Optimal control of a social epidemic model with media coverage

Figures & data

Figure 1. Transfer diagram for alcoholism model with media coverage.

Figure 2. when $R_0<1$, the alcohol free equilibrium $E_0$ is globally asymptotically stable.

Figure 3. When $R_0>1$, the alcohol present equilibrium $E^{\ast }$ is globally asymptotically stable.

Table 1. The parameters description of the alcoholism model.

$b$	Constant recruitment rate.	$0.55{\mathrm{year}}^{-1}$	estimated
$\mu$	Nature death rate.	$0.25{\mathrm{year}}^{-1}$	[19]
$\beta$	Transmission coefficient.	$0.03{\mathrm{year}}^{-1}$	[19]
$k_0$	Half-saturating constant.	$100{\mathrm{year}}^{-1}$	[18]
$k_1$	Half-saturating constant.	$80{\mathrm{year}}^{-1}$	estimated
$d$	Death rate due to heavy alcoholism.	$0.3{\mathrm{year}}^{-1}$	estimated
$q$	The permanently quit rate.	$0.2{\mathrm{year}}^{-1}$	[18]
$m$	The implementation rate of media coverage.	$0.05{\mathrm{year}}^{-1}$	[7]
$\gamma$	The depletion rate of media coverage.	$0.05{\mathrm{year}}^{-1}$	[18]

Figure 4. The influence of different values of m on the population of alcoholics.

Figure 5. The influence of different values of γ on the population of alcoholics.

Figure 6. Variations of population with different control, where $b_1=10$, $b_2=1$.

Figure 7. Variations of population with different control, where $b_1=1$, $b_2=10$.

Figure 8. The impact of different weight coefficients on optimal control $u_1$, $u_2$.

G. Mulone and B. Straughan, Modeling binge drinking, Int. J. Biomath. 5 (2012), pp. 57–70.

 Google Scholar

S.H. Ma, H.F. Huo and X.Y. Meng, Modelling alcoholism as a contagious disease: A mathematical model with awareness programs and time delay, Discrete Dynamics in Nature and Society, 2015, Article ID 260195, 13 pages.

 Google Scholar

P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci. 180 (2002), pp. 29–48.

 Google Scholar