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A dynamical model of drinking and smoking with optimal control analysis
Fredrick Asenso Wireko1, Sebastian Ndogum1, Botchew Abdul Nasiru1
1Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana.
Practicing both alcohol drinking and tobacco smoking is life-threatening. Mathematical modeling reveals that interventions like prevention and recovery efforts can significantly reduce co-dependence within eight weeks.
Area of Science:
- Mathematical modeling
- Epidemiology
- Public Health
Background:
- Combined alcohol and tobacco use poses significant health risks, leading to millions of deaths annually.
- Existing research often focuses on single substance use, neglecting the complex co-dynamics of dual addiction.
- Relapse is a common challenge in recovery from both alcohol and tobacco dependence.
Purpose of the Study:
- To develop a mathematical model investigating the co-dynamics of alcohol drinking and tobacco smoking.
- To analyze control strategies for mitigating the spread of dual substance use.
- To examine the influence of key parameters on secondary co-dependence infections.
Main Methods:
- Employed the next-generation matrix approach to determine the basic reproductive number.
- Conducted local and global stability analyses for various disease states.
- Performed numerical simulations and optimal control analysis with literature-based parameter values.
Main Results:
- Contact rates (a1, a2) directly correlate with the spread of drinking and smoking.
- Recovery rates (δ1, δ2) exhibit an inverse relationship with disease spread.
- Simulations demonstrated that control strategies can reduce the prevalence of smokers and drinkers within eight weeks.
Conclusions:
- Mathematical modeling provides valuable insights into the co-dynamics of alcohol and tobacco use.
- Targeted interventions, including prevention and recovery efforts, are effective in reducing dual substance dependence.
- Further research into control strategies can inform public health policies to combat co-addiction.
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