The large-scale use of antivirals during influenza pandemics poses a significant selection pressure for drug-resistant pathogens to emerge and spread in a population. This requires treatment strategies to minimize total infections as well as the emergence of resistance. Here we propose a mathematical model in which individuals infected with wild-type influenza, if treated, can develop de novo resistance and further spread the resistant pathogen. Our main purpose is to explore the impact of two important factors influencing treatment effectiveness: i) the relative transmissibility of the drug-resistant strain to wild-type, and ii) the frequency of de novo resistance. For the endemic scenario, we find a condition between these two parameters that indicates whether treatment regimes will be most beneficial at intermediate or more extreme values (e.g., the fraction of infected that are treated). Moreover, we present analytical expressions for effective treatment regimes and provide evidence of its applicability across a range of modeling scenarios: endemic behavior with deterministic homogeneous mixing, and single-epidemic behavior with deterministic homogeneous mixing and stochastic heterogeneous mixing. Therefore, our results provide insights for the control of drug-resistance in influenza across time scales.

Methicillin resistant Staphylococcus aureus (MRSA) is currently a major cause of skin and soft tissue infections (SSTI) in the United States. Seasonal variation of MRSA infections in hospital settings has been widely observed. However, systematic time-series analysis of incidence data is desirable to understand the seasonality of community acquired (CA)-MRSA infections at the population level. In this paper, using data on monthly SSTI incidence in children aged 0–19 years and enrolled in Medicaid in Maricopa County, Arizona, from January 2005 to December 2008, we carried out time-series and nonlinear regression analysis to determine the periodicity, trend, and peak timing in SSTI incidence in children at different age: 0-4 years, 5-9 years, 10-14 years, and 15-19 years. We also assessed the temporal correlation between SSTI incidence and meteorological variables including average temperature and humidity. Our analysis revealed a strong annual seasonal pattern of SSTI incidence with peak occurring in early September. This pattern was consistent across age groups. Moreover, SSTIs followed a significantly increasing trend over the 4-year study period with annual incidence increasing from 3.36% to 5.55% in our pediatric population of approximately 290,000. We also found a significant correlation between the temporal variation in SSTI incidence and mean temperature and specific humidity. Our findings could have potential implications on prevention and control efforts against CA-MRSA.

Background: The role of demographic factors, climatic conditions, school cycles, and connectivity patterns in shaping the spatio-temporal dynamics of pandemic influenza is not clearly understood. Here we analyzed the spatial, age and temporal evolution of the 2009 A/H1N1 influenza pandemic in Chile, a southern hemisphere country covering a long and narrow strip comprising latitudes 17°S to 56°S.

Methods: We analyzed the dissemination patterns of the 2009 A/H1N1 pandemic across 15 regions of Chile based on daily hospitalizations for severe acute respiratory disease and laboratory confirmed A/H1N1 influenza infection from 01-May to 31-December, 2009. We explored the association between timing of pandemic onset and peak pandemic activity and several geographical and demographic indicators, school vacations, climatic factors, and international passengers. We also estimated the reproduction number (R) based on the growth rate of the exponential pandemic phase by date of symptoms onset, estimated using maximum likelihood methods.

Results: While earlier pandemic onset was associated with larger population size, there was no association with connectivity, demographic, school or climatic factors. In contrast, there was a latitudinal gradient in peak pandemic timing, representing a 16-39-day lag in disease activity from the southern regions relative to the northernmost region (P < 0.001). Geographical differences in latitude of Chilean regions, maximum temperature and specific humidity explained 68.5% of the variability in peak timing (P = 0.01). In addition, there was a decreasing gradient in reproduction number from south to north Chile (P < 0.0001). The regional mean R estimates were 1.6-2.0, 1.3-1.5, and 1.2-1.3 for southern, central and northern regions, respectively, which were not affected by the winter vacation period.

Conclusions: There was a lag in the period of most intense 2009 pandemic influenza activity following a South to North traveling pattern across regions of Chile, significantly associated with geographical differences in minimum temperature and specific humidity. The latitudinal gradient in timing of pandemic activity was accompanied by a gradient in reproduction number (P < 0.0001). Intensified surveillance strategies in colder and drier southern regions could lead to earlier detection of pandemic influenza viruses and improved control outcomes.

Background: Dengue fever is a mosquito-borne disease that affects between 50 and 100 million people each year. Increasing our understanding of the heterogeneous transmission patterns of dengue at different spatial scales could have considerable public health value by guiding intervention strategies.

Methods: Based on the weekly number of dengue cases in Perú by province, we investigated the association between dengue incidence during the period 1994-2008 and demographic and climate factors across geographic regions of the country.

Results: Our findings support the presence of significant differences in the timing of dengue epidemics between jungle and coastal regions, with differences significantly associated with the timing of the seasonal cycle of mean temperature.

Conclusions: Dengue is highly persistent in jungle areas of Perú where epidemics peak most frequently around March when rainfall is abundant. Differences in the timing of dengue epidemics in jungle and coastal regions are significantly associated with the seasonal temperature cycle. Our results suggest that dengue is frequently imported into coastal regions through infective sparks from endemic jungle areas and/or cities of other neighboring endemic countries, where propitious environmental conditions promote year-round mosquito breeding sites. If jungle endemic areas are responsible for multiple dengue introductions into coastal areas, our findings suggest that curtailing the transmission of dengue in these most persistent areas could lead to significant reductions in dengue incidence in coastal areas where dengue incidence typically reaches low levels during the dry season.

Background: Influenza viruses are a major cause of morbidity and mortality worldwide. Vaccination remains a powerful tool for preventing or mitigating influenza outbreaks. Yet, vaccine supplies and daily administration capacities are limited, even in developed countries. Understanding how such constraints can alter the mitigating effects of vaccination is a crucial part of influenza preparedness plans. Mathematical models provide tools for government and medical officials to assess the impact of different vaccination strategies and plan accordingly. However, many existing models of vaccination employ several questionable assumptions, including a rate of vaccination proportional to the population at each point in time.

Methods: We present a SIR-like model that explicitly takes into account vaccine supply and the number of vaccines administered per day and places data-informed limits on these parameters. We refer to this as the non-proportional model of vaccination and compare it to the proportional scheme typically found in the literature.

Results: The proportional and non-proportional models behave similarly for a few different vaccination scenarios. However, there are parameter regimes involving the vaccination campaign duration and daily supply limit for which the non-proportional model predicts smaller epidemics that peak later, but may last longer, than those of the proportional model. We also use the non-proportional model to predict the mitigating effects of variably timed vaccination campaigns for different levels of vaccination coverage, using specific constraints on daily administration capacity.

Conclusions: The non-proportional model of vaccination is a theoretical improvement that provides more accurate predictions of the mitigating effects of vaccination on influenza outbreaks than the proportional model. In addition, parameters such as vaccine supply and daily administration limit can be easily adjusted to simulate conditions in developed and developing nations with a wide variety of financial and medical resources. Finally, the model can be used by government and medical officials to create customized pandemic preparedness plans based on the supply and administration constraints of specific communities.

Collective behaviors in social insect societies often emerge from simple local rules. However, little is known about how these behaviors are dynamically regulated in response to environmental changes. Here, we use a compartmental modeling approach to identify factors that allow harvester ant colonies to regulate collective foraging activity in response to their environment. We propose a set of differential equations describing the dynamics of: (1) available foragers inside the nest, (2) active foragers outside the nest, and (3) successful returning foragers, to understand how colony-specific parameters, such as baseline number of foragers, interactions among foragers, food discovery rates, successful forager return rates, and foraging duration might influence collective foraging dynamics, while maintaining functional robustness to perturbations. Our analysis indicates that the model can undergo a forward (transcritical) bifurcation or a backward bifurcation depending on colony-specific parameters. In the former case, foraging activity persists when the average number of recruits per successful returning forager is larger than one. In the latter case, the backward bifurcation creates a region of bistability in which the size and fate of foraging activity depends on the distribution of the foraging workforce among the model׳s compartments. We validate the model with experimental data from harvester ants (Pogonomyrmex barbatus) and perform sensitivity analysis. Our model provides insights on how simple, local interactions can achieve an emergent and robust regulatory system of collective foraging activity in ant colonies.

We describe a multi-parameter family of the minimum-uncertainty squeezed states for the harmonic oscillator in nonrelativistic quantum mechanics. They are derived by the action of the corresponding maximal kinematical invariance group on the standard ground state solution. We show that the product of the variances attains the required minimum value 1/4 only at the instances that one variance is a minimum and the other is a maximum, when the squeezing of one of the variances occurs. The generalized coherent states are explicitly constructed and their Wigner function is studied. The overlap coefficients between the squeezed, or generalized harmonic, and the Fock states are explicitly evaluated in terms of hypergeometric functions and the corresponding photon statistics are discussed. Some applications to quantum optics, cavity quantum electrodynamics and superfocusing in channelling scattering are mentioned. Explicit solutions of the Heisenberg equations for radiation field operators with squeezing are found.

Through the mathematical study of two models we quantify some of the theories of co-development and co-existence of focused groups in the social sciences. This work attempts to develop the mathematical framework behind the social sciences of community formation. By using well developed theories and concepts from ecology and epidemiology we hope to extend the theoretical framework of organizing and self-organizing social groups and communities, including terrorist groups. The main goal of our work is to gain insight into the role of recruitment and retention in the formation and survival of social organizations. Understanding the underlining mechanisms of the spread of ideologies under competition is a fundamental component of this work. Here contacts between core and non-core individuals extend beyond its physical meaning to include indirect interaction and spread of ideas through phone conversations, emails, media sources and other similar mean.

This work focuses on the dynamics of formation of interest groups, either ideological, economical or ecological and thus we explore the questions such as, how do interest groups initiate and co-develop by interacting within a common environment and how do they sustain themselves? Our results show that building and maintaining the core group is essential for the existence and survival of an extreme ideology. Our research also indicates that in the absence of competitive ability (i.e., ability to take from the other core group or share prospective members) the social organization or group that is more committed to its group ideology and manages to strike the right balance between investment in recruitment and retention will prevail. Thus under no cross interaction between two social groups a single trade-off (of these efforts) can support only a single organization. The more efforts that an organization implements to recruit and retain its members the more effective it will be in transmitting the ideology to other vulnerable individuals and thus converting them to believers.

Background: Elucidating the role of the underlying risk factors for severe outcomes of the 2009 A/H1N1 influenza pandemic could be crucial to define priority risk groups in resource-limited settings in future pandemics.

Methods: We use individual-level clinical data on a large series of ARI (acute respiratory infection) hospitalizations from a prospective surveillance system of the Mexican Social Security medical system to analyze clinical features at presentation, admission delays, selected comorbidities and receipt of seasonal vaccine on the risk of A/H1N1-related death. We considered ARI hospitalizations and inpatient-deaths, and recorded demographic, geographic, and medical information on individual patients during August-December, 2009.

Results: Seasonal influenza vaccination was associated with a reduced risk of death among A/H1N1 inpatients (OR = 0.43 (95% CI: 0.25, 0.74)) after adjustment for age, gender, geography, antiviral treatment, admission delays, comorbidities and medical conditions. However, this result should be interpreted with caution as it could have been affected by factors not directly measured in our study. Moreover, the effect of antiviral treatment against A/H1N1 inpatient death did not reach statistical significance (OR = 0.56 (95% CI: 0.29, 1.10)) probably because only 8.9% of A/H1N1 inpatients received antiviral treatment. Moreover, diabetes (OR = 1.6) and immune suppression (OR = 2.3) were statistically significant risk factors for death whereas asthmatic persons (OR = 0.3) or pregnant women (OR = 0.4) experienced a reduced fatality rate among A/H1N1 inpatients. We also observed an increased risk of death among A/H1N1 inpatients with admission delays >2 days after symptom onset (OR = 2.7). Similar associations were also observed for A/H1N1-negative inpatients.

Conclusions: Geographical variation in identified medical risk factors including prevalence of diabetes and immune suppression may in part explain between-country differences in pandemic mortality burden. Furthermore, access to care including hospitalization without delay and antiviral treatment and are also important factors, as well as vaccination coverage with the 2008–09 trivalent inactivated influenza vaccine.

Background: The impact of socio-demographic factors and baseline health on the mortality burden of seasonal and pandemic influenza remains debated. Here we analyzed the spatial-temporal mortality patterns of the 1918 influenza pandemic in Spain, one of the countries of Europe that experienced the highest mortality burden.

Methods: We analyzed monthly death rates from respiratory diseases and all-causes across 49 provinces of Spain, including the Canary and Balearic Islands, during the period January-1915 to June-1919. We estimated the influenza-related excess death rates and risk of death relative to baseline mortality by pandemic wave and province. We then explored the association between pandemic excess mortality rates and health and socio-demographic factors, which included population size and age structure, population density, infant mortality rates, baseline death rates, and urbanization.

Results: Our analysis revealed high geographic heterogeneity in pandemic mortality impact. We identified 3 pandemic waves of varying timing and intensity covering the period from Jan-1918 to Jun-1919, with the highest pandemic-related excess mortality rates occurring during the months of October-November 1918 across all Spanish provinces. Cumulative excess mortality rates followed a south–north gradient after controlling for demographic factors, with the North experiencing highest excess mortality rates. A model that included latitude, population density, and the proportion of children living in provinces explained about 40% of the geographic variability in cumulative excess death rates during 1918–19, but different factors explained mortality variation in each wave.

Conclusions: A substantial fraction of the variability in excess mortality rates across Spanish provinces remained unexplained, which suggests that other unidentified factors such as comorbidities, climate and background immunity may have affected the 1918-19 pandemic mortality rates. Further archeo-epidemiological research should concentrate on identifying settings with combined availability of local historical mortality records and information on the prevalence of underlying risk factors, or patient-level clinical data, to further clarify the drivers of 1918 pandemic influenza mortality.