Developing a realistic sexual network model of chlamydia transmission in Britain

Background  

A national chlamydia screening programme is currently being rolled out in the UK and other countries. However, much of the epidemiology remains poorly understood. In this paper we present a stochastic, individual based, dynamic sexual network model of chlamydia transmission and its parameterisation. Mathematical models provide a theoretical framework for understanding the key epidemiological features of chlamydia: sexual behaviour, health care seeking and transmission dynamics.     

A mathematical model for the transmission of Plasmodium vivax malaria

We have proposed a mathematical model for the transmission of Plasmodium vivax malaria quantitatively, which is adjusted to the infected region, Guadalcanal, in the Solomon Islands. The simulation of a transmission model will be instrumental in planning the malaria control strategy. A characteristic of the life cycle of P. vivax is that a sporozoite injected into the blood stream by a mosquito bite may sometimes stay in a hepatocyte as a hypnozoite. Therefore, we have incorporated a phenomenon of renewed infections caused by a relapse into the transmission model. Also through the simulations we have attempted to evaluate the decline in prevalence caused by the programs of selective mass drug administration (MDA) and vector control such as the distribution of permethrin-treated bednets. The simulations have indicated that the concentrated repetition of MDA at 1-week intervals would reduce the prevalence of vivax malaria swiftly in the beginning and would keep the parasite rate below 1% for a few years but the prevalence would increase thereafter. In contrast, the parasite rate would remain below 1% for a long time if a trial of 1 or 2 times MDA is accompanied with some reduction of the vectorial capacity by the enforcement of vector control. In any case, it is important to beware of relapse cases because even after the execution of MDA it takes a long time to decrease the proportion of hypnozoite carriers.     

A mathematical model for Zika virus transmission dynamics with a time-dependent mosquito biting rate

Background

Mathematical modeling has become a tool used to address many emerging diseases. One of the most basic and popular modeling frameworks is the compartmental model. Unfortunately, most of the available compartmental models developed for Zika virus (ZIKV) transmission were designed to describe and reconstruct only past, short-time ZIKV outbreaks in which the effects of seasonal change to entomological parameters can be ignored. To make an accurate long-term prediction of ZIKV transmission, the inclusion of seasonal effects into an epidemic model is unavoidable.

Methods

We developed a vector-borne compartmental model to analyze the spread of the ZIKV during the 2015–2016 outbreaks in Bahia, Brazil and to investigate the impact of two vector control strategies, namely, reducing mosquito biting rates and reducing mosquito population size. The model considered the influences of seasonal change on the ZIKV transmission dynamics via the time-varying mosquito biting rate. The model was also validated by comparing the model prediction with reported data that were not used to calibrate the model.

Results

We found that the model can give a very good fit between the simulation results and the reported Zika cases in Bahia (R-square?=?0.9989). At the end of 2016, the total number of ZIKV infected people was predicted to be 1.2087 million. The model also predicted that there would not be a large outbreak from May 2016 to December 2016 due to the decrease of the susceptible pool. Implementing disease mitigation by reducing the mosquito biting rates was found to be more effective than reducing the mosquito population size. Finally, the correlation between the time series of estimated mosquito biting rates and the average temperature was also suggested.

Conclusions

The proposed ZIKV transmission model together with the estimated weekly biting rates can reconstruct the past long-time multi-peak ZIKV outbreaks in Bahia.

     

Chancroid transmission dynamics: a mathematical modeling approach

Mathematical models have long been used to better understand disease transmission dynamics and how to effectively control them. Here, a chancroid infection model is presented and analyzed. The disease-free equilibrium is shown to be globally asymptotically stable when the reproduction number is less than unity. High levels of treatment are shown to reduce the reproduction number suggesting that treatment has the potential to control chancroid infections in any given community. This result is also supported by numerical simulations which show a decline in chancroid cases whenever the reproduction number is less than unity.     

Epileptiform activity in a neocortical network: a mathematical model

 A simple mathematical model describing the generation and propagation of epileptiform activity in a cerebral cortical network is presented. The model consists of a system of nonlinear delay differential equations. Physiological properties are taken into account as nonlinear transmission of signals at the synapse, temporal and spatial summation of incoming signals at the soma, active membrane characteristics, and dendritic and axonal propagation times. The influence of the connectivity and the temporal parameters on the oscillatory properties of the model is studied. The computer simulations are in agreement with experimental observations in cortical networks: whereas a weak excitatory or strong inhibitory synaptic connection strength produces a stationary status with short-lasting responses to external stimuli, increases in excitation or decreases in inhibition induce spontaneous and stimulus-evoked rhythmic discharges. Synaptic burst-like activity is observed only for an intermediate range of excitatory and inhibitory connection strengths and external inputs. The form and duration of the bursts can also be controlled by the temporal parameters. The results demonstrate that relatively simple mathematical equations are sufficient to model some of the network properties underlying the generation and propagation of epileptiform activity. Received: 2 October 2000 / Accepted in revised form: 4 March 2001     

Ketone body kinetics in humans: a mathematical model

A model has been developed to account for ketone body kinetics in man based on data following bolus injections of [14C]acetoacetate (A) and [14C]beta-OH butyrate (B) into normal humans in the postabsorptive state. The model consists of separate compartments for blood A and B that are linked by a tissue compartment in which rapid interconversion of the ketone bodies occurs. The probability of movement from blood into this compartment was assumed to be the same for both ketone bodies. Two slowly equilibrating tissue compartments are required to account for the slow components in the tracer data, and thus a five-compartment model is proposed. By modeling the transient tracer data with the tracee in a steady state, ketone body kinetics were defined in terms of the rapid interconversions of A and B, and the slow exchanges of carbon within the tissues. The rates of release of new A and B into blood, (UA and UB) were calculated. These rates were less than the apparent production rates, PRA and PRB, as the PR's included carbon atoms first released as the other ketone body. The exchange constants between the compartments were determined in addition to the fractional catabolic rates (FCR) and metabolic clearance rates (MCR) of A and B. The initial space of distribution was 10 L and the mean values +/- SD (n = 11), normalized to this volume, were UA = 6.4 +/- 5.0, UB = 8.8 +/- 8.0 (mumol L-1 min-1), FCRA = 0.226 +/- 0.142, FCRB = 0.188 +/- 0.124 (min-1), MCRA = 2.26 +/- 1.42, MCRB = 1.87 +/- 1.23 (L min-1) and PRA = 11.1 +/- 7.6, PRB = 12.7 +/- 10.0 (mumol L-1 min-1).     

Ratcheting in post-translational protein translocation: a mathematical model

We have developed a non-steady-state mathematical model describing post-translational protein translocation across the endoplasmic reticulum membrane. Movement of the polypeptide chain through the channel in the endoplasmic reticulum membrane is considered to be a stochastic process which is biased at the lumenal side of the channel by the binding of BiP (Kar2p), a member of the Hsp70 family of ATPases (ratcheting model). Assuming that movement of the chain through the channel is caused by passive diffusion (Brownian ratchet), the model describes all available experimental data. The optimum set of model parameters indicates that the ratcheting mechanism functions at near-maximum rate, being relatively insensitive to variations of the association or dissociation rate constants of BiP or its concentration. The estimated rate constant for diffusion of a polypeptide inside the channel indicates that the chain makes contact with the walls of the channel. Since fitting of the model to the data required that the backward rate constant be larger than the forward constant during early diffusion steps, translocation must occur against a force. The latter may arise, for example, from the unfolding of the polypeptide chain in the cytosol. Our results indicate that the ratchet can transport polypeptides against a free energy of about 25 kJ/mol without significant retardation of translocation. The modeling also suggests that the BiP ratchet is optimized, allowing fast translocation to be coupled with minimum consumption of ATP and rapid dissociation of BiP in the lumen of the ER. Finally, we have estimated the maximum hydrophobicity of a polypeptide segment up to which lateral partitioning from the channel into the lipid phase does not result in significant retardation of translocation.     

Turing instabilities in a mathematical model for signaling networks

GTPase molecules are important regulators in cells that continuously run through an activation/deactivation and membrane-attachment/membrane-detachment cycle. Activated GTPase is able to localize in parts of the membranes and to induce cell polarity. As feedback loops contribute to the GTPase cycle and as the coupling between membrane-bound and cytoplasmic processes introduces different diffusion coefficients a Turing mechanism is a natural candidate for this symmetry breaking. We formulate a mathematical model that couples a reaction–diffusion system in the inner volume to a reaction–diffusion system on the membrane via a flux condition and an attachment/detachment law at the membrane. We present a reduction to a simpler non-local reaction–diffusion model and perform a stability analysis and numerical simulations for this reduction. Our model in principle does support Turing instabilities but only if the lateral diffusion of inactivated GTPase is much faster than the diffusion of activated GTPase.     

Role of environmental persistence in pathogen transmission: a mathematical modeling approach

Although diseases such as influenza, tuberculosis and SARS are transmitted through an environmentally mediated mechanism, most modeling work on these topics is based on the concepts of infectious contact and direct transmission. In this paper we use a paradigm model to show that environmental transmission appears like direct transmission in the case where the pathogen persists little time in the environment. Furthermore, we formulate conditions for the validity of this modeling approximation and we illustrate them numerically for the cases of cholera and influenza. According to our results based on recently published parameter estimates, the direct transmission approximation fails for both cholera and influenza. While environmental transmission is typically chosen over direct transmission in modeling cholera, this is not the case for influenza.     

A mathematical model for the spread of Strepotococcus pneumoniae with transmission dependent on serotype

We examine a mathematical model for the transmission of Streptococcus Pneumoniae amongst young children when the carriage transmission coefficient depends on the serotype. Carriage means pneumococcal colonization. There are two sequence types (STs) spreading in a population each of which can be expressed as one of two serotypes. We derive the differential equation model for the carriage spread and perform an equilibrium and global stability analysis on it. A key parameter is the effective reproduction number R (e). For R (e) ≤ 1, there is only the carriage-free equilibrium (CFE) and the carriage will die out whatever be the starting values. For R (e) > 1, unless the effective reproduction numbers of the two STs are equal, in addition to the CFE there are two carriage equilibria, one for each ST. If the ST with the largest effective reproduction number is initially present, then in the long-term the carriage will tend to the corresponding equilibrium.     

A mathematical model of force transmission from intrafascicularly terminating muscle fibers

Many long skeletal muscles are comprised of fibers that terminate intrafascicularly. Force from terminating fibers can be transmitted through shear within the endomysium that surrounds fibers or through tension within the endomysium that extends from fibers to the tendon; however, it is unclear which pathway dominates in force transmission from terminating fibers. The purpose of this work was to develop mathematical models to (i) compare the efficacy of lateral (through shear) and longitudinal (through tension) force transmission in intrafascicularly terminating fibers, and (ii) determine how force transmission is affected by variations in the structure and properties of fibers and the endomysium. The models demonstrated that even though the amount of force that can be transmitted from an intrafascicularly terminating fiber is dependent on fiber resting length (the unstretched length at which passive stress is zero), endomysium shear modulus, and fiber volume fraction (the fraction of the muscle cross-sectional area that is occupied by fibers), fibers that have values of resting length, shear modulus, and volume fraction within physiologic ranges can transmit nearly all of their peak isometric force laterally through shearing of the endomysium. By contrast, the models predicted only limited force transmission ability through tension within the endomysium that extends from the fiber to the tendon. Moreover, when fiber volume fraction decreases to unhealthy ranges (less than 50%), the force-transmitting potential of terminating fibers through shearing of the endomysium decreases significantly. The models presented here support the hypothesis that lateral force transmission through shearing of the endomysium is an effective mode of force transmission in terminating fibers.     

The threshold bias model: a mathematical model for the nomothetic approach of suicide

Background

Comparative and predictive analyses of suicide data from different countries are difficult to perform due to varying approaches and the lack of comparative parameters.

Methodology/Principal Findings

A simple model (the Threshold Bias Model) was tested for comparative and predictive analyses of suicide rates by age. The model comprises of a six parameter distribution that was applied to the USA suicide rates by age for the years 2001 and 2002. Posteriorly, linear extrapolations are performed of the parameter values previously obtained for these years in order to estimate the values corresponding to the year 2003. The calculated distributions agreed reasonably well with the aggregate data. The model was also used to determine the age above which suicide rates become statistically observable in USA, Brazil and Sri Lanka.

Conclusions/Significance

The Threshold Bias Model has considerable potential applications in demographic studies of suicide. Moreover, since the model can be used to predict the evolution of suicide rates based on information extracted from past data, it will be of great interest to suicidologists and other researchers in the field of mental health.     

On a mathematical model for body tissue inflammation

In the present paper I will try to prove the mathematical validity of a model on the localized bacterial infection for tissue inflammation. This model was proposed by Lauffenburger and Kennedy [3], and it describes the inflammatory response to bacterial invasion of body tissue. I prove the mathematical validity of the model by means of a positivity theorem, an existence theorem and a uniqueness theorem. In spite of the apparent simplicity of the problem, the solution requires a delicate set of techniques. It seems very difficult to extend these techniques to a model in more than one dimension.     

Development of a mathematical model for mechanical transmission of trypanosomes and other pathogens of cattle transmitted by tabanids

Mechanical transmission of pathogens by biting insects is a non-specific phenomenon in which pathogens are transmitted from the blood of an infected host to another host during interrupted feeding of the insects. A large range of pathogens can be mechanically transmitted, e.g. hemoparasites, bacteria and viruses. Some pathogens are almost exclusively mechanically transmitted, while others are also cyclically transmitted. For agents transmitted both cyclically and mechanically (mixed transmission), such as certain African pathogenic trypanosomes, the relative impact of mechanical versus cyclical transmission is essentially unknown. We have developed a mathematical model of pathogen transmission by a defined insect population to evaluate the importance of mechanical transmission. Based on a series of experiments aimed at demonstrating mechanical transmission of African trypanosomes by tabanids, the main parameters of the model were either quantified (host parasitaemia, mean individual insect burden, initial prevalence of infection) or estimated (unknown parameters). This model allows us to simulate the evolution of pathogen prevalence under various predictive circumstances, including control measures and could be used to assess the risk of mechanical transmission under field conditions. If adjustments of parameters are provided, this model could be generalized to other pathogenic agents present in the blood of their hosts (Bovine Leukemia virus, Anaplasma, etc.) or other biting insects such as biting muscids (stomoxyines) and hippoboscids.     

Scrapie strain transmission studies in ovine PrP transgenic mice reveal dissimilar susceptibility

The Tg(OvPrP4) mouse line, expressing the sheep prion protein, is a sensitive model crucial for the identification of the bovine spongiform encephalopathy agent possibly present in natural sheep spongiform encephalopathies. It was also previously demonstrated as susceptible to infection with natural scrapie isolates from sheep harbouring various genotypes. The performance of this new transgenic mouse line in scrapie strain characterization was further assessed by intracranial inoculation of five groups of Tg(OvPrP4) mice with brain homogenate of the wild type mouse-adapted scrapie strains, C506M3, 22A, 79A, 87V, or Chandler. The Tg(OvPrP4) mice were susceptible to the scrapie agent transmitted using mouse-adapted scrapie strains but not equivalently. Strains 87V and Chandler were most readily transmissible followed by 79A and C506M3. Strain 22A was the least transmissible. Clinical signs, survival data, spongiosis, and PrP^sc distribution were also reported. These various data demonstrate the possibility of distinguishing between scrapie strains. Our findings are discussed with regard to agent strain and host factors and already demonstrate the dissimilar susceptibilities of Tg(OvPrP4) mice to the different murine strains studied, thus, reinforcing their potential use in strain typing studies.     

Analysis of unstable behavior in a mathematical model for erythropoiesis

We consider an age-structured model that describes the regulation of erythropoiesis through the negative feedback loop between erythropoietin and hemoglobin. This model is reduced to a system of two ordinary differential equations with two constant delays for which we show existence of a unique steady state. We determine all instances at which this steady state loses stability via a Hopf bifurcation through a theoretical bifurcation analysis establishing analytical expressions for the scenarios in which they arise. We show examples of supercritical Hopf bifurcations for parameter values estimated according to physiological values for humans found in the literature and present numerical simulations in agreement with the theoretical analysis. We provide a strategy for parameter estimation to match empirical measurements and predict dynamics in experimental settings, and compare existing data on hemoglobin oscillation in rabbits with predictions of our model.