Optimal control strategies for a heroin epidemic model with age-dependent susceptibility and recovery-age

Khan, Asaf; Zaman, Gul; Ullah, Roman; Naveed, Nawazish

doi:10.3934/math.2021086

Cited by 18 publications

(6 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Age-structured models (also known as Kermack–McKendrick models) can be used to mathematically describe the evolution of distinct population categories (e.g., susceptible and dead), where the dynamics and interactions among categories may depend on the distribution of age in the population. Different variants of age-structured models have been developed and applied to model heroin addiction as an epidemic [ 10 – 17 ]. Such models have also been applied to mechanistically describe cellular processes [ 18 , 19 ] and population dynamics associated with social interactions [ 20 ], birth control policies [ 21 ], and COVID-19 mortality [ 22 – 24 ].…”

Section: Introductionmentioning

confidence: 99%

Modeling and forecasting age-specific drug overdose mortality in the United States

Böttcher

Chou

D’Orsogna

2023

Eur. Phys. J. Spec. Top.

View full text Add to dashboard Cite

Drug overdose deaths continue to increase in the United States for all major drug categories. Over the past two decades the total number of overdose fatalities has increased more than fivefold; since 2013 the surge in overdose rates is primarily driven by fentanyl and methamphetamines. Different drug categories and factors such as age, gender, and ethnicity are associated with different overdose mortality characteristics that may also change in time. For example, the average age at death from a drug overdose has decreased from 1940 to 1990 while the overall mortality rate has steadily increased. To provide insight into the population-level dynamics of drug overdose mortality, we develop an age-structured model for drug addiction. Using an augmented ensemble Kalman filter (EnKF), we show through a simple example how our model can be combined with synthetic observation data to estimate mortality rate and an age-distribution parameter. Finally, we use an EnKF to combine our model with observation data on overdose fatalities in the United States from 1999 to 2020 to forecast the evolution of overdose trends and estimate model parameters.

show abstract

Section: Introductionmentioning

confidence: 99%

Modeling and forecasting age-specific drug overdose mortality in the United States

Böttcher

Chou

D’Orsogna

2023

Eur. Phys. J. Spec. Top.

View full text Add to dashboard Cite

show abstract

“…Age-structured models (also known as Kermack-McKendrick models) can be used to mathematically describe the evolution of distinct population categories (e.g., susceptible and dead), where the dynamics and interactions among categories may depend on the distribution of age in the population. Different variants of agestructured models have been developed and applied to model heroin addiction as an epidemic [10][11][12][13][14][15][16][17]. Such models have also been applied to mechanistically describe cellular processes [18,19] and population dynamics associated with social interactions [20], birth control policies [21], and COVID-19 mortality [22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Modeling and forecasting age-specific drug overdose mortality in the United States

Böttcher¹,

Chou²,

D’Orsogna³

2023

Preprint

View full text Add to dashboard Cite

Drug overdose deaths continue to increase in the United States for all major drug categories. Over the past two decades the total number of overdose fatalities has increased more than five-fold; since 2013 the surge in overdose rates is primarily driven by fentanyl and methamphetamines. Different drug categories and factors such as age, gender, and ethnicity are associated with different overdose mortality characteristics that may also change in time. For example, the average age at death from a drug overdose has decreased from 1940 to 1990 while the overall mortality rate has steadily increased. To provide insight into the population-level dynamics of drug-overdose mortality, we develop an age-structured model for drug addiction. Using an augmented ensemble Kalman filter (EnKF), we show through a simple example how our model can be combined with synthetic observation data to estimate mortality rate and an age-distribution parameter. Finally, we use an EnKF to combine our model with observation data on overdose fatalities in the United States from 1999 to 2020 to forecast the evolution of overdose trends and estimate model parameters.

show abstract

“…In [23,24], Ebola models with a preventive control in the form of education campaigns are investigated. Very recently, an age-structured heroin epidemic model is formulated with partial differential equations, under the assumption that susceptibility and recovery are age-dependent, keeping in view some control measures for heroin addiction and using optimal control for simulations, which show the effect on the entire population [25,26].…”

Section: Introductionmentioning

confidence: 99%

Optimal control of a heroin epidemic mathematical model

Sowndarrajan,

Shangerganesh,

Debbouche

et al. 2021

Preprint

View full text Add to dashboard Cite

A heroin epidemic mathematical model with prevention information and treatment, as control interventions, is analyzed, assuming that an individual's behavioral response depends on the spreading of information about the effects of heroin. Such information creates awareness, which helps individuals to participate in preventive education and self-protective schemes with additional efforts. We prove that the basic reproduction number is the threshold of local stability of a drug-free and endemic equilibrium. Then, we formulate an optimal control problem to minimize the total number of drug users and the cost associated with prevention education measures and treatment. We prove existence of an optimal control and derive its characterization through Pontryagin's maximum principle. The resulting optimality system is solved numerically. We observe that among all possible strategies, the most effective and cost-less is to implement both control policies.

show abstract

Optimal control strategies for a heroin epidemic model with age-dependent susceptibility and recovery-age

Cited by 18 publications

References 23 publications

Modeling and forecasting age-specific drug overdose mortality in the United States

Modeling and forecasting age-specific drug overdose mortality in the United States

Modeling and forecasting age-specific drug overdose mortality in the United States

Optimal control of a heroin epidemic mathematical model

Contact Info

Product

Resources

About