Tanya Kostova

Interplay of node connectivity and epidemic rates in the dynamics of epidemic networks

We present and analyze a discrete-time susceptible-infected epidemic network model which represents each host as a separate entity and allows heterogeneous hosts and contacts. We establish a necessary and sufficient condition for global stability of the disease-free equilibrium of the system (defined as epidemic controllability) which defines the epidemic reproduction number of the network. When this condition is not fulfilled, we show that the system has a unique, locally stable equilibrium. We further derive sufficient conditions for epidemic controllability in terms of the epidemic rates and the network topology.

GeneSV – an Approach to Help Characterize Possible Variations in Genomic and Protein Sequences

A computational approach for identification and assessment of genomic sequence variability (GeneSV) is described. For a given nucleotide sequence, GeneSV collects information about the permissible nucleotide variability (changes that potentially preserve function) observed in corresponding regions in genomic sequences, and combines it with conservation/variability results from protein sequence and structure-based analyses of evaluated protein coding regions. GeneSV was used to predict effects (functional vs. non-functional) of 37 amino acid substitutions on the NS5 polymerase (RdRp) of dengue virus type 2 (DENV-2), 36 of which are not observed in any publicly available DENV-2 sequence. 32 novel mutants with single amino acid substitutions in the RdRp were generated using a DENV-2 reverse genetics system. In 81% (26 of 32) of predictions tested, GeneSV correctly predicted viability of introduced mutations. In 4 of 5 (80%) mutants with double amino acid substitutions proximal in structure to one another GeneSV was also correct in its predictions. Predictive capabilities of the developed system were illustrated on dengue RNA virus, but described in the manuscript a general approach to characterize real or theoretically possible variations in genomic and protein sequences can be applied to any organism.

Toward an Ecological Framework for Assessing Risk to Vertebrate Populations from Brine and Petroleum Spills at Exploration and Production Sites

REFERENCE: Efroymson, R. A., Carlsen, T. M., Jager, H. I., Kostova, T., Carr, E. A., Hargrove, W. W., Kercher, J., and Ashwood, T. L., “Toward a Framework for Assessing Risk to Vertebrate Populations from Brine and Petroleum Spills at Exploration and Production Sites,” Landscape Ecology and Wildlife Habitat Evaluation: Critical Information for Ecological Risk Assessment, Land-Use Management Activities, and Biodiversity Enhancement Practices, ASTM STP 1458, L. Kapustka, H. Galbraith, M. Luxon, and G. R. Biddinger, Eds., ASTM International, West Conshohocken, PA, 2004. ABSTRACT: Brine and petroleum spills may affect terrestrial vertebrates through loss of reproductive habitat or reduced food availability rather than direct toxicity. A proposed ecological framework for evaluating impacts of these spills includes individual-based population models, a site conceptual trophic model, habitat suitability maps, and a stochastic brine spill generator. Simulation results for mammal populations in the Tallgrass Prairie Preserve petroleum exploration and production (EP above this threshold the time to extinction decreased with increasing spill area. Vole density was sensitive to the interaction of predation and fragmentation, with fragmentation causing population extinction in the presence of predation, yet stabilizing the population in the absence of predation. We anticipate that our results will aid in future development of “exclusion criteria” for leaving unrestored habitat at E&P sites.

Nonlinear age-dependent population dynamics with constant size

The existence of populations of constant size is studied for the Gurtin–MacCamy model. Necessary and sufficient conditions are given and some examples of their implications are considered.

Some Examples of Nonstationary Populations of Constant Size

Examples of nonstationary populations of constant size are explicitly constructed. Necessary and sufficient conditions for a constant birth function are established under mild restrictions on the death rate and the initial distribution and examples are provided.

Editorial: Vaccination in Human Populations

The battle between infectious diseases and humans was heavily lopsided for much of history. Man did not understand the cause of disease and had no idea how to prevent or treat it; therefore, when disease struck it usually took a heavy toll. This usual course suddenly changed direction in 1796 when Edward Jenner, a doctor who worked in Gloucestershire, noticed that individuals who had contracted cowpox (cow’s equivalent of smallpox) rarely caught the deadly human version. He then deliberately infected an eight-year-old boy with the pus from a cowpox sore, making the boy ill with cowpox. After the boy recovered, Dr. Jenner infected him with the normally deadly smallpox and, as he had predicted, the infection with the cowpox imparted protection to the boy who never caught smallpox. Thus was born the practice of modern vaccination. Perhaps the greatest success against infectious disease was achieved 181 years later when smallpox was eradicated as a result of worldwide vaccinations. Vaccination is one of the preventive= control measures that best lends itself to mathematical modeling, giving rather precise estimates of necessary vaccine take, efficacy, and coverage for eradication of the disease, as well as for a prescribed reduction of disease prevalence. The common thread of the three articles in this volume (based on talks presented at the Conference on Computational and Mathematical Population Dynamics in Trento, Italy, 2004) is vaccination in human populations. It includes two articles on vaccination models, addressing rather different issues, and a third looking at changes in risky contact rates induced by vaccination. One article is concerned with vaccination strategies for the eradication of rubella in England and Wales, while the other studies vaccination against pathogens that affect two species, one of which may act as a reservoir. The third article analyzes the influence of treatmentand vaccination-induced changes in risky contact rate on HIV transmission in the homosexual population of San Francisco. Mathematical models of disease are far from truly predictive because of the not-yet-fully-understood complexity of the infection process and the insufficiency of data at many levels. Yet each model is Mathematical Population Studies, 14:1–2, 2007 Copyright # Taylor & Francis Group, LLC ISSN: 0889-8480 print=1547-724X online DOI: 10.1080/08898480601090618

Epidemics in Wildlife

In June 2004, the first international Conference on Computational and Mathematical Population Dynamics (CMPD) was held in Trento, Italy. Over 300 participants contributed their scientific work to an extended overview of the field. This Conference was the result of merging two long-standing triennial meetings: the 7th edition of the Conference on Mathematical Population Dynamics (MPD) and the 3rd Conference on Deterministic and Stochastic Modeling of Biointeraction (DeStoBio). These two conferences had provided for nearly two decades a forum for scientific exchange and had empowered the growth of a wide community of scientists with interests in applied mathematics, computer science, biology, epidemiology, ecology. The first meeting of the CMPD series takes advantage of the rich experience and heritage of the previous conferences, and it is also an homage to the memory of Ovide Arino who contributed himself so much to keep alive the field of population dynamics by organizing the MPD series. He was still with us when the organization of the new series started and was, in fact, the one to propose the name for the joint meeting by putting ‘‘Computational’’ as the first word in the title. All of us—friends, collaborators, and participants in the Conference—missed him very much during the meeting. It was impossible to provide an extended collection of papers as proceedings of the Conference. Nevertheless some selected, peerreviewed contributions have been grouped and prepared to be published in different journals, thus providing a significant—albeit limited—follow-up to the work hosted in Trento. A number of manuscripts, focused on the modelling of epidemics, are now ready to be presented, and they will be the content of three special issues to be published in ‘‘Mathematical Population Studies. The mathematical description of epidemics is nowadays an important chapter of population dynamics. The investigation of the mechanisms underlying the spread of infectious diseases is more and more important both for purely theoretical reasons and for the advantages that public health services may draw from their knowledge. Thus, Mathematical Population Studies, 13:117–118, 2006 Copyright # Taylor & Francis Group, LLC ISSN: 0889-8480 print=1543-5253 online DOI: 10.1080/08898480600878500