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.

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 populations. 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 all types of stationary or quasi-stationary populations including to the future world of zero population growth (ZPG).

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.

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.

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.

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.

391. Small Towns, Big Cities: Rural and Urban Disparities Among Hospitalized Patients with COVID-19

Background

More than half of all hospitals in the U.S. are rural hospitals. Frequently understaffed and resource limited, community hospitals serve a population that tends to be older and have less access to care with increased poverty and medical co-morbidities. There is a lack of data surrounding the impact of COVID-19 among rural minority communities. This study seeks to determine rural and urban disparities among hospitalized individuals with COVID-19.

Methods

This is a descriptive, retrospective analysis of the first 155 adult patients admitted to a tertiary hospital with a positive COVID-19 nasopharyngeal PCR test. Augusta University Medical Center serves the surrounding rural and urban counties of the Central Savannah River Area. Rural and urban categories were determined using patient address and county census data. Demographics, comorbidities, admission data and 30-day outcomes were evaluated.

Results

Of the patients studied, 62 (40%) were from a rural county and 93 (60%) were from an urban county. No difference was found when comparing the number of comorbidities of rural vs urban individuals; however, African Americans had significantly more comorbidities compared to other races (p-value 0.02). In a three-way comparison, race was not found to be significantly different among admission levels of care. Rural patients were more likely to require an escalation in the level of care within 24 hours of admission (p-value 0.02). Of the patients that were discharged or expired at day 30, there were no differences in total hospital length of stay or ICU length of stay between the rural and urban populations.

Baseline Characteristics of Hospitalized Patients with COVID-19

Day 30 Outcomes and Characteristics

Level of Care at Time of Admission

Conclusion

This study suggests that patients in rural communities may be more critically ill or are at a higher risk of early decompensation at time of hospitalization compared to patients from urban communities. Nevertheless, both populations had similar lengths of stay and outcomes. Considering this data is from an academic medical center with a large referral area and standardized inpatient COVID-19 management, these findings may prompt further investigations into other disparate outcomes.

Disclosures

All Authors: No reported disclosures

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.

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.

1010. Effective Management of HIV in Rural Georgia Using Telemedicine

Background

The increasing incidence of HIV and lack of care in rural areas contributes to the ongoing epidemic. The dearth of specialized health services within remote communities and access of this population to available services poses a challenge to HIV care. Telemedicine (TM) is a potential tool to improve HIV care in these remote communities, but little is known about its effectiveness when compared to traditional (face-to-face) (F2F) care. The objective of this study is to examine the effectiveness of HIV care delivered through TM, and compare to F2F care.

Methods

This is a retrospective chart review of all HIV positive patients who attended either the F2F clinic (Augusta, GA) or the TM clinic (Dublin, GA) between May 2017 to April 2018. Data extracted included demographics, CD4 count, HIV PCR, co-morbidities, dates of clinic attendance, HIV resistance mutations and ART changes. Viral suppression and gain in CD4 counts were compared. T-test was conducted to test differences in characteristics and outcomes between the two groups.

Results

385 cases were included in the study (52.5% black, 82% females, F2F=200, TM=185). Mean CD4 count in the TM group was statistically higher (643.9 cells/mm³) than the F2F group (596.3 cells/mm³) (p< 0.001). There was no statistically significant difference in mean HIV viral load (F2F= 416.8 cp/ml, TM=713.4 cp/ml, p=0.3) and rates of year-round viral control (F2F= 73% vs TM = 77% p= 0.54). 38 patients achieved viral suppression during the study period (F2F= 24, TM =14) with a mean change of -3.34 x 10⁴ vs -1.24 x 10⁴, respectively. The difference in mean change was not statistically significant by Snedacor’s W Statistics. This indicates there was no significant difference between the two populations in terms of mean viral suppression among patients who were otherwise not suppressed before the study period.

Conclusion

To achieve an HIV cure, HIV care is required to extend to rural areas of the country and the world. Through delivery of care using TM, trained specialists can target communities with little or no health care. Moreover, use of TM achieves target outcome measures comparable to F2F clinics. Increase in the use of TM will improve the access to specialty HIV care and help achieve control of HIV in rural communities.

Disclosures

All Authors: No reported disclosures

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.

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.

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.

Role of Markov Modeling Approaches to Understand the Impact of Infertility Treatments

We are proposing to use Markov modeling type of analysis to understand data generated by treatments for infertility in women receiving ovarian stimulations. We describe the conceptual novelties, need for such an analysis, basics of the proposed methods, and theoretical constructions of various probabilities associated with practical level implementation of the Markov modeling procedures. This method can be adopted to infertility-related data visualizations whenever progression of outcome stages in infertility treatment is recorded. These methods if implemented should be able to enhance the understanding of treatment impacts of gonadotropins, clomiphene citrate, or an aromatase inhibitor at the beginning of treatment cycles of infertile women. This framework will be very useful for infertility treatment practitioners to compute the values of success rates of treatment for total population or population divided by demographic, clinical, and genetic factors. These methods can be continuously updated with newer data and translated into a mobile app to be used by clinical practitioners.

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

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The seven Eimeria spp. recognised to infect chickens are present globally.

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Cryptic Eimeria operational taxonomic units (OTUs) are common in the southern but not northern hemisphere.

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Parasite population structure appears to vary between Eimeria spp.

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 (F_ST 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.

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.

HIV/AIDS epidemic in India and predicting the impact of the national response: mathematical modeling and analysis

After two phases of AIDS control activities in India, the third phase of the National AIDS Control Programme (NACP III) was launched in July 2007. Our focus here is to predict the number of people living with HIV/AIDS (PLHA) in India so that the results can assist the NACP III planning team to determine appropriate targets to be activated during the project period (2007-2012). We have constructed a dynamical model that captures the mixing patterns between susceptibles and infectives in both low-risk and high-risk groups in the population. Our aim is to project the HIV estimates by taking into account general interventions for susceptibles and additional interventions, such as targeted interventions among high risk groups, provision of anti-retroviral therapy, and behavior change among HIV-positive individuals. Continuing the current level of interventions in NACP II, the model estimates there will be 5.06 million PLHA by the end of 2011. If 50 percent of the targets in NACP III are achieved by the end of the above period then about 0.8 million new infections will be averted in that year. The current status of the epidemic appears to be less severe compared to the trend observed in the late 1990s. The projections based on the second phase and the third phase of the NACP indicate prevention programmes which are directed towards the general and high-risk populations, and HIV-positive individuals will determine the decline or stabilization of the epidemic. Model based results are derived separately for the revised HIV estimates released in 2007. According to revised projections there will be 2.08 million PLHA by 2012 if 50 percent of the targets in NACP III are reached. We perform a Monte Carlo procedure for sensitivity analysis of parameters and model validation. We also predict a positive role of implementation of anti-retroviral therapy treatment of 90 percent of the eligible people in the country. We present methods for obtaining disease progression parameters using convolution approaches. We also extend our models to age-structured populations.

Modeling the rapid spread of avian influenza (H5N1) in India

Controlling the spread of avian bird flu has become a challenging tasks for Indian agriculture and health administrators. After the first evidence and control of the virus in 2006, the virus attacked five states by January 2008. Based on the evidence of rapid spread of the avian bird flu type H5N1 among the Indian states of Maharashtra, Manipur, and West Bengal, and in the partially affected states of Gujarat and Madhya Pradesh, a model is developed to understand the spread of the virus among birds and the effect of control measures on the dynamics of its spread. We predict that, in the absence of control measures, the total number of infected birds in West Bengal within ten and twenty days after initial discovery of infection were 780,000 and 2.1 million, respectively. When interventions are introduced, these values would have ranged from 65,000 to 225,000 after ten days and from 16,000 to 190,000 after twenty days. We show that the farm and market birds constitute the major proportion of total infected birds, followed by domestic birds and wild birds in West Bengal, where a severe epidemic hit recently. Culling 600,000 birds in ten days might have reduced the current epidemic before it spread extensively. Further studies on appropriate transmission parameters, contact rates of birds, population sizes of poultry and farms are helpful for planning.

A dynamic model for assessing universal Hepatitis A vaccination in Canada

Vaccination against Hepatitis A virus (HAV) in Canada is currently targeted toward high-risk groups. However, universal vaccination has been adopted in several other countries with a similar disease burden. Here we develop an age-structured compartmental model of HAV transmission and vaccination in Canada to assess potential universal vaccination strategies. The model predicts that universal vaccination at age 1 (respectively 4, 9, 15), with phasing out of targeted vaccination, would reduce reported incidence by 60% (respectively 52, 36, 31%) and mortality attributable to HAV by 56% (respectively 45, 26, 25%), relative to continued targeted vaccination, over 80 years.

Antiretroviral therapy and HIV prevention in India: modeling costs and consequences of policy options

OBJECTIVES

The objective of this study is to assess the costs, cost-effectiveness, and HIV epidemic impact of 3 antiretroviral therapy (ART) policy options.

STUDY DESIGN

We constructed an epidemiologic model to predict the course of the HIV epidemic in the absence of expanded ART availability. Based on background studies of the willingness to pay for ART among patients with AIDS, of the costs to the government of the alternative treatment interventions, and of ART's likely effects on HIV transmission, we simulated the consequences of 3 possible alternative government ART policies.

RESULTS

A program to reduce the negative consequences of the currently unstructured private-sector provision of ART is the most cost-effective of the 3 options at a 10% discount rate and least cost-effective at a 3% rate. The costs and cost-effectiveness of all options are highly sensitive to the effect of ART on condom use.

CONCLUSION

The design of ART policy should capitalize on the potential of ART to decrease HIV transmission through institutional arrangements that reward effective prevention programs, thereby raising the likelihood that treatment has beneficial rather than negative external effects.

Incubation-time distribution in back-calculation applied to hiv/aids data in India

In this article, HIV incidence density is estimated from prevalence data and then used together with reported cases of AIDS to estimate incubation-time distribution. We used the deconvolution technique and the maximum-likelihood method to estimate parameters. The effect of truncation in hazard was also examined. The mean and standard deviation obtained with the Weibull assumption were 12.9 and 3.0 years, respectively. The estimation seemed useful to investigate the distribution of time between report of HIV infection and that of AIDS development. If we assume truncation, the optimum truncating point was sensitive to the HIV growth assumed. This procedure was applied to US data for validating the results obtained from the Indian data. The results show that method works well.