Path integral control of a stochastic multi-risk SIR pandemic model

Pramanik, Paramahansa

doi:10.1007/s12064-023-00388-y

Cited by 10 publications

(11 citation statements)

References 73 publications

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“…In the context of infectious disease modeling, the widely used susceptibility-infectionrecovery (SIR) framework comes into play [22,23]. Our method allows for testing exchangeability by examining different SIR datasets between two regions.…”

Section: Discussionmentioning

confidence: 99%

“…In Figure 4, we juxtapose the simulations using Laplace approximation against the actual conditional tail expectations. In Figure 4a, the simulation results obtained in (22) are utilized, with fixed parameter values of α 1 = 0.85, α 2 = 0.90, β = 5, and δ = 1. The choice of δ = 1 is made to mitigate uneven fluctuations observed at higher and lower values.…”

Section: Type IImentioning

confidence: 99%

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Dependence on Tail Copula

Pramanik

2024

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In real-world scenarios, we encounter non-exchangeable dependence structures. Our primary focus is on identifying and quantifying non-exchangeability in the tails of joint distributions. The findings and methodologies presented in this study are particularly valuable for modeling bivariate dependence, especially in fields where understanding dependence patterns in the tails is crucial, such as quantitative finance, quantitative risk management, and econometrics. To grasp the intricate relationship between the strength of dependence and various types of margins, we explore three fundamental tail behavior patterns for univariate margins. Capitalizing on the probabilistic features of tail non-exchangeability structures, we introduce graphical techniques and statistical tests designed for analyzing data that may manifest non-exchangeability in the joint tail. The effectiveness of the proposed approaches is illustrated through a simulation study and a practical example.

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Section: Discussionmentioning

confidence: 99%

Section: Type IImentioning

confidence: 99%

Dependence on Tail Copula

Pramanik

2024

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“…Apart from that after considering humans as automatons, motor control and foraging for food becomes a big examples of minimization of costs (or the expected return) [15]. As control problems like motor controls are stochastic in nature because there is a noise in the relation between the muscle contraction and the actual displacement with joints with the change of the information environment over time, we consider Feynman path integral approach to calculate the stochastic control after assuming the opinion dynamics Equation (2.2) [19,[37][38][39]. The coefficient of the control term in Equation (2.1) is normalized to 1, without loss of generality.…”

Section: A S D G O Dmentioning

confidence: 99%

“…Similarly, agent i has infinitely opinions, out of them they choose the opnion corresponding to least cost given by the constraint explained in Equation (2.2). Furthermore, the advantage of Feynman approach is that, it can be used in both in linear and non-linear stochastic differential equation systems where constructing an HJB equation is almost impossible [32,43].…”

Section: (Ii) the Function Hmentioning

confidence: 99%

Consensus as a Nash Equilibrium of a Stochastic Differential Game

Pramanik

2023

Eur. J. Stat.

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In this paper a consensus has been constructed in a social network which is modeled by a stochastic differential game played by agents of that network. Each agent independently minimizes a cost function which represents their motives. A conditionally expected integral cost function has been considered under an agent’s opinion filtration. The dynamic cost functional is minimized subject to a stochastic differential opinion dynamics. As opinion dynamics represents an agent’s differences of opinion from the others as well as from their previous opinions, random influences and stubbornness make it more volatile. An agent uses their rate of change of opinion at certain time point as a control input. This turns out to be a non-cooperative stochastic differential game which have a feedback Nash equilibrium. A Feynman-type path integral approach has been used to determine an optimal feedback opinion and control. This is a new approach in this literature. Later in this paper an explicit solution of a feedback Nash equilibrium opinion is determined.

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“…Similarly, if more people are vaccinated, the virus will spread less and fewer people will be affected, thus saving more lives. In their study, Pramanik (2023) [10] determined the best way to decide when to shut down an economy and what rate of vaccination is optimal. They used a healthcare cost function that was minimized while taking into account a stochastic susceptibleinfectious-recovered (SIR) dynamic, which was first introduced in Aron et al (1984) [1].…”

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confidence: 99%

Path Integral Control in Infectious Disease Modeling

Pramanik

2023

Contributions to Pure and Applied Mathematics

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COVID-19, a pandemic that affected the whole world, claimed the lives of almost 1.1 million people in the United States and 7 million worldwide. Prior to the discovery of vaccines, many countries resorted to implementing lock downs to reduce the spread of the virus. Most economies have implemented this policy, except in essential sectors such as public health and safety. Different states in the US have imposed lock downs at different times, based on the severity of the outbreak in their respective regions. Lock downs involve reducing social interactions, leading to a decrease in the transmission of the virus. However, if lock downs remain in effect for too long, people may become hesitant to resume social activities for fear of contracting COVID-19 [3]. Hence, businesses are facing a reduction in the number of consumers and employees, resulting in a decrease in sustainable long-term protability. Furthermore, if a business fails to have enough inventory to with stand the crisis, it may eventually shut down. Since the government is not providing nancial support, it is easy to shut down a business, but dicult to restore it to its original employment levels [3]. It is recommended by the Centers for Disease Control and Prevention (CDC) that anyone infected with Omicron should isolate themselves for five days. This is because a person infected with the virus can spread it to others, so isolation helps reduce transmission. Similarly, if more people are vaccinated, the virus will spread less and fewer people will be affected, thus saving more lives. In their study, Pramanik (2023) [10] determined the best way to decide when to shut down an economy and what rate of vaccination is optimal. They used a healthcare cost function that was minimized while taking into account a stochastic susceptible infectious-recovered (SIR) dynamic, which was first introduced in Aron et al (1984) [1]. Most models of infectious disease transmission are based on the SIR model. Pramanik's construction can be extended to a generalized random surface to investigate unprecedented shocks, such as the emergence of a new COVID-19 variant, sudden infection due to random interactions caused by travel, and environmental calamities resulting in more exposure to the pandemic. The random surface replaces the jump diffusion of the stochastic differential equations.

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Path integral control of a stochastic multi-risk SIR pandemic model

Cited by 10 publications

References 73 publications

Dependence on Tail Copula

Dependence on Tail Copula

Consensus as a Nash Equilibrium of a Stochastic Differential Game

Path Integral Control in Infectious Disease Modeling

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