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).

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.

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.

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.

Identification of COVID-19 can be quicker through artificial intelligence framework using a mobile phone-based survey when cities and towns are under quarantine.

We propose the use of a machine learning algorithm to improve possible COVID-19 case identification more quickly using a mobile phone-based web survey. This method could reduce the spread of the virus in susceptible populations under quarantine.

Deep Learning of Markov Model-Based Machines for Determination of Better Treatment Option Decisions for Infertile Women.

In this technical article, we are proposing ideas, that we have been developing on how machine learning and deep learning techniques can potentially assist obstetricians/gynecologists in better clinical decision-making, using infertile women in their treatment options in combination with mathematical modeling in pregnant women as examples.

Cryptic Eimeria genotypes are common across the southern but not northern hemisphere.

The phylum Apicomplexa includes parasites of medical, zoonotic and veterinary significance. Understanding the global distribution and genetic diversity of these protozoa is of fundamental importance for efficient, robust and long-lasting methods of control. Eimeria spp. cause intestinal coccidiosis in all major livestock animals and are the most important parasites of domestic chickens in terms of both economic impact and animal welfare. Despite having significant negative impacts on the efficiency of food production, many fundamental questions relating to the global distribution and genetic variation of Eimeria spp. remain largely unanswered. Here, we provide the broadest map yet of Eimeria occurrence for domestic chickens, confirming that all the known species (Eimeria acervulina, Eimeria brunetti, Eimeria maxima, Eimeria mitis, Eimeria necatrix, Eimeria praecox, Eimeria tenella) are present in all six continents where chickens are found (including 21 countries). Analysis of 248 internal transcribed spacer sequences derived from 17 countries provided evidence of possible allopatric diversity for species such as E. tenella (FST values ⩽0.34) but not E. acervulina and E. mitis, and highlighted a trend towards widespread genetic variance. We found that three genetic variants described previously only in Australia and southern Africa (operational taxonomic units x, y and z) have a wide distribution across the southern, but not the northern hemisphere. While the drivers for such a polarised distribution of these operational taxonomic unit genotypes remains unclear, the occurrence of genetically variant Eimeria may pose a risk to food security and animal welfare in Europe and North America should these parasites spread to the northern hemisphere.

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.

Non-polio enterovirus association with persistent diarrhea in children as revealed by a follow-up study of an Indian cohort during the first two years of life.

BACKGROUND: We recently reported significant association of non-polio enteroviruses (NPEVs) with acute diarrhea in children. Persistent diarrhea (PD) remains a major cause of morbidity and mortality in infants below two years of age in developing countries. Understanding age-dependent frequency and duration of NPEV infections is important to determine their association with persistent diarrhea and disease burden. OBJECTIVES: A cohort of 140 infants was followed for 6 months to 2 years of age to determine the frequency, duration, and association with PD of NPEV infections in comparison with rotavirus and other agents. STUDY DESIGN: Stool samples were collected every 14 days, and diarrheal episodes and their duration were recorded. Enteroviruses were characterized by RT-PCR and VP1 gene sequence analysis, rotavirus by electropherotyping, and other agents by PCR. RESULTS: Of 4545 samples, negative for oral polio vaccine strains, 3907 (85.96%) and 638 (14.04%) were NPEV-negative and NPEV-positive, respectively, representing 403 (8.87%) infection episodes. About 68% of NPEV infections occurred during the first year with every child having at least one episode lasting between four days and four months. Approximately 38% and 22% of total diarrheal episodes were positive for NPEV and RV, respectively. While about 18% of NPEV infection episodes were associated with diarrhea, 6% being persistent, 13% of total diarrheal episodes were persistent involving infections by monotype NPEV strains or sequential infections by multiple strains and other agents. CONCLUSIONS: This is the first report revealing NPEVs as the single most frequently and persistently detected viral pathogen in every PD episode.

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.

Cohort effects in dynamic models and their impact on vaccination programmes: an example from hepatitis A.

BACKGROUND: Infection rates for many infectious diseases have declined over the past century. This has created a cohort effect, whereby older individuals experienced a higher infection rate in their past than younger individuals do now. As a result, age-stratified seroprevalence profiles often differ from what would be expected from constant infection rates. METHODS: Here, we account for the cohort effect by fitting an age-structured compartmental model with declining transmission rates to Hepatitis A seroprevalence data for Canadian-born individuals. We compare the predicted impact of universal vaccination with and without including the cohort effect in the dynamic model. RESULTS: We find that Hepatitis A transmissibility has declined by a factor of 2.8 since the early twentieth century. When the cohort effect is not included in the model, incidence and mortality both with and without vaccination are significantly over-predicted. Incidence (respectively mortality) over a 20 year period of universal vaccination is 34% (respectively 90%) higher than if the cohort effect is included. The percentage reduction in incidence and mortality due to vaccination are also over-predicted when the cohort effect is not included. Similar effects are likely for many other infectious diseases where infection rates have declined significantly over past decades and where immunity is lifelong. CONCLUSION: Failure to account for cohort effects has implications for interpreting seroprevalence data and predicting the impact of vaccination programmes with dynamic models. Cohort effects should be included in dynamic modelling studies whenever applicable.