Markov Chain Models for Cardiac Rhythm Dynamics in Patients Undergoing Catheter Ablation of Atrial Fibrillation.

We have developed a novel Markov Chain modeling system that considers vectors of patients with atrial fibrillation (AF) by their AF status over a period of time. Our model examines the impact of catheter ablation of AF upon the dynamics of a patient's AF status and their potential return to sinus rhythm. We prove several theorems to determine the probabilities of patients achieving sinus rhythm or progressing to permanent AF. Additionally, we observed aggregation of patients within the paroxysmal AF state in simulation. The aggregating property of Markov chains illustrated the potential benefits of catheter ablation on healthcare resource allocation.

Estimating Length of Stay for Simple Gastroschisis.

BACKGROUND: Length of stay (LOS) is an important measure of quality; however, estimating LOS for rare populations such as gastroschisis is problematic. Our objective was to identify explanatory variables for LOS and build a model to estimate LOS in neonates with simple gastroschisis. METHODS: In 73 neonates with simple gastroschisis (47% female, 67% White), statistical correlations for 31 potential explanatory variables for LOS were evaluated using multivariate linear regression. Poisson regression was used to estimate LOS in predetermined subpopulations, and a life table model was developed to estimate LOS for simple gastroschisis. RESULTS: Female sex (-2.4 d), "time to silo placement" (0.9 d), total parenteral nutrition days (0.6 d), need for any nasogastric feedings (11.4 d) and at discharge (-7 d), "feeding tolerance" (0.4 d), days to first postoperative stool (-0.3 d), and human milk exposure (-3.4 d) associated with LOS in simple gastroschisis. Estimated LOS for preterm neonates was longer than term infants (5.4 versus 4.6 wk) but similar for estimates based on sex and race. Based on these associations, we estimate that >50% of neonates with simple gastroschisis will be discharged by hospital day 35. CONCLUSIONS: We identified several associations that explained variations in LOS and developed a novel model to estimate LOS in simple gastroschisis, which may be applied to other rare populations.

A Partition Theorem for a Randomly Selected Large Population.

A theorem on the partitioning of a randomly selected large population into stationary and non-stationary components by using a property of the stationary population identity is stated and proved. The methods of partitioning demonstrated are original and these are helpful in real-world situations where age-wise data is available. Applications of this theorem for practical purposes are summarized at the end.

True epidemic growth construction through harmonic analysis.

In this paper, we have proposed a two-phase procedure (combining discrete graphs and wavelets) for constructing true epidemic growth. In the first phase, a graph-theory-based approach was developed to update partial data available and in the second phase, we used this partial data to generate plausible complete data through wavelets. We have provided two numerical examples. This procedure is novel and implementable and adaptable to machine learning modeling framework.

On the Three Properties of Stationary Populations and Knotting with Non-stationary Populations.

A population is considered stationary if the growth rate is zero and the age structure is constant. It thus follows that a population is considered non-stationary if either its growth rate is nonzero and/or its age structure is non-constant. We propose three properties that are related to the stationary population identity (SPI) of population biology by connecting it with stationary populations and non-stationary populations which are approaching stationarity. One of these important properties is that SPI can be applied to partition a population into stationary and non-stationary components. These properties provide deeper insights into cohort formation in real-world populations and the length of the duration for which stationary and non-stationary conditions hold. The new concepts are based on the time gap between the occurrence of stationary and non-stationary populations within the SPI framework that we refer to as Oscillatory SPI and the Amplitude of SPI.

Population, genetic, and antigenic diversity of the apicomplexan Eimeria tenella and their relevance to vaccine development.

The phylum Apicomplexa includes serious pathogens of humans and animals. Understanding the distribution and population structure of these protozoan parasites is of fundamental importance to explain disease epidemiology and develop sustainable controls. Predicting the likely efficacy and longevity of subunit vaccines in field populations relies on knowledge of relevant preexisting antigenic diversity, population structure, the likelihood of coinfection by genetically distinct strains, and the efficiency of cross-fertilization. All four of these factors have been investigated for Plasmodium species parasites, revealing both clonal and panmictic population structures with exceptional polymorphism associated with immunoprotective antigens such as apical membrane antigen 1 (AMA1). For the coccidian Toxoplasma gondii only genomic diversity and population structure have been defined in depth so far; for the closely related Eimeria species, all four variables are currently unknown. Using Eimeria tenella, a major cause of the enteric disease coccidiosis, which exerts a profound effect on chicken productivity and welfare, we determined population structure, genotype distribution, and likelihood of cross-fertilization during coinfection and also investigated the extent of naturally occurring antigenic diversity for the E. tenella AMA1 homolog. Using genome-wide Sequenom SNP-based haplotyping, targeted sequencing, and single-cell genotyping, we show that in this coccidian the functionality of EtAMA1 appears to outweigh immune evasion. This result is in direct contrast to the situation in Plasmodium and most likely is underpinned by the biology of the direct and acute coccidian life cycle in the definitive host.

Generalization of Carey's equality and a theorem on stationary population.

Carey's Equality pertaining to stationary models is well known. In this paper, we have stated and proved a fundamental theorem related to the formation of this Equality. This theorem will provide an in-depth understanding of the role of each captive subject, and their corresponding follow-up duration in a stationary population. We have demonstrated a numerical example of a captive cohort and the survival pattern of medfly populations. These results can be adopted to understand age-structure and aging process in stationary and non-stationary population models.

Stationary status of discrete and continuous age-structured population models.

From Leonhard Euler to Alfred Lotka and in recent years understanding the stationary process of the human population has been of central interest to scientists. Population reproductive measure NRR (net reproductive rate) has been widely associated with measuring the status of population stationarity and it is also included as one of the measures in the millennium development goals. This article argues how the partition theorem-based approach provides more up-to-date and timely measures to find the status of the population stationarity of a country better than the NRR-based approach. We question the timeliness of the value of NRR in deciding the stationary process of the country. We prove associated theorems on discrete and continuous age distributions and derive measurable functional properties. The partitioning metric captures the underlying age structure dynamic of populations at or near stationarity. As the population growth rates for an ever-increasing number of countries trend towards replacement levels and below, new demographic concepts and metrics are needed to better characterize this emerging global demography.

Congressional Symmetry: Years Remaining Mirror Years Served in the U.S. House and Senate.

Our overarching goal in this paper was to both test and identify applications for a fundamental theorem of replacement-level populations known as the Stationary Population Identity (SPI), a mathematical model that equates the fraction of a population age x and the fraction with x years to live. Since true stationarity is virtually non-existent in human populations as well as in populations of non-human species, we used historical data on the memberships in both chambers of the U.S. Congress as population proxies. We conceived their fixed numbers (e.g., 100 Senators; 435 Representatives) as stationary populations, and their years served and years remaining as the equivalent of life lived and life remaining. Our main result was the affirmation of the mathematical prediction-i.e., the robust symmetry of years served and years remaining in Congress over the approximately 230 years of its existence (1789-2022). A number of applications emerged from this regularity and the distributional patterns therein including (1) new metrics such as Congressional half-life and other quantiles (e.g., 95% turnover); (2) predictability of the distribution of member's years remaining; (3) the extraordinary information content of a single number-the mean number of years served [i.e., derive birth (b) and death (d) rates; use of d as exponential rate parameter for model life tables]; (4) the concept of and metrics associated with period-specific populations (Congress); (5) Congressional life cycle concept with Formation, Growth, Senescence and Extinction Phases; and (6) longitudinal party transition rates for 100% Life Cycle turnover (Democrat/Republican) i.e., each seat from predecessor party-to-incumbent party and from incumbent party-to-successor party. Although our focus is on the use of historical data for Congressional members, we believe that most of the results are general and thus both relevant and applicable to most types of stationary or quasi-stationary populations including to the future world of zero population growth (ZPG).

Current oral hygiene and recreational behavioral trends in HIV disease.

OBJECTIVE: HIV disease is evolving with more HIV+ persons experiencing a high quality of life with well-controlled viremia. We recently enrolled a large cohort of HIV+ and clinically relevant HIV- persons for oral microbiome analyses that included a questionnaire related to oral hygiene and recreational behaviors. Here, the questionnaire responses were analyzed for behavioral trends within the cohort, together with trends over time by comparison to a previous geographically centered HIV+ cohort. METHODS: Data were collected by questionnaire at baseline visits as cross-sectional assessments. Multivariable analyses were conducted for associations of HIV status as well as age, race, and sex, on oral hygiene/recreational behaviors. RESULTS: HIV+ subjects had reduced brushing frequency, but increased incidence of past cleanings and frequency of dry mouth, compared to the HIV- subjects. Within the entire cohort, positive associations were identified between age and several oral hygiene practices, and between age, race, and sex for several recreational behaviors. In comparison to the historical cohort, the contemporary HIV+ cohort participated in fewer high-risk behaviors, but with similar trends for smoking and oral hygiene practices. CONCLUSION: HIV status had little association with oral hygiene and recreational behaviors despite several differences in age, race, and sex. Behavioral trends over time support a higher quality of life in people currently living with HIV.

Understanding theoretically the impact of reporting of disease cases in epidemiology.

In conducting preliminary analysis during an epidemic, data on reported disease cases offer key information in guiding the direction to the in-depth analysis. Models for growth and transmission dynamics are heavily dependent on preliminary analysis results. When a particular disease case is reported more than once or alternatively is never reported or detected in the population, then in such a situation, there is a possibility of existence of multiple reporting or under reporting in the population. In this work, a theoretical approach for studying reporting error in epidemiology is explored. The upper bound for the error that arises due to multiple reporting is higher than that which arises due to under reporting. Numerical examples are provided to support the arguments. This paper mainly treats reporting error as deterministic and one can explore a stochastic model for the same.

Mathematical analysis and topology of SARS-CoV-2, bonding with cells and unbonding.

We consider the structure of the novel coronavirus (SARS-Cov-2) in terms of the number of spikes that are critical in bonding with the cells in the host. Bonding formation is considered for selection criteria with and without any treatments. Functional mappings from the discrete space of spikes and cells and their analysis are performed. We found that careful mathematical constructions help in understanding the treatment impacts, and the role of vaccines within a host. Smale's famous 2-D horseshoe examples inspired us to create 3-D visualizations and understand the topological diffusion of spikes from one human organ to another organ. The pharma industry will benefit from such an analysis for designing efficient treatment and vaccine strategies.

Ground reality versus model-based computation of basic reproductive numbers in epidemics.

Computation of basic reproductive numbers is one of the primary goals of epidemic modelers. There are several challenges in such computations, especially when the data from the virus transmission networks are not so easy to collect; this makes model validation almost impossible. We provide a technical comment on the precautions to be taken while computing model-based basic reproductive numbers so that the ground realities of such computation are maintained. Basic reproductive numbers need to be adjusted retrospectively to compensate for reporting errors within the epidemic spread networks. Such an adjustment would lead to revised pandemic preparedness and mitigation plans.

Strengthening India's Response to HIV/AIDS Epidemic Through Strategic Planning, Innovative Financing, and Mathematical Modeling: Key Achievements over the Last 3 Decades.

Indian HIV/AIDS numbers during the 2000s did not reach the high proportion of estimations provided by the WHO and UNAIDS. The number of HIV infections was high around 2.4 million in the 2020s, but given the country's population of 1.38 billion, the general positivity rate remained very low compared with several countries. There were several reasons for a successful control of the epidemic in India, for example, setting-up of the National AIDS Control Programs, strategic priorities, surveillance and data management, mathematical modeling, and coordinating with the civil society and galvanizing public response. In this review article, we will provide a recollection of India's response and management of the HIV/AIDS epidemic, challenges, and successful model building, and future challenges that play important role in sustaining the epidemic at a lower level and plan for reducing the future transmissions.

Rapid initiation of nasal saline irrigation to reduce severity in high-risk COVID+ outpatients.

OBJECTIVE: To determine whether initiating saline nasal irrigation after COVID-19 diagnosis reduces hospitalization and death in high-risk outpatients compared with observational controls, and if irrigant composition impacts severity. METHODS: Participants 55 and older were enrolled within 24 hours of a + PCR COVID-19 test between September 24 and December 21, 2020. Among 826 screened, 79 participants were enrolled and randomly assigned to add 2.5 mL povidone-iodine 10% or 2.5 mL sodium bicarbonate to 240 mL of isotonic nasal irrigation twice daily for 14 days. The primary outcome was hospitalization or death from COVID-19 within 28 days of enrollment by daily self-report confirmed with phone calls and hospital records, compared to the CDC Surveillance Dataset covering the same time. Secondary outcomes compared symptom resolution by irrigant additive. RESULTS: Seventy-nine high-risk participants were enrolled (mean [SD] age, 64 [8] years; 36 [46%] women; 71% Non-Hispanic White), with mean BMI 30.3. Analyzed by intention-to-treat, by day 28, COVID-19 symptoms resulted in one ED visit and no hospitalizations in 42 irrigating with alkalinization, one hospitalization of 37 in the povidone-iodine group, (1.27%) and no deaths. Of nearly three million CDC cases, 9.47% were known to be hospitalized, with an additional 1.5% mortality in those without hospitalization data. Age, sex, and percentage with pre-existing conditions did not significantly differ by exact binomial test from the CDC dataset, while reported race and hospitalization rate did. The total risk of hospitalization or death (11%) was 8.57 times that of enrolled nasal irrigation participants (SE = 2.74; P = .006). Sixty-two participants completed daily surveys (78%), averaging 1.8 irrigations/day. Eleven reported irrigation-related complaints and four discontinued use. Symptom resolution was more likely for those reporting twice daily irrigation (X2 = 8.728, P = .0031) regardless of additive. CONCLUSION: SARS-CoV-2+ participants initiating nasal irrigation were over 8 times less likely to be hospitalized than the national rate.

Small Towns, Big Cities: Rural and Urban Disparities Among Hospitalized Patients With COVID-19 in the Central Savannah River Area.

BACKGROUND: There is a lack of data surrounding the impact of coronavirus disease 2019 (COVID-19) among rural and urban communities. This study aims to determine whether there are differences in epidemiologic characteristics and clinical outcomes among individuals with COVID-19 among these communities. METHODS: This was a retrospective analysis of 155 patients admitted to a single-center tertiary academic hospital located in Augusta, Georgia, with a large proportion of hospitalized patients transferred from or residing in rural and urban counties. Hospitalized adult patients were included in the study if they were admitted to AUMC between March 13, 2020, and June 25, 2020, and had a positive polymerase chain reaction test for severe acute respiratory syndrome coronavirus 2 regardless of the presence or absence of symptomatology. Demographics, admission data, and 30-day outcomes were examined overall and by geographical variation. RESULTS: Urban patients were more likely to be admitted to the general medical floor (P = .01), while rural patients were more likely to require an escalation in the level of care within 24 hours of admission (P = .02). In contrast, of the patients who were discharged or expired at day 30, there were no statistically significant differences in either total hospital length of stay or intensive care unit length of stay between the populations. CONCLUSIONS: There may be many social determinants of health that limit a rural patient's ability to seek prompt medical care and contribute to decompensation within the first 24 hours of admission. This study provides insight into the differences in clinical course among patients admitted from different community settings and when accounting for comorbid conditions.

Dynamical Systems: From Classical Mechanics and Astronomy to Modern Methods.

We describe topological dynamics over a space by starting from a simple ODE emerging out of two coupled variables. We describe the dynamics of the evolution of points in space within the deterministic and stochastic frameworks. Historically dynamical systems were associated with celestial mechanics. The core philosophies of two kinds of dynamics emerging from Poincaré and Lyapunov are described. Smale's contributions are highlighted. Markovian models are considered. Semi-group actions are a tool in this study.