobacter. Theoretical work exploring the effects of multiple transmission pathways on disease dynamics is incomplete. Here, we consider a simple ODE model that extends the classical SIR framework by adding a compartment (W) that tracks pathogen concentration in the water. Infected individuals shed pathogen into the water compartment, and new infections arise both through exposure to contaminated water, as well as by the classical SIR person–person transmission pathway. We compute the basic reproductive number (ℛ₀), epidemic growth rate, and final outbreak size for the resulting “SIWR” model, and examine how these fundamental quantities depend upon the transmission parameters for the different pathways. We prove that the endemic disease equilibrium for the SIWR model is globally stable. We identify the pathogen decay rate in the water compartment as a key parameter determining when the distinction between the different transmission routes in the SIWR model is important. When the decay rate is slow, using an SIR model rather than the SIWR model can lead to under-estimates of the basic reproductive number and over-estimates of the infectious period.     

Fluctuating Environments and Phytoplankton Community Structure: A Stochastic Model

Spatial heterogeneity in organism and resource distributions can generate temporal heterogeneity in resource access for simple organisms like phytoplankton. The role of temporal heterogeneity as a structuring force for simple communities is investigated via models of phytoplankton with contrasting life histories competing for a single fluctuating resource. A stochastic model in which environmental and demographic stochasticity are treated separately is compared with a model with deterministic resource variation to assess the importance of stochasticity. When compared with the deterministic model, the stochastic model allows for coexistence over a wider range of parameter values (or life-history types). The model suggests that demographic stochasticity alone is far more important in increasing the possibility of coexistence than environmental stochasticity alone. However, the combined effects of both types of stochasticity produce the largest likelihood of coexistence. Finally, the influence of relative nutrient levels and nutrient pulse frequency on these results is addressed. We relate our findings to variable environment theory with evidence for both relative nonlinearity and the storage effect acting in this model. We show for the first time that temporal dynamics generated by demographic stochasticity may operate like the storage effect at particular spatial scales.     

Exploring of Primate Models of Tick-Borne Flaviviruses Infection for Evaluation of Vaccines and Drugs Efficacy

Tick-borne encephalitis virus (TBEV) is one of the most prevalent and medically important tick-borne arboviruses in Eurasia. There are overlapping foci of two flaviviruses: TBEV and Omsk hemorrhagic fever virus (OHFV) in Russia. Inactivated vaccines exist only against TBE. There are no antiviral drugs for treatment of both diseases. Optimal animal models are necessary to study efficacy of novel vaccines and treatment preparations against TBE and relative flaviviruses. The models for TBE and OHF using subcutaneous inoculation were tested in Cercopithecus aethiops and Macaca fascicularis monkeys with or without prior immunization with inactivated TBE vaccine. No visible clinical signs or severe pathomorphological lesions were observed in any monkey infected with TBEV or OHFV. C. aethiops challenged with OHFV showed massive hemolytic syndrome and thrombocytopenia. Infectious virus or viral RNA was revealed in visceral organs and CNS of C. aethiops infected with both viruses; however, viremia was low. Inactivated TBE vaccines induced high antibody titers against both viruses and expressed booster after challenge. The protective efficacy against TBE was shown by the absence of virus in spleen, lymph nodes and CNS of immunized animals after challenge. Despite the absence of expressed hemolytic syndrome in immunized C. aethiops TBE vaccine did not prevent the reproduction of OHFV in CNS and visceral organs. Subcutaneous inoculation of M. fascicularis with two TBEV strains led to a febrile disease with well expressed viremia, fever, and virus reproduction in spleen, lymph nodes and CNS. The optimal terms for estimation of the viral titers in CNS were defined as 8–16 days post infection. We characterized two animal models similar to humans in their susceptibility to tick-borne flaviviruses and found the most optimal scheme for evaluation of efficacy of preventive and therapeutic preparations. We also identified M. fascicularis to be more susceptible to TBEV than C. aethiops.     

A Stochastic Model for Estimating Adolescent Sterility

In this article, a simple stochastic model for the time to first conception of a cohort of married women is developed, by identifying three states, ‘adolescent sterile’, ‘ovulating’ and ‘conceived‘, into which they can be placed. It is demonstrated that the model provides a close fit to observed data. The estimates of the parameters in the model, can be used to calculate the number of women in each state at different points of time and also to obtain estimates of the probabilities of conception for the two categories of women, adolescent sterile and biologically mature.     

A Stochastic Model for Coupled Enzyme System

The molecular biology of transformed cancer cells singles out key enzymes as sensitive targets of anti-cancer drugs. Here we use one substrate–one intermediate–one final product model for a coupled enzyme system. The transfer rates for the mechanism are taken as continuous but subject to random fluctuations. Explicit formulae for the first moments of the distribution of the process are obtained. These formulae allow us to take into account not only the variability between the subjects, but also the variability of the process for a single subject. The present results allow us also to build the prediction interval for a particular time period given the observations for some preceding moments.     

犬恶丝虫病病原生物学研究进展

从虫体的分类、分布、宿主、发育生物学和内共生体等几个方面综述了近年来在犬恶丝虫病病原生物学研究上取得成果,并提出了研究该病病原的现实意义和今后研究的主要方向.