1
|
Numfor E, Tuncer N, Martcheva M. Optimal control of a multi-scale HIV-opioid model. JOURNAL OF BIOLOGICAL DYNAMICS 2024; 18:2317245. [PMID: 38369811 DOI: 10.1080/17513758.2024.2317245] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2023] [Accepted: 02/05/2024] [Indexed: 02/20/2024]
Abstract
In this study, we apply optimal control theory to an immuno-epidemiological model of HIV and opioid epidemics. For the multi-scale model, we used four controls: treating the opioid use, reducing HIV risk behaviour among opioid users, entry inhibiting antiviral therapy, and antiviral therapy which blocks the viral production. Two population-level controls are combined with two within-host-level controls. We prove the existence and uniqueness of an optimal control quadruple. Comparing the two population-level controls, we find that reducing the HIV risk of opioid users has a stronger impact on the population who is both HIV-infected and opioid-dependent than treating the opioid disorder. The within-host-level antiviral treatment has an effect not only on the co-affected population but also on the HIV-only infected population. Our findings suggest that the most effective strategy for managing the HIV and opioid epidemics is combining all controls at both within-host and between-host scales.
Collapse
Affiliation(s)
- Eric Numfor
- Department of Mathematics, Augusta University, Augusta, GA, USA
| | - Necibe Tuncer
- Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL, USA
| | - Maia Martcheva
- Department of Mathematics, University of Florida, Gainesville, FL, USA
| |
Collapse
|
2
|
Spence C, Kurz ME, Sharkey TC, Miller BL. Scoping Literature Review of Disease Modeling of the Opioid Crisis. J Psychoactive Drugs 2024:1-14. [PMID: 38909286 DOI: 10.1080/02791072.2024.2367617] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2023] [Accepted: 03/28/2024] [Indexed: 06/24/2024]
Abstract
Opioid misuse continues to cause significant harm. To investigate current research, we conducted a scoping literature review of disease spread models of opioid misuse from January 2000 to December 2022. In total, 85 studies were identified and examined for the opioids modeled, model type, data sources used and model calibration and validation. Most of the studies (58%, 49) only modeled heroin; the next largest categories were prescription opioids and unspecified opioids which accounted for 9% (8) each. Most models were theoretical compartmental models (57) or applied compartmental models (21). Previously published research was the most used data source (38), and a majority of the model validation involved the researchers setting initial conditions to verify theoretical results (30). To represent typical opioid use more accurately, multiple opioids need to be incorporated into the disease spread models, and applying different modeling techniques may allow other insights into opioid misuse spread.
Collapse
Affiliation(s)
- Chelsea Spence
- Department of Industrial Engineering, Clemson University, Clemson, SC, USA
| | - Mary E Kurz
- Department of Industrial Engineering, Clemson University, Clemson, SC, USA
| | - Thomas C Sharkey
- Department of Industrial Engineering, Clemson University, Clemson, SC, USA
| | - Bryan Lee Miller
- Department of Sociology, Anthropology and Criminal Justice, Clemson University, Clemson, SC, USA
| |
Collapse
|
3
|
Gupta C, Tuncer N, Martcheva M. A network immuno-epidemiological model of HIV and opioid epidemics. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2023; 20:4040-4068. [PMID: 36899616 DOI: 10.3934/mbe.2023189] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
In this paper, we introduce a novel multi-scale network model of two epidemics: HIV infection and opioid addiction. The HIV infection dynamics is modeled on a complex network. We determine the basic reproduction number of HIV infection, $ \mathcal{R}_{v} $, and the basic reproduction number of opioid addiction, $ \mathcal{R}_{u} $. We show that the model has a unique disease-free equilibrium which is locally asymptotically stable when both $ \mathcal{R}_{u} $ and $ \mathcal{R}_{v} $ are less than one. If $ \mathcal{R}_{u} > 1 $ or $ \mathcal{R}_{v} > 1 $, then the disease-free equilibrium is unstable and there exists a unique semi-trivial equilibrium corresponding to each disease. The unique opioid only equilibrium exist when the basic reproduction number of opioid addiction is greater than one and it is locally asymptotically stable when the invasion number of HIV infection, $ \mathcal{R}^{1}_{v_i} $ is less than one. Similarly, the unique HIV only equilibrium exist when the basic reproduction number of HIV is greater than one and it is locally asymptotically stable when the invasion number of opioid addiction, $ \mathcal{R}^{2}_{u_i} $ is less than one. Existence and stability of co-existence equilibria remains an open problem. We performed numerical simulations to better understand the impact of three epidemiologically important parameters that are at the intersection of two epidemics: $ q_v $ the likelihood of an opioid user being infected with HIV, $ q_u $ the likelihood of an HIV-infected individual becoming addicted to opioids, and $ \delta $ recovery from opioid addiction. Simulations suggest that as the recovery from opioid use increases, the prevalence of co-affected individuals, those who are addicted to opioids and are infected with HIV, increase significantly. We demonstrate that the dependence of the co-affected population on $ q_u $ and $ q_v $ are not monotone.
Collapse
Affiliation(s)
- Churni Gupta
- Center for Pharmacometrics and Systems Pharmacology, University of Florida, USA
| | - Necibe Tuncer
- Department of Mathematical Sciences, Florida Atlantic University, USA
| | | |
Collapse
|
4
|
Modeling Syphilis and HIV Coinfection: A Case Study in the USA. Bull Math Biol 2023; 85:20. [PMID: 36735105 PMCID: PMC9897625 DOI: 10.1007/s11538-023-01123-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2022] [Accepted: 01/12/2023] [Indexed: 02/04/2023]
Abstract
Syphilis and HIV infections form a dangerous combination. In this paper, we propose an epidemic model of HIV-syphilis coinfection. The model always has a unique disease-free equilibrium, which is stable when both reproduction numbers of syphilis and HIV are less than 1. If the reproduction number of syphilis (HIV) is greater than 1, there exists a unique boundary equilibrium of syphilis (HIV), which is locally stable if the invasion number of HIV (syphilis) is less than 1. Coexistence equilibrium exists and is stable when all reproduction numbers and invasion numbers are greater than 1. Using data of syphilis cases and HIV cases from the US, we estimated that both reproduction numbers for syphilis and HIV are slightly greater than 1, and the boundary equilibrium of syphilis is stable. In addition, we observed competition between the two diseases. Treatment for primary syphilis is more important in mitigating the transmission of syphilis. However, it might lead to increase of HIV cases. The results derived here could be adapted to other multi-disease scenarios in other regions.
Collapse
|
5
|
Wang W, Lu S, Tang H, Wang B, Sun C, Zheng P, Bai Y, Lu Z, Kang Y. A Scoping Review of Drug Epidemic Models. INTERNATIONAL JOURNAL OF ENVIRONMENTAL RESEARCH AND PUBLIC HEALTH 2022; 19:ijerph19042017. [PMID: 35206206 PMCID: PMC8872096 DOI: 10.3390/ijerph19042017] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/09/2021] [Revised: 01/21/2022] [Accepted: 01/26/2022] [Indexed: 02/05/2023]
Abstract
The phenomenon of drug epidemics has been a global issue in the past decades, causing enormous damages to the physical and mental health of drug users and social well-being. Despite great efforts to curb drug epidemics at the governmental or social level, the total number of drug users has still been on the rise in recent years, along with illicit production and trafficking around the world. Inspired by dynamical epidemic models of infectious disease, a flourishment of promising results has been observed in the exploration of drug epidemic models. In this review, we aim to provide a scoping review of all existing drug epidemic modeling studies, and it has been shown that most studies focused on analyses of theoretical behaviors of the model systems, lacking emphasis on practical applications in real settings. We found that the drug epidemic models were characterized by a longer time scale, no incubation period, no significant prevention vaccines interfered, and population specificity. This review could assist policymakers and public health workers in gaining deeper insights into modeling tools, and help modelers improve their works, thus narrowing gaps between mathematical epidemiology and public health studies.
Collapse
Affiliation(s)
- Wei Wang
- Institute of Environmental Information, Chinese Research Academy of Environmental Sciences, Beijing 100012, China; (W.W.); (B.W.); (C.S.)
| | - Sifen Lu
- Precision Medicine Key Laboratory of Sichuan Province and Precision Medicine Center, West China Hospital, Sichuan University, Chengdu 610041, China;
| | - Haoxiang Tang
- Department of Biomedical Engineering, College of Engineering, Peking University, Beijing 100871, China;
| | - Biao Wang
- Institute of Environmental Information, Chinese Research Academy of Environmental Sciences, Beijing 100012, China; (W.W.); (B.W.); (C.S.)
| | - Caiping Sun
- Institute of Environmental Information, Chinese Research Academy of Environmental Sciences, Beijing 100012, China; (W.W.); (B.W.); (C.S.)
| | - Pai Zheng
- Department of Occupational and Environmental Health Science, School of Public Health, Peking University, Beijing 100871, China;
| | - Yi Bai
- Department of Epidemiology and Biostatistics, School of Public Health, Peking University, Beijing 100871, China;
| | - Zuhong Lu
- State Key Lab of Bioelectronics, National Demonstration Center for Experimental Biomedical Engineering Education, School of Biological Science and Medical Engineering, Southeast University, Nanjing 210096, China;
| | - Yulin Kang
- Institute of Environmental Information, Chinese Research Academy of Environmental Sciences, Beijing 100012, China; (W.W.); (B.W.); (C.S.)
- Correspondence:
| |
Collapse
|
6
|
Gupta C, Tuncer N, Martcheva M. Immuno-epidemiological co-affection model of HIV infection and opioid addiction. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:3636-3672. [PMID: 35341268 DOI: 10.3934/mbe.2022168] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
In this paper, we present a multi-scale co-affection model of HIV infection and opioid addiction. The population scale epidemiological model is linked to the within-host model which describes the HIV and opioid dynamics in a co-affected individual. CD4 cells and viral load data obtained from morphine addicted SIV-infected monkeys are used to validate the within-host model. AIDS diagnoses, HIV death and opioid mortality data are used to fit the between-host model. When the rates of viral clearance and morphine uptake are fixed, the within-host model is structurally identifiable. If in addition the morphine saturation and clearance rates are also fixed the model becomes practical identifiable. Analytical results of the multi-scale model suggest that in addition to the disease-addiction-free equilibrium, there is a unique HIV-only and opioid-only equilibrium. Each of the boundary equilibria is stable if the invasion number of the other epidemic is below one. Elasticity analysis suggests that the most sensitive number is the invasion number of opioid epidemic with respect to the parameter of enhancement of HIV infection of opioid-affected individual. We conclude that the most effective control strategy is to prevent opioid addicted individuals from getting HIV, and to treat the opioid addiction directly and independently from HIV.
Collapse
Affiliation(s)
- Churni Gupta
- Faculty of Pharmacy, University of Montreal, Montreal, QC, Canada
| | - Necibe Tuncer
- Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL, United States of America
| | - Maia Martcheva
- Department of Mathematics, University of Florida, Gainesville, FL, United States of America
| |
Collapse
|