Virus load and antigenic diversity

In this paper, we analyse mathematical models for the interaction between virus replication and immune responses. We show that the immune system can provide selection pressure for or against viral diversity. The paper provides new insights into the relationship between virus load (=the abundance of virus in an infected individual) and antigenic diversity. Antigenic variation can increase virus load during infections, but the correlation between load and diversity in comparisons among different infected individuals can be positive or negative, depending on whether individuals differ in their cross-reactive or strain-specific immune responses. We derive two models: our first model applies to any replicating parasite that can escape from immune responses; our second model includes immune function impairment, and specifically describes infections with the human immunodeficiency virus (HIV).     

Coexistence of cytoplasmic incompatibility and male-killing-inducing endosymbionts, and their impact on host gene flow

Male-killing (MK) and cytoplasmic incompatibility (CI) inducing bacteria are among the most common endosymbionts of arthropods. Previous theoretical research has demonstrated that these two types of endosymbionts cannot stably coexist within a single unstructured host population if no doubly infected host individuals occur. Here, we analyse a model of two host subpopulations connected by migration. We demonstrate that coexistence of MK- and CI-inducing endosymbionts is possible if migration rates are sufficiently low. In particular, our results suggest that for coexistence to be possible, migration rates into the subpopulation infected predominantly with MK-inducing endosymbionts must be considerably low, while migration rates from the MK- to the CI-infected subpopulation can be very high. We also analyse how the presence of MK- and CI-inducing endosymbionts affects host gene flow between the two subpopulations. Employing the concept of the 'effective migration rate', we demonstrate that compared with an uninfected subdivided population, gene flow is increased towards the MK-infected island, but decreased towards the CI-infected island. We discuss our results with respect to the butterfly Hypolimnas bolina, in which infection polymorphism of CI- and MK-inducing Wolbachia has been reported across South-Pacific island populations.     

Revealing the True Incidence of Pandemic A(H1N1)pdm09 Influenza in Finland during the First Two Seasons — An Analysis Based on a Dynamic Transmission Model

The threat of the new pandemic influenza A(H1N1)pdm09 imposed a heavy burden on the public health system in Finland in 2009-2010. An extensive vaccination campaign was set up in the middle of the first pandemic season. However, the true number of infected individuals remains uncertain as the surveillance missed a large portion of mild infections. We constructed a transmission model to simulate the spread of influenza in the Finnish population. We used the model to analyse the two first years (2009-2011) of A(H1N1)pdm09 in Finland. Using data from the national surveillance of influenza and data on close person-to-person (social) contacts in the population, we estimated that 6% (90% credible interval 5.1 – 6.7%) of the population was infected with A(H1N1)pdm09 in the first pandemic season (2009/2010) and an additional 3% (2.5 – 3.5%) in the second season (2010/2011). Vaccination had a substantial impact in mitigating the second season. The dynamic approach allowed us to discover how the proportion of detected cases changed over the course of the epidemic. The role of time-varying reproduction number, capturing the effects of weather and changes in behaviour, was important in shaping the epidemic.     

Acephaline gregarine parasites (Monocystis sp.) are not transmitted sexually among their lumbricid earthworm hosts

The precise transmission mode(s) of acephaline gregarines in their earthworm hosts has long been questioned, yet a rigorous experimental evaluation of sexual transmission is currently lacking. That Monocystis sp., a common gregarine parasite of the earthworm Lumbricus terrestris, infects the sexual organs of its host is suggestive of sexual transmission. Considering the divergent evolutionary consequences of various modes of transmission, excluding or proving sexual transmission in this host-parasite system is critical to fully understanding it. We cultured uninfected earthworms from cocoons and subsequently mated them to either an infected or uninfected partner (from the wild). We then compared these individuals with an orally infected group, which were infected using a newly developed gavage (oral injection) method. Our data have unambiguously established that (1) horizontal sexual transmission does not play a significant role in the transmission of Monocystis sp., and (2) oral transmission through the soil is likely the principal mode of transmission between earthworms. This finding is important to models of mate-choice because infection avoidance does not appear to drive mating decisions. Finally, we further report a successful and relatively simple method to obtain infection-free individuals, which can subsequently be infected via oral gavage and used in empirical studies.     

Fatal disease and demographic Allee effect: population persistence and extinction

If a healthy stable host population at the disease-free equilibrium is subject to the Allee effect, can a small number of infected individuals with a fatal disease cause the host population to go extinct? That is, does the Allee effect matter at high densities? To answer this question, we use a susceptible–infected epidemic model to obtain model parameters that lead to host population persistence (with or without infected individuals) and to host extinction. We prove that the presence of an Allee effect in host demographics matters even at large population densities. We show that a small perturbation to the disease-free equilibrium can eventually lead to host population extinction. In addition, we prove that additional deaths due to a fatal infectious disease effectively increase the Allee threshold of the host population demographics.     

A Data-Driven Mathematical Model of CA-MRSA Transmission among Age Groups: Evaluating the Effect of Control Interventions

Community associated methicillin-resistant Staphylococcus aureus (CA-MRSA) has become a major cause of skin and soft tissue infections (SSTIs) in the US. We developed an age-structured compartmental model to study the spread of CA-MRSA at the population level and assess the effect of control intervention strategies. We used Monte-Carlo Markov Chain (MCMC) techniques to parameterize our model using monthly time series data on SSTIs incidence in children (≤19 years) during January 2004 -December 2006 in Maricopa County, Arizona. Our model-based forecast for the period January 2007–December 2008 also provided a good fit to data. We also carried out an uncertainty and sensitivity analysis on the control reproduction number, which we estimated at 1.3 (95% CI [1.2,1.4]) based on the model fit to data. Using our calibrated model, we evaluated the effect of typical intervention strategies namely reducing the contact rate of infected individuals owing to awareness of infection and decolonization strategies targeting symptomatic infected individuals on both and the long-term disease dynamics. We also evaluated the impact of hypothetical decolonization strategies targeting asymptomatic colonized individuals. We found that strategies focused on infected individuals were not capable of achieving disease control when implemented alone or in combination. In contrast, our results suggest that decolonization strategies targeting the pediatric population colonized with CA-MRSA have the potential of achieving disease elimination.     

Fatal disease and demographic Allee effect: population persistence and extinction

If a healthy stable host population at the disease-free equilibrium is subject to the Allee effect, can a small number of infected individuals with a fatal disease cause the host population to go extinct? That is, does the Allee effect matter at high densities? To answer this question, we use a susceptible-infected epidemic model to obtain model parameters that lead to host population persistence (with or without infected individuals) and to host extinction. We prove that the presence of an Allee effect in host demographics matters even at large population densities. We show that a small perturbation to the disease-free equilibrium can eventually lead to host population extinction. In addition, we prove that additional deaths due to a fatal infectious disease effectively increase the Allee threshold of the host population demographics.     

On an interacting particle system modeling an epidemic

We consider an interacting particle system onZ ^dto model an epidemic. Each site ofZ ^dcan be in either one of three states: empty, healthy or infected. Healthy and infected individuals give birth at different rates to healthy individuals on empty sites. Healthy individuals get infected by infected individuals. Infected and healthy individuals die at different rates. We prove that in dimension 1 and with nearest-neighbor interactions the epidemic may persist forever if and only if the rate at which infected individuals give birth to healthy individuals is high enough. This is in sharp contrast with models analysed by Andjel and Schinazi (1994) and Sato et al. (1994) where infected individuals do not give birth. We also show that some results in the latter reference can be obtained easily and rigorously using probabilistic coupling to the contact process.     

Schistosoma mansoni antigen-driven interleukin-10 production in infected asthmatic individuals

Asthmatics infected with Schistosoma mansoni have a less severe course of asthma and an inhibition of the Th2 inflammatory response that seems to be mediated by interleukin (IL-10). The objective of this study was to evaluate the capacity of some S. mansoni antigens to stimulate IL-10 production in vitro by cells of asthmatic infected individuals. Peripheral bloods mononuclear cells were stimulated with the S. mansoni recombinant antigens Sm22.6, Sm14, P24, and PIII antigen. IL-10 was measured in the supernatants of cultures. As the recombinant antigens were cloned in Escherichia coli, we blocked contaminant endotoxin with polymyxin B added to the cultures. We demonstrated that all antigens used drove high production of IL-10 in S. mansoni infected individuals (n = 13, 408 +/- 514 and 401 +/- 383 pg/ml, 484 +/- 245 pg/ml, 579 +/- 468 pg/ml, respectively). In asthmatics infected with S. mansoni (n = 21) rP24 induced higher levels of IL-10 (565 +/- 377 pg/ml) when compared to PIII, rSm14 and rSm22.6 (184 +/- 209 pg/ml; 292 +/- 243 pg/ml; 156 +/- 247 pg/ml, respectively). Conclusion: the S. mansoni antigens evaluated in this study stimulated IL-10 production by cells from infected individuals and therefore they have the potential to be used as a modulator of the inflammatory response in asthma.     

The influence of sexually active non-reproductive groups on persistent sexually transmitted diseases

We describe several population models exposed to a mild life-long sexually transmitted disease, i.e. without significant increased mortality among infected individuals and providing no immunity/recovery. We then modify these models to include non-reproductive groups consisting of those isolated from sexual contact and those who are sexually active but infertile due to choice, medical or other reasons. We analyse the potential effect on the dynamics of the population. We are interested in how the isolated class may curb the growth of the infected group while keeping the healthy population at acceptable levels. We also analyse the difference between being sexually active and abstained within the non-reproductive class and its impact on the epidemic reproductive number and the nature of the bifurcation around the disease-free equilibrium. We provide a comparison with our models introduced in a previous article, which include only the isolated from sexual contact class.     

The influence of sexually active non-reproductive groups on persistent sexually transmitted diseases

We describe several population models exposed to a mild life-long sexually transmitted disease, i.e. without significant increased mortality among infected individuals and providing no immunity/recovery. We then modify these models to include non-reproductive groups consisting of those isolated from sexual contact and those who are sexually active but infertile due to choice, medical or other reasons. We analyse the potential effect on the dynamics of the population. We are interested in how the isolated class may curb the growth of the infected group while keeping the healthy population at acceptable levels. We also analyse the difference between being sexually active and abstained within the non-reproductive class and its impact on the epidemic reproductive number and the nature of the bifurcation around the disease-free equilibrium. We provide a comparison with our models introduced in a previous article, which include only the isolated from sexual contact class.     

A deterministic model for the dynamics of furunculosis in chinook salmon Oncorhynchus tshawytscha

Studies were undertaken to determine the parameters of transmission of Aeromonas salmonicida in chinook salmon Oncorhynchus tshawytscha, and to develop a deterministic model of the dynamics of experimental furunculosis. For determination of disease transmission coefficient (beta), disease-related mortality rate (alpha) and natural mortality rate (gamma), fish in 70 tanks (approximately 42 fish tank(-1)) were each exposed to a single infectious donor fish, 7 tanks were randomly selected daily and all individuals were examined for the presence of A. salmonicida in the kidney. The proportion of susceptible (S), infected (I) and removed (R, dead) individuals were determined daily. The parameters beta, alpha, gamma, reproductive ratio (R0) and threshold density were estimated to be 0.0214 infected ind. d(-1), 0.29 infected ind. d(-1), 0.00015 ind. d(-1), 3.23 and 13.56 ind., respectively. Using these parameters, a deterministic disease model of A. salmonicida infection as a cause of furunculosis was constructed. The net rate at which new individuals became infected (the incidence rate) per unit time was proportional to S x I x beta. The model-produced data for S were significantly associated with experimental data (r2 = 0.92). In brief, a simple SIR (susceptible-infected-removed) model was successfully utilized to simulate observed data     

Robustness of group testing in the estimation of proportions

In binomial group testing, unlike one-at-a-time testing, the test unit consists of a group of individuals, and each group is declared to be defective or nondefective. A defective group is one that is presumed to include one or more defective (e.g., infected, positive) individuals and a nondefective group to contain only nondefective individuals. The usual binomial model considers the individuals being grouped as independent and identically distributed Bernoulli random variables. Under the binomial model and presuming that groups are tested and classified without error, it has been shown that, when the proportion of defective individuals is low, group testing is often preferable to individual testing for identifying infected individuals and for estimating proportions of defectives. We discuss the robustness of group testing for estimating proportions when the underlying assumptions of (i) no testing errors and (ii) independent individuals are violated. To evaluate the effect of these model violations, two dilution-effect models and a serial correlation model are considered. Group testing proved to be quite robust to serial correlation. In the presence of a dilution effect, smaller group sizes should be used, but most of the benefits of group testing can still be realized.     

Household Epidemics: Modelling Effects of Early Stage Vaccination

A Markovian susceptible → infectious → removed (SIR) epidemic model is considered in a community partitioned into households. A vaccination strategy, which is implemented during the early stages of the disease following the detection of infected individuals is proposed. In this strategy, the detection occurs while an individual is infectious and other susceptible household members are vaccinated without further delay. Expressions are derived for the influence on the reproduction numbers of this vaccination strategy for equal and unequal household sizes. We fit previously estimated parameters from influenza and use household distributions for Sweden and Tanzania census data. The results show that the reproduction number is much higher in Tanzania (6 compared with 2) due to larger households, and that infected individuals have to be detected (and household members vaccinated) after on average 5 days in Sweden and after 3.3 days in Tanzania, a much smaller difference.     

Optimal treatment of an SIR epidemic model with time delay

In this paper the optimal control strategies of an SIR (susceptible–infected–recovered) epidemic model with time delay are introduced. In order to do this, we consider an optimally controlled SIR epidemic model with time delay where a control means treatment for infectious hosts. We use optimal control approach to minimize the probability that the infected individuals spread and to maximize the total number of susceptible and recovered individuals. We first derive the basic reproduction number and investigate the dynamical behavior of the controlled SIR epidemic model. We also show the existence of an optimal control for the control system and present numerical simulations on real data regarding the course of Ebola virus in Congo. Our results indicate that a small contact rate(probability of infection) is suitable for eradication of the disease (Ebola virus) and this is one way of optimal treatment strategies for infectious hosts.     

Epidemiology of Chagas disease in non-endemic countries: the role of international migration

Human infection with the protozoa Trypanosoma cruzi extends through North, Central, and South America, affecting 21 countries. Most human infections in the Western Hemisphere occur through contact with infected bloodsucking insects of the triatomine species. As T. cruzi can be detected in the blood of untreated infected individuals, decades after infection took place; the infection can be also transmitted through blood transfusion and organ transplant, which is considered the second most common mode of transmission for T. cruzi. The third mode of transmission is congenital infection. Economic hardship, political problems, or both, have spurred migration from Chagas endemic countries to developed countries. The main destination of this immigration is Australia, Canada, Spain, and the United States. In fact, human infection through blood or organ transplantation, as well as confirmed or potential cases of congenital infections has been described in Spain and in the United States. Estimates reported here indicates that in Australia in 2005-2006, 1067 of the 65,255 Latin American immigrants (16 per 1000) may be infected with T. cruzi, and in Canada, in 2001, 1218 of the 131,135 immigrants (9 per 1000) whose country of origin was identified may have been also infected. In Spain, a magnet for Latin American immigrants since the 2000, 6141 of 38,777 to 339,954 [corrected] legal immigrants in 2003 (25 per 1000), could be infected. In the United States, 56,028 to 357,205 of the 7,20 million, legal immigrants (8 to 50 per 1000), depending on the scenario, from the period 1981-2005 may be infected with T. cruzi. On the other hand, 33,193 to 336,097 of the estimated 5,6 million undocumented immigrants in 2000 (6 to 59 per 1000) could be infected. Non endemic countries receiving immigrants from the endemic ones should develop policies to protect organ recipients from T. cruzi infection, prevent tainting the blood supply with T. cruzi, and implement secondary prevention of congenital Chagas disease.     

Avian cestodes affect the behaviour of their intermediate host Artemia parthenogenetica: an experimental study

The brine shrimp Artemia parthenogenetica (Crustacea, Branchiopoda) is intermediate host for several cestode species whose final hosts are waterbirds. Previous field studies have shown that brine shrimps infected with cestodes have a bright red colour and are spatially segregated in the water column. However, the ethological mechanisms explaining such field observations are unknown. Changes in appearance and behaviour induced by trophically transmitted parasites have been shown to increase the risk of predation by the final host. In this experimental study, we compared the behaviour of uninfected Artemia and those infected by avian cestodes. We found that parasitised individuals behave differently from unparasitised ones in several ways. In contrast to uninfected individuals, infected brine shrimps were photophilous and showed increased surface-swimming behaviour. These observations suggest that the modified behaviour (in addition to the bright red colour of the majority of the infected individuals) results in infected brine shrimps becoming more vulnerable to avian final hosts, which facilitates parasite transmission. We discuss our results in terms of the adaptive nature of behavioural changes and their potential implications for the hypersaline ecosystem.     

Limits of a multi-patch SIS epidemic model

 We start from a stochastic SIS model for the spread of epidemics among a population partitioned into M sites, each containing N individuals; epidemic spread occurs through within-site (`local') contacts and global contacts. We analyse the limit behaviour of the system as M and N increase to ∞. Two limit procedures are considered, according to the order in which M and N go to ∞; independently of the order, the limiting distribution of infected individuals across sites is a probability measure, whose evolution in time is governed by the weak form of a PDE. Existence and uniqueness of the solutions to this problem is shown. Finally, it is shown that the infected distribution converges, as time goes to infinity, to a Dirac measure at the value x ^* , the equilibrium of a single-patch SIS model with contact rate equal to the sum of local and global contacts. Received: 18 July 2001 / Revised version: 16 March 2002 / Published online: 26 September 2002 Mathematics Subject Classification (2000): 92D30, 60F99 Key words or phrases: SIS epidemic – Metapopulation – Markov population processes – Weak convergence of measures     

Altered behavior of the snail Biomphalaria glabrata as a result of infection with Schistosoma mansoni

In this comparative behavioral study, the effect of infection with Schistosoma mansoni on its snail intermediate host Biomphalaria glabrata was investigated. Three groups of snails were compared for their activity: (1) uninfected, (2) infected with male parasites, and (3) infected with female parasites. In solitary movement trials, uninfected snails traveled greater distances at faster rates, explored more surface area, and had shorter rest periods than snails infected with either male or female schistosomes. In Y-maze experiments designed to determine attraction, the uninfected snails more often and more quickly moved toward other snails than the infected individuals. Snails from all 3 groups were more attracted to infected individuals than to uninfected ones. There was no difference in attraction toward snails infected with male or female parasites. These experiments provide evidence that behavioral alterations as a result of infection may lead to aggregation of infected snails in the field. We propose that such an effect may result in enhanced parasite transmission.