VTechWorks staff will be away for the Thanksgiving holiday beginning at noon on Wednesday, November 27, through Friday, November 29. We will resume normal operations on Monday, December 2. Thank you for your patience.

Browsing by Author "Blackwood, Julie C."

Now showing 1 - 5 of 5
  • Thumbnail Image
    Immunoepidemiological Modeling of Dengue Viral Infection
    Nikin-Beers, Ryan Patrick (Virginia Tech, 2018-04-25)
    Dengue viral infection is a mosquito-borne disease with four distinct strains, where the interactions between these strains have implications on the severity of the disease outcomes. The two competing hypotheses for the increased severity during secondary infections are antibody dependent enhancement and original antigenic sin. Antibody dependent enhancement suggests that long-lived antibodies from primary infection remain during secondary infection but do not neutralize the virus. Original antigenic sin proposes that T cells specific to primary infection dominate cellular immune responses during secondary infections, but are inefficient at clearing cells infected with non-specific strains. To analyze these hypotheses, we developed within-host mathematical models. In previous work, we predicted a decreased non-neutralizing antibody effect during secondary infection. Since this effect accounts for decreased viral clearance and the virus is in quasi-equilibrium with infected cells, we could be accounting for reduced cell killing and the original antigenic sin hypothesis. To further understand these interactions, we develop a model of T cell responses to primary and secondary dengue virus infections that considers the effect of T cell cross-reactivity in disease enhancement. We fit the models to published patient data and show that the overall infected cell killing is similar in dengue heterologous infections, resulting in dengue fever and dengue hemorrhagic fever. The contribution to overall killing, however, is dominated by non-specific T cell responses during the majority of secondary dengue hemorrhagic fever cases. By contrast, more than half of secondary dengue fever cases have predominant strain-specific T cell responses. These results support the hypothesis that cross-reactive T cell responses occur mainly during severe disease cases of heterologous dengue virus infections. Finally, using the results from our within-host models, we develop a multiscale model of dengue viral infection which couples the within-host virus dynamics to the population level dynamics through a system of partial differential equations. We analytically determine the relationship between the model parameters and the characteristics of the solutions, and find thresholds under which infections persist in the population. Furthermore, we develop and implement a full numerical scheme for our model.
  • Thumbnail Image
    An introduction to compartmental modeling for the budding infectious disease modeler
    Blackwood, Julie C.; Childs, Lauren M. (Taylor & Francis, 2018-08-16)
    Mathematical models are ubiquitous in the study of the transmission dynamics of infectious diseases, In particular, the classic ‘susceptible-infectious-recovered’ (SIR) paradigm provides a modeling framework that can be adapted to describe the core transmission dynamics of a range of human and wildlife diseases. These models provide an important tool for uncovering the mechanisms generating observed disease dynamics, evaluating potential control strategies, and predicting future outbreaks. With ongoing advances in computational tools as well as access to disease incidence data, the use of such models continues to increase. Here, we provide a basic introduction to disease modeling that is primarily intended for individuals who are new to developing SIR-type models. In particular, we highlight several common issues encountered when structuring and analyzing these models.
  • Thumbnail Image
    Modelling Allee effects in a transgenic mosquito population during range expansion
    Walker, Melody (Virginia Tech, 2018-06-20)
    Mosquitoes are vectors for many diseases that cause significant mortality and morbidity across the globe such as malaria, dengue fever and Zika. As mosquito populations expand their range into new areas, they may undergo mate-finding Allee effects such that their ability to successfully reproduce becomes difficult at low population densities. With new technology, creating target specific gene modification may now be a viable method for mosquito population control. We develop a mathematical model to investigate the effects of releasing transgenic mosquitoes into newly established low-density mosquito populations. Our model consists of two life stages (aquatic and adult), which are further divided into three genetically distinct groups: heterogeneous and homogeneous transgenic alleles that cause female infertility and a homogeneous wild type. We perform analytical and numerical analyses on the equilibria to determine the level of saturation needed to eliminate mosquitoes in a given area. This model demonstrates the potential for a gene drive system to reduce the spread of invading mosquito populations.
  • Thumbnail Image
    Modelling Allee effects in a transgenic mosquito population during range expansion
    Walker, Melody; Blackwood, Julie C.; Brown, Vicki; Childs, Lauren M. (Taylor & Francis, 2018-04-27)
    Mosquitoes are vectors for many diseases that cause significant mortality and morbidity. As mosquito populations expand their range, they may undergo mate-finding Allee effects such that their ability to successfully reproduce becomes difficult at low population density. With new technology, creating target specific gene modification may be a viable method for mosquito population control. We develop a mathematical model to investigate the effects of releasing transgenic mosquitoes into newly established, low-density mosquito populations. Our model consists of two life stages (aquatic and adults), which are divided into three genetically distinct groups: heterogeneous and homogeneous transgenic that cause female infertility and a homogeneous wild type. We perform analytical and numerical analyses on the equilibria to determine the level of saturation needed to eliminate mosquitoes in a given area. This model demonstrates the potential for a gene drive system to reduce the spread of invading mosquito populations.
  • Thumbnail Image
    Nonsmooth Bifurcations and the Role of Density Dependence in a Chaotic Infectious Disease Model
    Hughes, Ryan Patrick (Virginia Tech, 2020-01-23)
    Discrete dynamical systems can exhibit rich and interesting dynamics at lower dimensions (and co-dimensions) than that of ODE models. Classically, the minimal dimension to observe chaotic behavior in an ODE model is three; whereas it can be achieved in a one-dimensional discrete map. It is often the choice of mathematical biologists to use discrete systems as it fills many roles such as sparse data, incorporation of life cycle stages and noisy measurements. This work is analyzes a discrete time model of an infected salmon population. It provides an in-depth analysis of non-smooth bifurcations for alternate functional forms for density dependence in the growth function of a given model. These demonstrate interesting structures and chaotic behaviors with biologically feasible interpretations such as intrinsic growth rate and probability of death. The choice of density dependence function, as well as parameterization, leads to whether chaos occurs or not.