Mathematical models for hantavirus infection in rodents

Mathematical Model of the Spread of Hantavirus Infection

A mathematical epidemiological model incorporating the mobility of rodents and human groups among zones of less or major contact between them is presented. The hantavirus infection dynamics is expressed using a model type SEIR (Susceptible-Exposed-Infectious-Removed), which incorporates the displacement of the rodent and the human, between the urban and rural sector, the latter being subdivided in populated and non-populated. The results show the impact that rodent or human displacement may have on the propagation of hantavirus infection. Human mobility is more significant than rodents in increasing the number of hantavirus infection cases. The results found may be used as a reference by the health authorities to develop more specific campaigns on the territorial dynamics of the rodent, attend to the mobility of humans in these territories, mainly agricultural and forestry workers, and strengthen control-prevention actions in the community, to prevent future outbreaks that are fatal.

Modeling of hantavirus cardiopulmonary syndrome

Introduction Hantavirus cardiopulmonary syndrome is an infection caused by rodents of the Bunyanvirales family towards humans. This disease in Chile is considered endemic, which has a high fatality rate. At present, some studies show the contagion between people of the Andes virus, whose locality is concentrated in Argentina and Chile. Objectives Analyze the possibility of hantavirus transmission between humans using an SEIR-type mathematical model. Methods An SEIR (Susceptible, Exposed, Infectious and Recovered) mathematical model to express the dynamics of hantavirus disease is proposed, including the possibility of human-to-human transmission and the perception of risk. Results The peak of human-to-human contagion decreases by about 25% after increasing people’s perception of risk by reducing the rate of resistance to changeand increasing the speed of people’s reaction. Conclusions It is urgent to review risk communication strategies and prevention measures in the face of this possibility of massive human-tohuman infections, in addition to strengthening research and planning the development of a vaccine to protect populations exposed to this disease with a high fatality rate.

Impact of Predator Exclusion and Habitat on Seroprevalence of New World Orthohantavirus Harbored by Two Sympatric Rodents within the Interior Atlantic Forest

Understanding how perturbations to trophic interactions influence virus-host dynamics is essential in the face of ongoing biodiversity loss and the continued emergence of RNA viruses and their associated zoonoses. Herein, we investigated the role of predator exclusion on rodent communities and the seroprevalence of hantaviruses within the Reserva Natural del Bosque Mbaracayú (RNBM), which is a protected area of the Interior Atlantic Forest (IAF). In the IAF, two sympatric rodent reservoirs, Akodon montensis and Oligoryzomys nigripes, harbor Jaborá and Juquitiba hantavirus (JABV, JUQV), respectively. In this study, we employed two complementary methods for predator exclusion: comprehensive fencing and trapping/removal. The goal of exclusion was to preclude the influence of predation on small mammals on the sampling grids and thereby potentially reduce rodent mortality. Following baseline sampling on three grid pairs with different habitats, we closed the grids and began predator removal. By sampling three habitat types, we controlled for habitat-specific effects, which is important for hantavirus-reservoir dynamics in neotropical ecosystems. Our six-month predator exclusion experiment revealed that the exclusion of terrestrial mammalian predators had little influence on the rodent community or the population dynamics of A. montensis and O. nigripes. Instead, fluctuations in species diversity and species abundances were influenced by sampling session and forest degradation. These results suggest that seasonality and landscape composition play dominant roles in the prevalence of hantaviruses in rodent reservoirs in the IAF ecosystem.

Convergent evolution of diverse Bacillus anthracis outbreak strains toward altered surface oligosaccharides that modulate anthrax pathogenesis

Bacillus anthracis, a spore-forming gram-positive bacterium, causes anthrax. The external surface of the exosporium is coated with glycosylated proteins. The sugar additions are capped with the unique monosaccharide anthrose. The West African Group (WAG) B. anthracis have mutations rendering them anthrose deficient. Through genome sequencing, we identified 2 different large chromosomal deletions within the anthrose biosynthetic operon of B. anthracis strains from Chile and Poland. In silico analysis identified an anthrose-deficient strain in the anthrax outbreak among European heroin users. Anthrose-deficient strains are no longer restricted to West Africa so the role of anthrose in physiology and pathogenesis was investigated in B. anthracis Sterne. Loss of anthrose delayed spore germination and enhanced sporulation. Spores without anthrose were phagocytized at higher rates than spores with anthrose, indicating that anthrose may serve an antiphagocytic function on the spore surface. The anthrose mutant had half the LD50 and decreased time to death (TTD) of wild type and complement B. anthracis Sterne in the A/J mouse model. Following infection, anthrose mutant bacteria were more abundant in the spleen, indicating enhanced dissemination of Sterne anthrose mutant. At low sample sizes in the A/J mouse model, the mortality of ΔantC-infected mice challenged by intranasal or subcutaneous routes was 20% greater than wild type. Competitive index (CI) studies indicated that spores without anthrose disseminated to organs more extensively than a complemented mutant. Death process modeling using mouse mortality dynamics suggested that larger sample sizes would lead to significantly higher deaths in anthrose-negative infected animals. The model was tested by infecting Galleria mellonella with spores and confirmed the anthrose mutant was significantly more lethal. Vaccination studies in the A/J mouse model showed that the human vaccine protected against high-dose challenges of the nonencapsulated Sterne-based anthrose mutant. This work begins to identify the physiologic and pathogenic consequences of convergent anthrose mutations in B. anthracis.

Why Hantavirus Prevalence Does Not Always Increase With Host Density: Modeling the Role of Host Spatial Behavior and Maternal Antibodies

For wildlife diseases, one often relies on host density to predict host infection prevalence and the subsequent force of infection to humans in the case of zoonoses. Indeed, if transmission is mainly indirect, i.e., by way of the environment, the force of infection is expected to increase with host density, yet the laborious field data supporting this theoretical claim are often absent. Hantaviruses are among those zoonoses that have been studied extensively over the past decades, as they pose a significant threat to humans. In Europe, the most widespread hantavirus is the Puumala virus (PUUV), which is carried by the bank vole and causes nephropathia epidemica (NE) in humans. Extensive field campaigns have been carried out in Central Finland to shed light on this supposed relationship between bank vole density and PUUV prevalence and to identify other drivers for the infection dynamics. This resulted in the surprising observation that the relationship between bank vole density and PUUV prevalence is not purely monotonic on an annual basis, contrary to what previous models predicted: a higher vole density does not necessary result in a higher infection prevalence, nor in an increased number of humans reported having NE. Here, we advance a novel individual-based spatially-explicit model which takes into account the immunity provided by maternal antibodies and which simulates the spatial behavior of the host, both possible causes for this discrepancy that were not accounted for in previous models. We show that the reduced prevalence in peak years can be attributed to transient immunity, and that the density-dependent spatial vole behavior, i.e., the fact that home ranges are smaller in high density years, plays only a minor role. The applicability of the model is not limited to the study and prediction of PUUV (and NE) occurrence in Europe, as it could be easily adapted to model other rodent-borne diseases, either with indirect or direct transmission.

Stochastic models in seed dispersals: random walks and birth-death processes

Seed dispersals deal with complex systems through which the data collected using advanced seed tracking facilities pose challenges to conventional approaches, such as empirical and deterministic models. The use of stochastic models in current seed dispersal studies is encouraged. This review describes three existing stochastic models: the birth-death process (BDP), a 2 dimensional ( 2D ) symmetric random walks and a 2D intermittent walks. The three models possess Markovian property, which make them flexible for studying natural phenomena. Only a few of applications in ecology are found in seed dispersals. The review illustrates how the models are to be used in seed dispersals context. Using the nonlinear BDP, we formulate the individual-based models for two competing plant species while the cover time model is formulated by the symmetric and intermittent random walks. We also show that these three stochastic models can be formulated using the Gillespie algorithm. The full cover time obtained by the symmetric random walks can approximate the Gumbel distribution pattern as the other searching strategies do. We suggest that the applications of these models in seed dispersals may lead to understanding of many complex systems, such as the seed removal experiments and behaviour of foraging agents, among others.

The Ecology and Phylogeny of Hosts Drive the Enzootic Infection Cycles of Hantaviruses

Hantaviruses (Family: Hantaviridae; genus: Orthohantavirus) and their associated human diseases occur globally and differ according to their geographic distribution. The structure of small mammal assemblages and phylogenetic relatedness among host species are suggested as strong drivers for the maintenance and spread of hantavirus infections in small mammals. We developed predictive models for hantavirus infection prevalence in rodent assemblages using defined ecological correlates from our current knowledge of hantavirus-host distributions to provide predictive models at the global and continental scale. We utilized data from published research between 1971–2014 and determined the biological and ecological characteristics of small mammal assemblages to predict the prevalence of hantavirus infections. These models are useful in predicting hantavirus disease outbreaks based on environmental and biological information obtained through the surveillance of rodents.

Routine and pulse vaccination for Lassa virus could reduce high levels of endemic disease: A mathematical modelling study

Lassa fever is an acute viral illness caused by Lassa virus (LASV), a rodent-borne pathogen. LASV is endemic to much of Sub-Saharan West Africa, where seasonal outbreaks cause significant morbidity and mortality. Increased global awareness of LASV has led to development of improved diagnostic tests, treatments and vaccines. As vaccine candidates are trialled, it is essential to assess the potential outcomes of introducing a LASV vaccination program in endemic regions. This study investigates the potential outcomes of routine and pulse vaccination strategies using a deterministic mathematical model that captures seasonal LASV transmission between rodents and humans. For plausible parameter values, we find that immunization of 40% of infants at 70% vaccine effectiveness achieves a population-level reduction in infectious case numbers of 30%, while coverage of 60% at 90% vaccine effectiveness achieves a 56% reduction. Similar reductions can be achieved more rapidly via population-wide pulse vaccination at 11% coverage (30% reduction at 70% effectiveness) or 23% coverage (56% reduction at 90% effectiveness) repeated every 10 years. Similar pulse vaccine doses delivered at reduced frequency, but increased coverage achieves a greater reduction in infectious cases. Findings around infant vaccination are sensitive to our assumption that immunity is life-long, while pulse-vaccination has only slightly reduced effect if immunity lasts 10-30 years. An effective LASV vaccination program would incorporate pulse vaccination in addition to routine childhood immunization to limit disease. Estimates of feasible vaccine coverage and effectiveness are needed to fully quantify the likely benefits of a vaccination program in LASV endemic regions.

Shifted Boubaker Lagrangian approach for solving biological systems

Mathematical models and computer simulations are useful experimental tools for building and testing theories. Many mathematical models in biology can be formulated by a nonlinear system of ordinary differential equations. This work deals with the numerical solution of the hantavirus infection model, the human immunodeficiency virus (HIV) infection model of CD4[Formula: see text]T cells and the susceptible–infected–removed (SIR) epidemic model using a new reliable algorithm based on shifted Boubaker Lagrangian (SBL) method. This method reduces the solution of such system to a system of linear or nonlinear algebraic equations which are solved using the Newton iteration method. The obtained results of the proposed method show highly accurate and valid for an arbitrary finite interval. Also, those are compared with fourth-order Runge–Kutta (RK4) method and with the solutions obtained by some other methods in the literature.

Numerical solution of a spatio-temporal gender-structured model for hantavirus infection in rodents

In this article we describe the transmission dynamics of hantavirus in rodents using a spatio-temporal susceptible-exposed-infective-recovered (SEIR) compartmental model that distinguishes between male and female subpopulations [L.J.S. Allen, R.K. McCormack and C.B. Jonsson, Bull. Math. Biol. 68 (2006), 511--524]. Both subpopulations are assumed to differ in their movement with respect to local variations in the densities of their own and the opposite gender group. Three alternative models for the movement of the male individuals are examined. In some cases the movement is not only directed by the gradient of a density (as in the standard diffusive case), but also by a non-local convolution of density values as proposed, in another context, in [R.M. Colombo and E. Rossi, Commun. Math. Sci., 13 (2015), 369--400]. An efficient numerical method for the resulting convection-diffusion-reaction system of partial differential equations is proposed. This method involves techniques of weighted essentially non-oscillatory (WENO) reconstructions in combination with implicit-explicit Runge-Kutta (IMEX-RK) methods for time stepping. The numerical results demonstrate significant differences in the spatio-temporal behavior predicted by the different models, which suggest future research directions.

Hemorrhagic fever with renal syndrome in China: Mechanisms on two distinct annual peaks and control measures

Hemorrhagic fever with renal syndrome (HFRS) is a rodent-borne disease caused by several serotypes of hantavirus and 90% of all reported HFRS cases occur in China. However, the dynamics of such outbreak, particularly the characteristics of two distinct annual peaks in China, are not well understood. Here, we investigate several of the biologically plausible causes for the peaks in monthly HFRS cases, and find that the key factor is the interplay between periodic transmission rates and rodent periodic birth rate. Analysis of dynamical model reveals that vaccination plays a significant role in the control of HFRS in China. Sensitive analysis of different interventions demonstrates that integrating rodent culling and environmental management with the current vaccination program is effective for HFRS control. Our results suggest that for diseases from animals to human beings, the features of both animals and humans beings should be taken into account in the control and prevention strategies.

MONTHLY PERIODIC OUTBREAK OF HEMORRHAGIC FEVER WITH RENAL SYNDROME IN CHINA

Hemorrhagic fever with renal syndrome (HFRS) spreading from rodent to human beings is a major public health problem in China, which causes high mortality rate. Data obtained from the China Ministry of Health shows that cases of HFRS in China exhibited monthly periodic outbreak. To well reveal the mechanisms about the outbreak of HFRS, we established a dynamical model to explain the periodic behaviors of HFRS in China. We obtained the basic reproduction number [Formula: see text], analyzed the dynamical behavior of the model, and used the model to fit the monthly data of HFRS cases. Our results demonstrated that periodic transmission rates and rodent periodic birth rate of HFRS in China can give rise to the periodic outbreak of HFRS, hence providing insights into taking measures to control HFRS in China.

The association between hantavirus infection and selenium deficiency in mainland China

Hemorrhagic fever with renal syndrome (HFRS) caused by hantaviruses and transmitted by rodents is a significant public health problem in China, and occurs more frequently in selenium-deficient regions. To study the role of selenium concentration in HFRS incidence we used a multidisciplinary approach combining ecological analysis with preliminary experimental data. The incidence of HFRS in humans was about six times higher in severe selenium-deficient and double in moderate deficient areas compared to non-deficient areas. This association became statistically stronger after correction for other significant environment-related factors (low elevation, few grasslands, or an abundance of forests) and was independent of geographical scale by separate analyses for different climate regions. A case-control study of HFRS patients admitted to the hospital revealed increased activity and plasma levels of selenium binding proteins while selenium supplementation in vitro decreased viral replication in an endothelial cell model after infection with a low multiplicity of infection (MOI). Viral replication with a higher MOI was not affected by selenium supplementation. Our findings indicate that selenium deficiency may contribute to an increased prevalence of hantavirus infections in both humans and rodents. Future studies are needed to further examine the exact mechanism behind this observation before selenium supplementation in deficient areas could be implemented for HFRS prevention.

Maripa hantavirus in French Guiana: phylogenetic position and predicted spatial distribution of rodent hosts

A molecular screening of wild-caught rodents was conducted in French Guiana, South America to identify hosts of the hantavirus Maripa described in 2008 in a hantavirus pulmonary syndrome (HPS) case. Over a 9-year period, 418 echimyids and murids were captured. Viral RNA was detected in two sigmodontine rodents, Oligoryzomys fulvescens and Zygodontomys brevicauda, trapped close to the house of a second HPS case that occurred in 2009 and an O. fulvescens close to the fourth HPS case identified in 2013. Sequences from the rodents had 96% and 97% nucleotide identity (fragment of S and M segments, respectively) with the sequence of the first human HPS case. Phylogenetic reconstructions based on the complete sequence of the S segment show that Maripa virus is closely related to Rio Mamore hantavirus. Using environmental descriptors of trapping sites, including vegetation, landscape units, rain, and human disturbance, a maximal entropy-based species distribution model allowed for identification of areas of higher predicted occurrence of the two rodents, where emergence risks of Maripa virus are expected to be higher.

CAN CULLING TO PREVENT MONKEYPOX INFECTION BE COUNTER-PRODUCTIVE? SCENARIOS FROM A THEORETICAL MODEL

In the last two decades, monkeypox outbreaks in human populations in Africa and North America have reminded us that smallpox is not the only poxvirus with potential to cause harm in human populations. Monkeypox transmission is sustained in animal reservoirs, and animal–human contacts are responsible for sporadic outbreaks in humans. Here, we develop and analyze a deterministic epizootic (animal-based) transmission model capturing disease dynamics in an animal population, disease dynamics in an age-structured human population, and their coupling through animal–human contacts. We develop a single-patch model as well as a two-patch meta-population extension. We derive mathematical expressions for the basic reproduction number, which governs the likelihood of a large outbreak. We also investigate the effectiveness of culling strategies and the impact of changes in the animal–human contact rate. Numerical analysis of the model suggests that, for some parameter values, culling can actually have the counter-productive outcome of increasing monkeypox infection in children, if animal reproduction is a density-dependent process. The likelihood of this happening, as well as the prevalence of monkeypox in humans, depends sensitively on the animal–human contact rate. We also find that ignoring age structure in human populations can lead to overestimating the transmissibility of monkeypox in humans. The effectiveness of monkeypox control strategies such as culling can strongly depend on the details of demography and epidemiology in the animal reservoirs that sustain it. Therefore, to better understand how to prevent and control monkeypox outbreaks in humans, better empirical data from wild animal populations where monkeypox is endemic must be collected, and these data must be incorporated into highly structured theoretical models.

Mathematical Modeling of Viral Zoonoses in Wildlife

Zoonoses are a worldwide public health concern, accounting for approximately 75% of human infectious diseases. In addition, zoonoses adversely affect agricultural production and wildlife. We review some mathematical models developed for the study of viral zoonoses in wildlife and identify areas where further modeling efforts are needed.

Biogeographic and ecological regulation of disease: prevalence of Sin Nombre virus in island mice is related to island area, precipitation, and predator richness

The relative roles of top-down and bottom-up forces in affecting disease prevalence in wild hosts is important for understanding disease dynamics and human disease risk. We found that the prevalence of Sin Nombre virus (SNV), the agent of a severe disease in humans (hantavirus pulmonary syndrome), in island deer mice from the eight California Channel Islands was greater with increased precipitation (a measure of productivity), greater island area, and fewer species of rodent predators. In finding a strong signal of the ecological forces affecting SNV prevalence, our work highlights the need for future work to understand the relative importance of average rodent density, population fluctuations, behavior, and specialist predators as they affect SNV prevalence. In addition to illustrating the importance of both bottom-up and top-down limitation of disease prevalence, our results suggest that predator richness may have important bearing on the risk of exposure to animal-borne diseases that affect humans.

A global perspective on hantavirus ecology, epidemiology, and disease

Hantaviruses are enzootic viruses that maintain persistent infections in their rodent hosts without apparent disease symptoms. The spillover of these viruses to humans can lead to one of two serious illnesses, hantavirus pulmonary syndrome and hemorrhagic fever with renal syndrome. In recent years, there has been an improved understanding of the epidemiology, pathogenesis, and natural history of these viruses following an increase in the number of outbreaks in the Americas. In this review, current concepts regarding the ecology of and disease associated with these serious human pathogens are presented. Priorities for future research suggest an integration of the ecology and evolution of these and other host-virus ecosystems through modeling and hypothesis-driven research with the risk of emergence, host switching/spillover, and disease transmission to humans.

A habitat-based model for the spread of hantavirus between reservoir and spillover species

New habitat-based models for spread of hantavirus are developed which account for interspecies interaction. Existing habitat-based models do not consider interspecies pathogen transmission, a primary route for emergence of new infectious diseases and reservoirs in wildlife and man. The modeling of interspecies transmission has the potential to provide more accurate predictions of disease persistence and emergence dynamics. The new models are motivated by our recent work on hantavirus in rodent communities in Paraguay. Our Paraguayan data illustrate the spatial and temporal overlaps among rodent species, one of which is the reservoir species for Jabora virus and others which are spillover species. Disease transmission occurs when their habitats overlap. Two mathematical models, a system of ordinary differential equations (ODE) and a continuous-time Markov chain (CTMC) model, are developed for spread of hantavirus between a reservoir and a spillover species. Analysis of a special case of the ODE model provides an explicit expression for the basic reproduction number, R(0), such that if R(0)<1, then the pathogen does not persist in either population but if R(0)>1, pathogen outbreaks or persistence may occur. Numerical simulations of the CTMC model display sporadic disease incidence, a new behavior of our habitat-based model, not present in other models, but which is a prominent feature of the seroprevalence data from Paraguay. Environmental changes that result in greater habitat overlap result in more encounters among various species that may lead to pathogen outbreaks and pathogen establishment in a new host.

Hantavirus transmission in sylvan and peridomestic environments

We developed a compartmental model for hantavirus infection in deer mice (Peromyscus maniculatus) with the goal of comparing relative importance of direct and indirect transmission in sylvan and peridomestic environments. A direct transmission occurs when the infection is mediated by the contact of an infected and an uninfected mouse, while an indirect transmission occurs when the infection is mediated by the contact of an uninfected mouse with, for instance, infected soil. Based on population dynamics data and estimates of hantavirus decay in the two types of environments, our model predicts that direct transmission dominates in the sylvan environment, while both pathways are important in peridomestic environments. The model allows us to compute a basic reproduction number R(0), which indicates whether the virus will be endemic or eradicated from the mouse population, in both an autonomous and a time-periodic model. Our analysis can be used to evaluate various eradication strategies.

The basic reproduction number in epidemic models with periodic demographics

Patterns of contact in social behaviour and seasonality due to environmental influences often affect the spread and persistence of diseases. Models of epidemics with seasonality and patterns in the contact rate include time-periodic coefficients, making the systems nonautonomous. No general method exists for calculating the basic reproduction number, the threshold for disease extinction, in nonautonomous epidemic models. However, for some epidemic models with periodic coefficients and constant population size, the time-averaged basic reproduction number has been shown to be a threshold for disease extinction. We extend these results by showing that the time-averaged basic reproduction number is a threshold for disease extinction when the population demographics are periodic. The results are shown to hold in epidemic models with periodic demographics that include temporary immunity, isolation, and multiple strains.

The role of heterogeneity in the persistence and prevalence of Sin Nombre virus in deer mice

Many diseases persist at a relatively low prevalence, seemingly close to extinction. For a chronic disease in a homogeneous population, reducing the transmission rate by a fraction proportional to the prevalence would be sufficient to eradicate the disease. This study examines how higher prevalence of the Sin Nombre virus in male deer mice (Peromyscus maniculatus) might contribute to disease persistence. Analyzing data from over 2,000 individual mice captured in 19 sites over 4 years, we found prevalences of 18.5% in males and 8.8% in females. By examining recaptures, we determined that males are more likely to contract the infection because of higher susceptibility or higher encounter rates. Comparing across 86 sampling periods, we found a higher proportion of males when population densities were low. A capture-recapture analysis indicates that males live longer than females. A mathematical model based on the measured parameters and population size trajectories suggests that the combined heterogeneity in encounters, susceptibility, and mortality may buffer the disease from extinction by concentrating disease in the subgroup most likely to transmit the disease. This buffering effect is not significantly stronger in a fluctuating population, indicating that these forms of heterogeneity might not be the key for disease persistence through host population bottlenecks.

Models for an arenavirus infection in a rodent population: consequences of horizontal, vertical and sexual transmission

Arenaviruses are associated with rodent-transmitted diseases in humans. Five arenaviruses are known to cause human illness: Lassa virus, Junin virus, Machupo virus, Guanarito virus and Sabia virus. In this investigation, we model the spread of Machupo virus in its rodent host Calomys callosus. Machupo virus infection in humans is known as Bolivian hemorrhagic fever (BHF) which has a mortality rate of approximately 5-30% [31]. Machupo virus is transmitted among rodents through horizontal (direct contact), vertical (infected mother to offspring) and sexual transmission. The immune response differs among rodents infected with Machupo virus. Either rodents develop immunity and recover (immunocompetent) or they do not develop immunity and remain infected (immunotolerant). We formulate a general deterministic model for male and female rodents consisting of eight differential equations, four for females and four for males. The four states represent susceptible, immunocompetent, immunotolerant and recovered rodents, denoted as S, I( t), I( c)and R, respectively. A unique disease-free equilibrium (DFE) is shown to exist and a basic reproduction number R( 0)is computed using the next generation matrix approach. The DFE is shown to be locally asymptotically stable if R(0) < 1and unstable if R( 0) > 1. Special cases of the general model are studied, where there is only one immune stage, either I(t) or I(c). In the first model, SI(c)R( c), it is assumed that all infected rodents are immunocompetent and recover. In the second model, SI(t), it is assumed that all infected rodents are immunotolerant. For each of these models, the basic reproduction numbers are computed and their relationship to the basic reproduction number of the general model determined. For the SI( t)model, it is shown that bistability may occur, the DFE and an enzootic equilibrium, with all rodents infectious, are locally asymptotically stable for the same set of parameter values. A simplification of the SI( t)model yields a third model, where the sexes are not differentiated, and therefore, there is no sexual transmission. For this third simplified model, the dynamics are completely analyzed. It is shown that there exists a DFE and possibly two additional equilibria, one of which is globally asymptotically stable for any given set of parameter values; bistability does not occur. Numerical examples illustrate the dynamics of the models. The biological implications of the results and future research goals are discussed in the conclusion.

Sex differences in the recognition of and innate antiviral responses to Seoul virus in Norway rats

Among rodents that carry hantaviruses, more males are infected than females. Male rats also have elevated copies of Seoul virus RNA and reduced transcription of immune-related genes in the lungs than females. To further characterize sex differences in antiviral defenses and whether these differences are mediated by gonadal hormones, we examined viral RNA in the lungs, virus shedding in saliva, and antiviral defenses among male and female rats that were intact, gonadectomized neonatally, or gonadectomized in adulthood. Following inoculation with Seoul virus, high amounts viral RNA persisted longer in lungs from intact males than intact females. Removal of the gonads in males reduced the amount of viral RNA to levels comparable with intact females at 40 days post-inoculation (p.i.). Intact males shed more virus in saliva than intact females 15 days p.i.; removal of the gonads during either the neonatal period or in adulthood increased virus shedding in females and decreased virus shedding in males. Induction of pattern recognition receptors (PRRs; Tlr7 and Rig-I), expression of antiviral genes (Myd88, Visa, Jun, Irf7, Ifnbeta, Ifnar1, Jak2, Stat3, and Mx2), and production of Mx protein was elevated in the lungs of intact females compared with intact males. Gonadectomy had more robust effects on the induction of PRRs than on downstream IFNbeta or Mx2 expression. Putative androgen and estrogen response elements are present in the promoters of several of these antiviral genes, suggesting the propensity for sex steroids to directly affect dimorphic antiviral responses against Seoul virus infection.

How host population dynamics translate into time-lagged prevalence: an investigation of Sin Nombre virus in deer mice

Human cases of hantavirus pulmonary syndrome caused by Sin Nombre virus are the endpoint of complex ecological cascade from weather conditions, population dynamics of deer mice, to prevalence of SNV in deer mice. Using population trajectories from the literature and mathematical modeling, we analyze the time lag between deer mouse population peaks and peaks in SNV antibody prevalence in deer mice. Because the virus is not transmitted vertically, rapid population growth can lead initially to reduced prevalence, but the resulting higher population size may later increase contact rates and generate increased prevalence. Incorporating these factors, the predicted time lag ranges from 0 to 18 months, and takes on larger values when host population size varies with a longer period or higher amplitude, when mean prevalence is low and when transmission is frequency-dependent. Population size variation due to variation in birth rates rather than death rates also increases the lag. Predicting future human outbreaks of hantavirus pulmonary syndrome may require taking these effects into account.

Multi-patch deterministic and stochastic models for wildlife diseases

Spatial heterogeneity and host demography have a direct impact on the persistence or extinction of a disease. Natural or human-made landscape features such as forests, rivers, roads, and crops are important to the persistence of wildlife diseases. Rabies, hantaviruses, and plague are just a few examples of wildlife diseases where spatial patterns of infection have been observed. We formulate multi-patch deterministic and stochastic epidemic models and use these models to investigate problems related to disease persistence and extinction. We show in some special cases that a unique disease-free equilibrium exists. In these cases, a basic reproduction number ℝ(0) can be computed and shown to be bounded below and above by the minimum and maximum patch reproduction numbers ℝ(j), j=1, …, n. The basic reproduction number has a simple form when there is no movement or when all patches are identical or when the movement rate approaches infinity. Numerical examples of the deterministic and stochastic models illustrate the disease dynamics for different movement rates between three patches.