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.

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.

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.

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.

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.

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.

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.