Mathematics & Computer Science Tag

Sri Sathya Sai Institute of Higher Learning (SSSIHL) appreciates Casualty Actuarial Society for awarding the 2022 Individual Research Grant to the Actuarial Data Science group, Department of Mathematics and Computer Science.

The project team is led by Professor Pallav Kumar Baruah and Satya Sai Mudigonda.

About Individual Grants Competition:

The Casualty Actuarial Society (CAS) and the Society of Actuaries’ (SOA) Committee on Knowledge Extension Research (CKER) announce the 2022 Individual Grants Competition to support the advancement of knowledge in actuarial science and contribute in an important way to areas of interest to the actuarial profession.

About CAS:

The Casualty Actuarial Society (CAS) is a leading international organization for credentialing and professional education. Founded in 1914, the CAS is the world’s only actuarial organization focused exclusively on property and casualty risks and serves over 9,100 members worldwide. CAS members are experts in property and casualty insurance, reinsurance, finance, risk management, and enterprise risk management. Professionals educated by the CAS empower business and government to make well-informed strategic, financial and operational decisions.

About SSSIHL Actuarial Data Science:

SSSIHL is actively involved in actuarial data science research, specifically in the area of fraud detection. It has to its credit about 30 research papers/book chapters, 20 dissertations in non-life actuarial stream and 2 PhDs awarded in the area of actuarial data science. In fact, SSSIHL is one of the first University to award PhD in Actuarial Science in India.

About the Project:

The project is in the area of Insurance Fraud Detection using Actuarial and Data Science techniques. The project commenced on 1st June 2022 and will end by March 2023.

We wish the SSSIHL Actuarial Data Science Team all the best for the execution of this project.

Identifying the Issue

COVID -19 pandemic has caused the most severe health problems to adults over 60 years of age, with particularly fatal consequences for those over 80. In this case, age-structured mathematical modelling could be useful to determine the spread of the disease and to develop a better control strategy for different age groups. In this study, we first propose an age-structured model considering two different age groups, the first group with population age below 30 years and the second with population age above 30 years, and discuss the stability of the equilibrium points and the sensitivity of the model parameters. In the second part of the study, we propose an optimal control problem to understand the age-specific role of treatment in controlling the spread of COVID -19 infection.

Objective of the Research

• We propose to study the stability analysis of an age-structured model incorporating the saturation in medical treatment
• We propose to study the optimal control problem to study the effectiveness of treatment in reducing COVID-19 infection

Who should read this?

Academics, Mathematics, Bio-Mathematics, Mathematical Modelling, Doctors-Physicians, Research

Solution

In this research article we work on age-structured models considering two different age groups, the first group with population age below 30 years and the second with population age above 30 years. The results and findings of the modelling studies shows that infection decreases with the implementation of an optimal treatment strategy namely a combined treatment strategy considering treatment for both age groups is effective in keeping cumulative infection low in severe epidemics. Cumulative infection was found to increase with increasing saturation in medical treatment.

Key Features and Benefits

• It is found that the behaviour of the system depends on the value of basic reproduction number. Stability changes based on the value of basic reproduction number
• The results from the optimal control study suggests that with optimal treatment COVID-19 infection can be decreased

Impact

• The work presented in this paper could enhance our understanding of complex COVID-19 dynamics
• It can help physicians with decision making in the treatment of life-threatening COVID-19 pneumonia

Team

• Sri Bishal Chhetri, Research Scholar, Dept. of Mathematics & Computer Science, SSSIHL
• Dr. D K K Vamsi, Asst. Professor, Dept. of Mathematics & Computer Science, SSSIHL
• Prof. (Dr) Carani B Sanjeevi, Vice-Chancellor, SSSIHL

Paper Published in: Differential Equations and Dynamical Systems

Title of paper: Optimal Control Studies on Age Structured Modeling of COVID-19 in Presence of Saturated Medical Treatment of Holling Type III

Read Paper Here: https://doi.org/10.1007/s12591-022-00593-z

This chapter is part of the Book titled “Pandemic and Problems: Lessons for Recovery and Resilience” released by The Tamil Nadu Dr. MGR Medical University.

Identifying the Issue

In this work, we discuss the within-host, the between-host and the multi-scale mathematical models for COVID-19 viral infections. We also present the outcomes of our study.

Objective of the Research

We propose to study the natural history of COVID-19 model and also the role and efficacies of various control strategies including the antiviral drugs and immunomodulators.

Who should read this?

Academics, Mathematics, Bio-Mathematics, Mathematical Modelling, Doctors-Physicians, Research

Solution

In this work, we discuss the within-host, the between-host and the multi-scale mathematical models for COVID-19 viral infections. The results from the natural history of the within-host model suggests that the proposed model undergoes trans-critical bifurcation when the value of basic reproduction number is one. Results from optimal control theory suggests that combined drug therapy is the best strategy to be used to contain the spread of infection at within-host level. At the between-host level, combined use of vaccination and treatment is found to be effective in lowering infection at the population level. From multi-scale work it is found that the spread of infection at community level is influenced by the within-host parameters.

Key Features and Benefits

• It is observed that the viral load decreases the most when antiviral drugs and immunomodulators are used together. This could help doctors and physicians to look for combination therapy as one of the alternative to stop the multiplication of virus in the body
• Vaccination along with treatments can reduce COVID-19 infection
• The spread of infection at community level is influenced by the within-host parameters

Impact

• The work presented in this paper could enhance our understanding of complex interplay of immune response and virus particles in the body
• It can help physicians with decision making in the treatment of life-threatening COVID-19 pneumonia

Team

• Sri Bishal Chhetri, Research Scholar, Dept. of Mathematics & Computer Science, SSSIHL
• Dr. D K K Vamsi, Asst. Professor, Dept. of Mathematics & Computer Science, SSSIHL
• Prof. (Dr) Carani B Sanjeevi, Vice -Chancellor, SSSIHL

Chapter Title: Mathematical Modelling Studies with Reference to COVID-19 Pandemic

Book Title: Pandemic and Problems: Lessons for Recovery and Resilience

The book was released by the Chief Minister of Tamil Nadu, Shri M K Stalin at the Annual Convocation of The Tamil Nadu Dr MGR Medical University, Chennai, held on 20 December 2021.

Identifying the Issue

• While there are many predator-prey models developed to study the dynamics of populations of species, there are very few works done to study the controllability aspects to reach the desired state in finite time. None of the current models have developed control strategies based on the quality of additional food for predator-prey systems with type IV response (inhibitory effect f prey). Furthermore, we have considered two models for covering the various approaches in providing food supplements
• In this work, we have also examined the role of the inhibitory effect of prey species in achieving the desired outcome

Objective of the Research

• We consider two different models of the additional food provided prey-predator systems involving Holling type IV functional response (with the inhibitory effect of prey)
• The main objective is to drive the system to a desired state in minimum (finite) time. We wish to achieve bio-conservation and bio-control by providing optimal quality of additional food as a control
• Both the models are relevant

Who should read this?

Academicians, Mathematics, Bio-Mathematics, Mathematical Modelling, Eco-Managers, Experimental Ecologists

Solution

In this work, we formulate and study optimal control problems to achieve the desired outcomes in minimum (finite) time. We consider two different models of additional food provided prey-predator systems involving Holling type IV functional response (with the inhibitory effect of prey). In the first scenario, additional food is incorporated implicitly into the predator’s functional response with a possibility of achieving biological conservation through the co-existence of species and biological control by maintaining prey at a level that is least harmful to the system. In the second, the effect of additional food is incorporated explicitly into the predator’s compartment with the goal of pest management by maintaining prey density at a very minimal damaging level. For both cases, appropriate optimal control strategies are derived and the theoretical findings are illustrated by numerical simulation.

Key Features and Benefits

• When additional food supplements are provided to the predators, the quantity of additional food is generally determined by the gut volume of the species. Thus, it is important to ensure that the quality of additional food is monitored regularly. In this work, we provide strategies to the eco-managers based on the quality of additional food.
• Both biological conservation and bio-control can be achieved in finite time.

Impact

• The work presented in this paper provides a minimum-time approach to drive predator-prey systems towards biological conservation and pest management
• Eco-Managers could benefit from the findings of this work in supplying appropriate quality of additional food provided to achieve the desired outcome

Team

• Sri Ananth V S, Department of Mathematics and Computer Science, SSSIHL
• Dr. D K K Vamsi, Department of Mathematics and Computer Science, SSSIHL

Paper Published in: Acta Biotheoretica, Volume 70, Article Number5 (2022) (Impact Factor: 1.74, SCI Indexed)

Title: Achieving Minimum-Time Biological Conservation and Pest Management for Additional Food provided Predator-Prey Systems involving Inhibitory Effect: A Qualitative Investigation

Read Paper Here: https://doi.org/10.1007/s10441-021-09430-2

Identifying the Issue

• While there are many vector-host models developed to study the spread of COVID-19 at population level, there are very few works done to understand the interplay of the immune response and the virus particles in the body. Also there is no mathematical modelling studies that talks about the time optimal control studies on COVID-19
• In this work, firstly, a mathematical model is developed incorporating inter-cellular time delay and the stability analysis of the equilibrium points admitted by the model is performed. Secondly, an optimal control problem is studied with antiviral agents and second-line drugs as control measures incorporating the adverse events caused by antiviral drugs. Lastly, a time-optimal control problem is formulated with the objective to drive the system from any given initial state to the desired infection-free equilibrium state in minimal time

Objective of the Research

• We propose to study the role and efficacies of the first line and second line drugs in reducing COVID-19 burden by framing an optimal control problem
• We propose to perform the stability analysis of the equilibrium points and find the condition for the global stability of the infection-free state
• We propose to frame and study the time-optimal control problem to drive the system from any given initial state to the desired infection-free equilibrium state in minimal time

Who should read this?

Academics, Mathematics, Bio-Mathematics, Mathematical Modelling, Doctors-Physicians, Research

Solution

In this study, we first develop SIV model at within-host level by incorporating the intercellular time delay and analyzing the stability of equilibrium points. The model dynamics admits a disease-free equilibrium and an infected equilibrium with their stability based on the value of the basic reproduction number $R_0$. We then formulate an optimal control problem with antiviral drugs and second-line drugs as control measures and study their roles in reducing the number of infected cells and viral load. The comparative study conducted in the optimal control problem suggests that if the first-line antiviral drugs show adverse effects, considering these drugs in reduced amounts along with the second-line drugs would be very effective in reducing the number of infected cells and viral load in a COVID-19 infected patient. Later, we formulate a time-optimal control problem with the goal of driving the system from any initial state to the desired infection-free equilibrium state in finite minimal time. Using Pontryagin’s Minimum Principle, it is shown that the optimal control strategy is of the bang-bang type, with the possibility of switching between two extreme values of the optimal controls. Numerically, it is shown that the desired infection-free state is achieved in a shorter time when the higher values of the optimal controls. The results of this study may be very helpful to researchers, epidemiologists, clinicians and physicians working in this field.
 

Key Features and Benefits

• When the first line antiviral drugs starts showing adverse events, considering first line antiviral drugs in reduced quantity along with the second line drug is found to be highly effective in reducing the infected cells and viral load in a COVID infected patients and this alternative also proved to be cost effective
• It is found that with higher values of first line and second line drugs the time to reach the desired infection free state decreases. This would imply that the infected cells and viral load in the body of a COVID infected individual becomes zero in short period of time with the higher values of the first line and second line drugs

Impact

• The work presented in this paper could enhance our understanding of complex interplay of immune response and virus particles in the body
• It can help physicians with decision making in the treatment of life-threatening COVID-19 pneumonia

Team

Bishal Chhetri, Vijay M. Bhagat, Swapna Muthusamy, Ananth V S, D. K. K. Vamsi, Carani B Sanjeevi

Paper Published in: RSC Advances (Royal Society of Chemistry)

Title: Time Optimal Control Studies on COVID-19 Incorporating Adverse Events of the Antiviral Drugs

Read Paper Here: Computational and Mathematical Biophysics, 2021, 9:214 – 241

Identifying the Issue

• Number of reports has suggested symptoms of dyspnea, an indication of impaired lung function with reduced diffusion capacity post SARS-CoV-2 infection
• Need for a more reliable and accurate oxygen monitoring device that can complement pulse oximetry in the remote management of COVID-19 recovered individuals

Objective of the Research

• Monitoring of O2 uptake in SARS-CoV-2 recovered participants to assess their lung function in comparison with healthy individuals
• Designing of a low-cost, eco-friendly, high sensitive, plasmonics based sensor

Who should read this?

COVID-19 researchers, COVID-19 recovered patients, Pulmonologists, COVID Care health experts, Chemical sensor & nanotechnology scientists.

Solution

The trilateral international collaboration between the Sri Sathya Sai Institute of Higher Learning (SSSIHL), India, Macquarie University, Australia (MACQ) and University of Maryland Baltimore County (UMBC), United States of America began in the year 2017. Over the years, the collaboration has grown stronger with multiple collaborative projects and publications between these institutions.

In one such successful research collaboration, a new research study is now published in ACS Sensors. The technology developed is:

• A wood-microfluidics chip & plasmon-coupling based biodegradable and eco-friendly O2 sensor with ultrafast response time (~0.2 sec) and high sensitivity
• This is suggestive that SARS-CoV-2 recovered participants had comparatively lower oxygen uptake than healthy participants
• While this clinical data is preliminary in nature, this unique study presents novel insights into an under researched problem that is of paramount significance given the larger health implications of this ongoing pandemic and the nascent understanding of the post-acute sequelae of SARS-CoV-2

Key Features and Benefits

• Next-gen breath sensors that will help achieve low-cost lung health diagnostic devices
• This technology will help in understanding the impact of COVID-19 on lung health through non-invasive mode of evaluation
• Use of novel, biodegradable wood chips for microfluidics will help save environment from plastic-based one-time use microfluidic chips

Impact

• First time 27-fold phosphorescence emission enhancement using surface plasmon-coupled emission platform
• Use of novel and reusable Au(III) complexes having fluorescence and phosphorescence emission for designing ratiometric O2 sensor
• Highly potential technology for post-COVID lung health monitoring

Team

• STAR Laboratory, Department of Chemistry, Sri Sathya Sai Institute of Higher Learning: Bebeto Rai, Dr. Venkatesh Srinivasan Dr. Kalathur Mohan Ganesh, Dr. Naga Sai Visweswar Kambhampati, Prof. Carani B Sanjeevi and Dr. Sai Sathish Ramamurthy
• MQ Photonics Research Centre, MQ Sustainable Research Centre, Macquarie University: Dr. Robert Malmberg and Dr. Koushik Venkatesan.
• Center for Advanced Sensor Technology, University of Maryland, Baltimore County: Dr. Abhay Andar, Dr. Sai Sathish Ramamurthy and Prof. Govind Rao

Paper Published in: ACS Sensors

Title: Surface Plasmon-Coupled Dual Emission Platform for Ultrafast Oxygen Monitoring after SARS-CoV-2 Infection

Read Paper Here: https://pubs.acs.org/doi/10.1021/acssensors.1c01665

Identifying the Issue

While there are vector-host models developed to study the dengue virus at population level, very few works performed to understand the dengue viral dynamics in human body. None of the current models as per our study has considered the role of innate immune response in the defence to the dengue viral attack until recently one of them by Rotem Ben-Shachar and Katia Koelle, introduced innate immune response and showed that it can reproduce the characteristic features of the primary infection.

In this paper, a non-linear model is proposed which incorporates innate and adaptive (both cellular and humoral) immune responses, studying the Dengue virus at cellular level using a mathematical model.

Objective of the Research

• We propose to study the dynamics of within-host epidemic model of dengue infection which incorporates both innate immune response and adaptive immune response (Cellular and Humoral)
• The proposed model also incorporates the time delay for production of antibodies from B cells and understand the dynamics of this model using the dynamical systems approach by performing the stability and sensitivity analysis
• Both the above can help detect and control the dengue virus better and understand the dengue viral dynamics in human body

Who should read this?

Those working in the field of Mathematics, Bio-Mathematics, Mathematical Modeling, research, and other related academic fields, and Doctors, especially Physicians.

Solution

The critical level of the antibody recruitment rate(q) was found to be responsible for the existence and stability of various steady states. The stability of endemic state was found to be dependent on time delay. The sensitivity analysis identified the production rate of antibodies (q) to be highly sensitive parameter.

• The existence and stability conditions for the equilibrium states of the disease have been obtained
• The threshold value of time delay has been computed which is critical for change in stability of the endemic state

Key Features and Benefits

• It has been observed that that innate response co-relates with the virus titer in the early stages of the infection which can help in an early detection of a serious disease
• The production rate of antibodies (q) was found to be highly sensitive
• It was observed that the burst rate of virus particles (k) has a predictable behaviour and the rate of infection(β1) is sensitive only in some interval range

Impact

• The works presented in this paper could enhance our understanding of this complex immune response
• The model can help in detection of the disease in the early stages of the infection

Team

• Deva Siva Sai Murari Kanumoori: University of L’Aquila, L’Aquila, Italy
• D Bhanu Prakash: Department of Mathematics and Computer Science, Sri Sathya Sai Institute of Higher Learning – SSSIHL, India
• D. K. K. Vamsi: Department of Mathematics and Computer Science, Sri Sathya Sai Institute of Higher Learning – SSSIHL, India
• Carani B Sanjeevi: Vice-Chancellor, Sri Sathya Sai Institute of Higher Learning -SSSIHL

Paper Published In: Computational and Mathematical Biophysics 9, no. 1 (2021): 66-80

Read Paper Here: https://doi.org/10.1515/cmb-2020-0118