Metapopulation Dynamics with Migration and Local Competition

MSC2000: primary 34D15, 34D23, 92B05; secondary 34K60, 34E13, 92D40.Many patch-based metapopulation models assume that the local population within each patch is at its equilibrium and independent of changes in patch occupancy. We study a metapopulation model which explicitly incorporates the local population dynamics of two competing species. Singular perturbation method is used to separate the fast dynamics of the local competition and the slow process of patch colonization and extinction. Our results show that the coupled system leads to much more complex outcomes than simple patch models that do not include explicit local dynamics.The first author was partially supported by NSF grant DMS-9974389 and NSF grant ESE-0119908. The second author was partially supported by NSF grant DMS-9803581. The third author was partially supported by a Canadian NSERC postdoctoral fellowship

From the Guest Editors: Special issue dedicated to Carlos Castillo-Chavez on his 60th birthday

Carlos Castilo-Chavez is a Regents Professor, a Joaquin Bustoz Jr. Professor of Mathematical Biology, and a Distinguished Sustainability Scientist at Arizona State University. His research program is at the interface of the mathematical and natural and social sciences with emphasis on (i) the role of dynamic social landscapes on disease dispersal; (ii) the role of environmental and social structures on the dynamics of addiction and disease evolution, and (iii) Dynamics of complex systems at the interphase of ecology, epidemiology and the social sciences. Castillo-Chavez has co-authored over two hundred publications (see goggle scholar citations) that include journal articles and edited research volumes. Specifically, he co-authored a textbook in Mathematical Biology in 2001 (second edition in 2012); a volume (with Harvey Thomas Banks) on the use of mathematical models in homeland security published in SIAM\u27s Frontiers in Applied Mathematics Series (2003); and co-edited volumes in the Series Contemporary Mathematics entitled ``Mathematical Studies on Human Disease Dynamics: Emerging Paradigms and Challenges\u27\u27 (American Mathematical Society, 2006) and Mathematical and Statistical Estimation Approaches in Epidemiology (Springer-Verlag, 2009) highlighting his interests in the applications of mathematics in emerging and re-emerging diseases. Castillo-Chavez is a member of the Santa Fe Institute\u27s external faculty, adjunct professor at Cornell University, and contributor, as a member of the Steering Committee of the ``Committee for the Review of the Evaluation Data on the Effectiveness of NSF-Supported and Commercially Generated Mathematics Curriculum Materials,\u27\u27 to a 2004 NRC report. The CBMS workshop ``Mathematical Epidemiology with Applications\u27\u27 lectures delivered by C. Castillo-Chavez and F. Brauer in 2011 have been published by SIAM in 2013

Troublesome toxins: time to re-think plant-herbivore interactions in vertebrate ecology

Earlier models of plant-herbivore interactions relied on forms of functional response that related rates of ingestion by herbivores to mechanical or physical attributes such as bite size and rate. These models fail to predict a growing number of findings that implicate chemical toxins as important determinants of plant-herbivore dynamics. Specifically, considerable evidence suggests that toxins set upper limits on food intake for many species of herbivorous vertebrates. Herbivores feeding on toxin-containing plants must avoid saturating their detoxification systems, which often occurs before ingestion rates are limited by mechanical handling of food items. In light of the importance of plant toxins, a new approach is needed to link herbivores to their food base. We discuss necessary features of such an approach, note recent advances in herbivore functional response models that incorporate effects of plant toxins, and mention predictions that are consistent with observations in natural systems. Future ecological studies will need to address explicitly the importance of plant toxins in shaping plant and herbivore communities

Modeling the waning and boosting of immunity from infection or vaccination

Immunity following natural infection or immunization may wane, increasing susceptibility to infection with time since infection or vaccination. Symptoms, and concomitantly infectiousness, depend on residual immunity. We quantify these phenomena in a model population composed of individuals whose susceptibility, infectiousness, and symptoms all vary with immune status. We also model age, which affects contact, vaccination and possibly waning rates. The resurgences of pertussis that have been observed wherever effective vaccination programs have reduced typical disease among young children follow from these processes. As one example, we compare simulations with the experience of Sweden following resumption of pertussis vaccination after the hiatus from 1979 to 1996, reproducing the observations leading health authorities to introduce booster doses among school-aged children and adolescents in 2007 and 2014, respectively. Because pertussis comprises a spectrum of symptoms, only the most severe of which are medically attended, accurate models are needed to design optimal vaccination programs where surveillance is less effective. (C) 2020 The Authors. Published by Elsevier Ltd

Evaluation of Targeted Influenza Vaccination Strategies via Population Modeling

Background Because they can generate comparable predictions, mathematical models are ideal tools for evaluating alternative drug or vaccine allocation strategies. To remain credible, however, results must be consistent. Authors of a recent assessment of possible influenza vaccination strategies conclude that older children, adolescents, and young adults are the optimal targets, no matter the objective, and argue for vaccinating them. Authors of two earlier studies concluded, respectively, that optimal targets depend on objectives and cautioned against changing policy. Which should we believe? Methods and Findings In matrices whose elements are contacts between persons by age, the main diagonal always predominates, reflecting contacts between contemporaries. Indirect effects (e.g., impacts of vaccinating one group on morbidity or mortality in others) result from off-diagonal elements. Mixing matrices based on periods in proximity with others have greater sub- and super-diagonals, reflecting contacts between parents and children, and other off-diagonal elements (reflecting, e.g., age-independent contacts among co-workers), than those based on face-to-face conversations. To assess the impact of targeted vaccination, we used a time-usage study\u27s mixing matrix and allowed vaccine efficacy to vary with age. And we derived mortality rates either by dividing observed deaths attributed to pneumonia and influenza by average annual cases from a demographically-realistic SEIRS model or by multiplying those rates by ratios of (versus adding to them differences between) pandemic and pre-pandemic mortalities. Conclusions In our simulations, vaccinating older children, adolescents, and young adults averts the most cases, but vaccinating either younger children and older adults or young adults averts the most deaths, depending on the age distribution of mortality. These results are consistent with those of the earlier studies

31st Annual Meeting and Associated Programs of the Society for Immunotherapy of Cancer (SITC 2016) : part two

Background The immunological escape of tumors represents one of the main ob- stacles to the treatment of malignancies. The blockade of PD-1 or CTLA-4 receptors represented a milestone in the history of immunotherapy. However, immune checkpoint inhibitors seem to be effective in specific cohorts of patients. It has been proposed that their efficacy relies on the presence of an immunological response. Thus, we hypothesized that disruption of the PD-L1/PD-1 axis would synergize with our oncolytic vaccine platform PeptiCRAd. Methods We used murine B16OVA in vivo tumor models and flow cytometry analysis to investigate the immunological background. Results First, we found that high-burden B16OVA tumors were refractory to combination immunotherapy. However, with a more aggressive schedule, tumors with a lower burden were more susceptible to the combination of PeptiCRAd and PD-L1 blockade. The therapy signifi- cantly increased the median survival of mice (Fig. 7). Interestingly, the reduced growth of contralaterally injected B16F10 cells sug- gested the presence of a long lasting immunological memory also against non-targeted antigens. Concerning the functional state of tumor infiltrating lymphocytes (TILs), we found that all the immune therapies would enhance the percentage of activated (PD-1pos TIM- 3neg) T lymphocytes and reduce the amount of exhausted (PD-1pos TIM-3pos) cells compared to placebo. As expected, we found that PeptiCRAd monotherapy could increase the number of antigen spe- cific CD8+ T cells compared to other treatments. However, only the combination with PD-L1 blockade could significantly increase the ra- tio between activated and exhausted pentamer positive cells (p= 0.0058), suggesting that by disrupting the PD-1/PD-L1 axis we could decrease the amount of dysfunctional antigen specific T cells. We ob- served that the anatomical location deeply influenced the state of CD4+ and CD8+ T lymphocytes. In fact, TIM-3 expression was in- creased by 2 fold on TILs compared to splenic and lymphoid T cells. In the CD8+ compartment, the expression of PD-1 on the surface seemed to be restricted to the tumor micro-environment, while CD4 + T cells had a high expression of PD-1 also in lymphoid organs. Interestingly, we found that the levels of PD-1 were significantly higher on CD8+ T cells than on CD4+ T cells into the tumor micro- environment (p < 0.0001). Conclusions In conclusion, we demonstrated that the efficacy of immune check- point inhibitors might be strongly enhanced by their combination with cancer vaccines. PeptiCRAd was able to increase the number of antigen-specific T cells and PD-L1 blockade prevented their exhaus- tion, resulting in long-lasting immunological memory and increased median survival

Malaria Epidemics and the Sickle-Cell Gene Dynamics

A mathematical model incorporating both malaria epidemics and human population genetics of the sickle-cell gene is studied. The dynamics of the model can be separated into two time-scales with a faster time-scale for the epidemics and a slower time-scale for the change in gene frequencies. A complete analysis of the dynamics on the slow manifold is conducted, which provides insights into how malaria epidemics may have an impact on the maintenance of the sickle-cell gene in a population where malaria is prevalent.The first author is partially supported by NSF grant DMS-9974389. The second author is partially supported by NSF grant DMS-9803581. The third author is partially supported by a Canadian NSERC postdoctoral fellowship