Some epidemiological models with nonlinear incidence

Epidemiological models with nonlinear incidence rates can have very different dynamic behaviors than those with the usual bilinear incidence rate. The first model considered here includes vital dynamics and a disease process where susceptibles become exposed, then infectious, then removed with temporary immunity and then susceptible again. When the equilibria and stability are investigated, it is found that multiple equilibria exist for some parameter values and periodic solutions can arise by Hopf bifurcation from the larger endemic equilibrium. Many results analogous to those in the first model are obtained for the second model which has a delay in the removed class but no exposed class.Research supported in part by Centers for Disease Control Contract 200-87-0515. Support services provided at University House Research Center at the University of IowaResearch supported in part by NSERC A-8965 and the University of Victoria President's Committee on Faculty Research and Travel     

Integral equation models for endemic infectious diseases

Summary Endemic infectious diseases for which infection confers permanent immunity are described by a system of nonlinear Volterra integral equations of convolution type. These constant-parameter models include vital dynamics (births and deaths), immunization and distributed infectious period. The models are shown to be well posed, the threshold criteria are determined and the asymptotic behavior is analysed. It is concluded that distributed delays do not change the thresholds and the asymptotic behaviors of the models.This work was partially supported by NIH Grant AI 13233.     

B cells regulate murine gammaherpesvirus 68 latency

The dynamics of the establishment of, and reactivation from, gammaherpesviruses latency has not been quantitatively analyzed in the natural host. Gammaherpesvirus 68 (gammaHV68) is a murine gammaherpesvirus genetically related to primate gammaherpesviruses that establishes a latent infection in infected mice. We used limiting dilution reactivation (frequency of cells reactivating gammaHV68 in vitro) and limiting dilution PCR (frequency of cells carrying gammaHV68 genome) assays to compare gammaHV68 latency in normal (C57BL/6) and B-cell-deficient (MuMT) mice. After intraperitoneal (i.p.) inoculation, latent gammaHV68 was detected in the spleen, bone marrow, and peritoneal cells. Both B-cell-deficient and C57BL/6 mice established latent infection in peritoneal cells after either i.p. or intranasal (i.n.) inoculation. In contrast, establishment of splenic latency was less efficient in B-cell-deficient than in C57BL/6 mice after i.n. inoculation. Analysis of reactivation efficiency (reactivation frequency compared to frequency of cells carrying gammaHV68 genome) revealed that (i) regardless of route or mouse strain, splenic cells reactivated gammaHV68 less efficiently than peritoneal cells, (ii) the frequency of cells carrying gammaHV68 genome was generally comparable over the course of infection between C57BL/6 and B-cell-deficient mice, (iii) between 28 and 250 days after infection, cells from B-cell-deficient mice reactivated gammaHV68 10- to 100-fold more efficiently than cells from C57BL/6 mice, (iv) at 7 weeks postinfection, B-cell-deficient mice had more genome-positive peritoneal cells than C57BL/6 mice, and (v) mixing cells (ratio of 3 to 1) that reactivated inefficiently with cells that reactivated efficiently did not significantly decrease reactivation efficiency. Consistent with a failure to normally regulate chronic gammaHV68 infection, the majority of infected B-cell-deficient mice died between 100 and 200 days postinfection. We conclude that (i) B cells are not required for establishment of gammaHV68 latency, (ii) there are organ-specific differences in the efficiency of gammaHV68 reactivation, (iii) B cells play a crucial role in regulating reactivation of gammaHV68 from latency, and (iv) B cells are important for controlling chronic gammaHV68 infection.     

Modeling the effects of varicella vaccination programs on the incidence of chickenpox and shingles

Two possible dangers of an extensive varicella vaccination program are more varicella (chickenpox) cases in adults, when the complication rates are higher, and an increase in cases of zoster (shingles). Here an age-structured epidemiologic—demographic model with vaccination is developed for varicella and zoster. Parameters are estimated from epidemiological data. This mathematical and computer simulation model is used to evaluate the effects of varicella vaccination programs. Although the age distribution of varicella cases does shift in the simulations, this does not seem to be a danger because many of the adult cases occur after vaccine-induced immunity wanes, so they are mild varicella cases with fewer complications. In the simulations, zoster incidence increases in the first three decades after initiation of a vaccination program, because people who had varicella in childhood age without boosting, but then it decreases. Thus the simulations validate the second danger of more zoster cases.     

Phospho-NHE3 forms membrane patches and interacts with beta-actin to sense and maintain constant direction during cell migration

The Na(+)/H(+) exchanger NHE3 colocalizes with beta-actin at the leading edge of directionally migrating cells. Using human osteosarcoma cells (SaOS-2), rat osteoblasts (calvaria), and human embryonic kidney (HEK) cells, we identified a novel role for NHE3 via beta-actin in anode and cathode directed motility, during electrotaxis. NHE3 knockdown by RNAi revealed that NHE3 expression is required to achieve constant directionality and polarity in migrating cells. Phosphorylated NHE3 (pNHE3) and beta-actin complex formation was impaired by the NHE3 inhibitor S3226 (IC50 0.02 µM). Fluorescence cross-correlation spectroscopy (FCCS) revealed that the molecular interactions between NHE3 and beta-actin in membrane protrusions increased 1.7-fold in the presence of a directional cue and decreased 3.3-fold in the presence of cytochalasin D. Data from flow cytometric analysis showed that membrane potential of cells (V_mem) decreases in directionally migrating, NHE3-deficient osteoblasts and osteosarcoma cells whereas only V_mem of wild type osteoblasts is affected during directional migration. These findings suggest that pNHE3 has a mechanical function via beta-actin that is dependent on its physiological activity and V_mem. Furthermore, phosphatidylinositol 3,4,5-trisphosphate (PIP3) levels increase while PIP2 remains stable when cells have persistent directionality. Both PI3 kinase (PI3K) and Akt expression levels change proportionally to NHE3 levels. Interestingly, however, the content of pNHE3 level does not change when PI3K/Akt is inhibited. Therefore, we conclude that NHE3 can act as a direction sensor for cells and that NHE3 phosphorylation in persistent directional cell migration does not involve PI3K/Akt during electrotaxis.     

Porcine reproductive and respiratory syndrome virus (PRRSV) infection spreads by cell-to-cell transfer in cultured MARC-145 cells, is dependent on an intact cytoskeleton, and is suppressed by drug-targeting of cell permissiveness to virus infection

Background

Porcine reproductive and respiratory syndrome virus (PRRSV) is the etiologic agent of PRRS, causing widespread chronic infections which are largely uncontrolled by currently available vaccines or other antiviral measures. Cultured monkey kidney (MARC-145) cells provide an important tool for the study of PRRSV replication. For the present study, flow cytometric and fluorescence antibody (FA) analyses of PRRSV infection of cultured MARC-145 cells were carried out in experiments designed to clarify viral dynamics and the mechanism of viral spread. The roles of viral permissiveness and the cytoskeleton in PRRSV infection and transmission were examined in conjunction with antiviral and cytotoxic drugs.

Results

Flow cytometric and FA analyses of PRRSV antigen expression revealed distinct primary and secondary phases of MARC-145 cell infection. PRRSV antigen was randomly expressed in a few percent of cells during the primary phase of infection (up to about 20–22 h p.i.), but the logarithmic infection phase (days 2–3 p.i.), was characterized by secondary spread to clusters of infected cells. The formation of secondary clusters of PRRSV-infected cells preceded the development of CPE in MARC-145 cells, and both primary and secondary PRRSV infection were inhibited by colchicine and cytochalasin D, demonstrating a critical role of the cytoskeleton in viral permissiveness as well as cell-to-cell transmission from a subpopulation of cells permissive for free virus to secondary targets. Cellular expression of actin also appeared to correlate with PRRSV resistance, suggesting a second role of the actin cytoskeleton as a potential barrier to cell-to-cell transmission. PRRSV infection and cell-to-cell transmission were efficiently suppressed by interferon-γ (IFN-γ), as well as the more-potent experimental antiviral agent AK-2.

Conclusion

The results demonstrate two distinct mechanisms of PRRSV infection: primary infection of a relatively small subpopulation of innately PRRSV-permissive cells, and secondary cell-to-cell transmission to contiguous cells which appear non-permissive to free virus. The results also indicate that an intact cytoskeleton is critical for PRRSV infection, and that viral permissiveness is a highly efficient drug target to control PRRSV infection. The data from this experimental system have important implications for the mechanisms of PRRSV persistence and pathology, as well as for a better understanding of arterivirus regulation.     

Hypoxia. Hypoxia in the pathogenesis of systemic sclerosis

Autoimmunity, microangiopathy and tissue fibrosis are hallmarks of systemic sclerosis (SSc). Vascular alterations and reduced capillary density decrease blood flow and impair tissue oxygenation in SSc. Oxygen supply is further reduced by accumulation of extracellular matrix (ECM), which increases diffusion distances from blood vessels to cells. Therefore, severe hypoxia is a characteristic feature of SSc and might contribute directly to the progression of the disease. Hypoxia stimulates the production of ECM proteins by SSc fibroblasts in a transforming growth factor-β-dependent manner. The induction of ECM proteins by hypoxia is mediated via hypoxia-inducible factor-1α-dependent and -independent pathways. Hypoxia may also aggravate vascular disease in SSc by perturbing vascular endothelial growth factor (VEGF) receptor signalling. Hypoxia is a potent inducer of VEGF and may cause chronic VEGF over-expression in SSc. Uncontrolled over-expression of VEGF has been shown to have deleterious effects on angiogenesis because it leads to the formation of chaotic vessels with decreased blood flow. Altogether, hypoxia might play a central role in pathogenesis of SSc by augmenting vascular disease and tissue fibrosis.     

Vascular alterations upon activation of TGFβ signaling in fibroblasts - implications for systemic sclerosis

Tissue fibrosis and vascular disease are hallmarks of systemic sclerosis (SSc). Transforming growth factor β (TGFβ) is a key-player in fibroblast activation and tissue fibrosis in SSc. In contrast to fibrosis, evidence for a role of TGFβ in vascular disease of SSc is scarce. Using a transgenic mouse model with fibroblast-specific expression of a kinase-deficient TGFβ receptor type II, Derrett-Smith and colleagues demonstrate that aberrant TGFβ signaling in fibroblasts might result in activation of vascular smooth muscle cells and architectural changes of the vessel wall of the aorta.     

An SIS epidemic model with variable population size and a delay

The SIS epidemiological model has births, natural deaths, disease-related deaths and a delay corresponding to the infectious period. The thresholds for persistence, equilibria and stability are determined. The persistence of the disease combined with the disease-related deaths can cause the population size to decrease to zero, to remain finite, or to grow exponentially with a smaller growth rate constant. For some parameter values, the endemic infective-fraction equilibrium is asymptotically stable, but for other parameter values, it is unstable and a surrounding periodic solution appears by Hopf bifurcation.Research Supported in part by NSERC grant A-8965 and the University of Victoria Committee on Faculty Research & Travel