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.

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.

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.

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).

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.

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.

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.

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.

Mathematical modeling of impact of eCD4-Ig molecule in control and management of HIV within a host.

Eradication and eventually cure of the HIV virus from the infected individual should be the primary goal in all HIV therapy. This has yet to be achieved, however development of broadly neutralizing antibodies (bNabs) and eCD4-Ig and its related particles are promising therapeutic alternatives to eliminate the HIV virus from the host. Past studies have found superior protectivity and efficacy eradicating the HIV virus with the use of eCD4-Igs over bNabs, which has proposed the antibody-dependent cell-mediated cytotoxicity (ADCC) effect as one of the key-factors for antibody design. In this study, we evaluated the dynamics of the HIV virus, CD4 T-cells, and eCD4-Ig in humans using a gene-therapy approach which has been evaluated in primates previously. We utilized a mathematical model to investigate the relationship between eCD4-Ig levels, ADCC effects, and the neutralization effect on HIV elimination. In addition, a balance between ADCC and viral neutralization effect of eCD4-Ig has been investigated in order to understand the condition of which HIV eliminating antibodies needs to satisfy. Our analysis indicated some level of ADCC effect, which was missing from ART, was required for viral elimination. The results will be helpful in designing future drugs or therapeutic strategies.

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.

HIV Treatment Outcomes in Rural Georgia Using Telemedicine.

BACKGROUND: The increasing shortage of specialized health care services contributes to the ongoing HIV epidemic. Telemedicine (TM) is a potential tool to improve HIV care, but little is known about its effectiveness when compared with traditional (face-to-face [F2F]) care in rural populations. The objective of this study was to compare the effectiveness of HIV care delivered through TM with the F2F model. METHODS: We conducted a retrospective chart review of a subset of patients with HIV who attended a TM clinic in Dublin, Georgia, and an F2F clinic in Augusta, Georgia, between May 2017 and April 2018. All TM patients were matched to F2F patients based on gender, age, and race. HIV viral load (VL) and CD4 count gain were compared using t test and Mann-Whitney U statistics. RESULTS: Three hundred eighty-five patients were included in the analyses (F2F = 200; TM = 185). The mean CD4 in the TM group was higher (643.9 cells/mm3) than that of the F2F group (596.3 cells/mm3; P < .001). There was no statistically significant difference in VL reduction, control, or mean VL (F2F = 416.8 cp/mL; TM = 713.4 cp/mL; P = .30). Thirty-eight of eighty-five patients with detectable VL achieved viral suppression during the study period (F2F = 24/54; TM = 14/31), with a mean change of 3.34 × 104 and -1 to 0.24 × 104, respectively (P = 1.00). CONCLUSIONS: TM was associated with outcome measures comparable to F2F. Increased access to specialty HIV care through TM can facilitate HIV control in communities with limited health care access in the rural United States. Rigorous prospective evaluation of TM for HIV care effectiveness is warranted.

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.

Data Science for Virtual Tourism Using Cutting-Edge Visualizations: Information Geometry and Conformal Mapping.

We highlight the advantages of virtual tourism and the use of data science to improve existing television and internet-based experiences with new technologies. Information geometry and conformal mappings can improve audiovisual experiences based on drone recordings. The data collection, assimilation, and transformation requirements for a seamless and user-friendly service are discussed along with the precautions to ensure that this technology is used appropriately to protect human safety and the environment.