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December  2018, 15(6): 1315-1343. doi: 10.3934/mbe.2018061

## Modeling the control of infectious diseases: Effects of TV and social media advertisements

 1 Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi - 221005, India 2 College of Science and Engineering, Department of Physics and Mathematics, Aoyama Gakuin University, Kanagawa 252-5258, Japan

* Corresponding author: Arvind Kumar Misra

Received  September 26, 2017 Revised  April 25, 2018 Published  September 2018

Citation: Arvind Kumar Misra, Rajanish Kumar Rai, Yasuhiro Takeuchi. Modeling the control of infectious diseases: Effects of TV and social media advertisements. Mathematical Biosciences & Engineering, 2018, 15 (6) : 1315-1343. doi: 10.3934/mbe.2018061
##### References:

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##### References:
Effect of changing the values of $\lambda$ and $M_0$ on $R_1$
Non-linear stability behavior of model system (2) in $I-A-M$ space for $\lambda = 0.00003$, keeping rest of parameter values same as given in Table 1, which shows that all solution trajectory attains their equilibrium $E^*$ inside the region of attraction $\Omega$
Variation of $S(t)$, $I(t)$, $A(t)$ and $M(t)$ with respect to time $t$ for $r = 0.005$, which shows that the equilibrium $E^*$ is stable and we have damped oscillation
Phase portrait of model system (2) for $r = 0.005$ in $I-A-M$ space, which shows that the equilibrium $E^*$ is stable
Variation of $S(t)$, $I(t)$, $A(t)$ and $M(t)$ with respect to time $t$ for $r = 0.011$, which shows that the equilibrium $E^*$ is unstable and we have undamped sustained oscillation
Appearance of limit cycle of model system (2) for $r = 0.011$ in $I-A-M$ space, which shows that the equilibrium $E^*$ is unstable
Bifurcation diagram of infected population $I(t)$, aware population $A(t)$ and the cumulative number of TV and social media ads $M(t)$ with respect to $r$, keeping rest of parameters same as given in Table 1
Bifurcation diagram of infected population $I(t)$, aware population $A(t)$ and the cumulative number of TV and social media ads $M(t)$ with respect to $\lambda$ for $r = 0.05$, $\omega = 60$, keeping rest of parameters same as given in Table 1
Parameter values for the model system (2)
 Parameter Values Parameter Values $\Lambda$ $5$ ${\rm{day}}^{-1}$ $\beta$ $0.0000030$ ${\rm{day}}^{-1}$ $\lambda$ $0.012$ ${\rm{day}}^{-1}$ $\lambda_0$ $0.008$ ${\rm{day}}^{-1}$ $\nu$ $0.2$ ${\rm{day}}^{-1}$ $\alpha$ $0.00001$ ${\rm{day}}^{-1}$ $d$ $0.00004$ ${\rm{day}}^{-1}$ $r$ $0.006$ ${\rm{day}}^{-1}$ $r_0$ $0.005$ ${\rm{day}}^{-1}$ $\theta$ $0.0005$ $\omega$ $6000$ $p$ $1200$ $M_0$ $500$
 Parameter Values Parameter Values $\Lambda$ $5$ ${\rm{day}}^{-1}$ $\beta$ $0.0000030$ ${\rm{day}}^{-1}$ $\lambda$ $0.012$ ${\rm{day}}^{-1}$ $\lambda_0$ $0.008$ ${\rm{day}}^{-1}$ $\nu$ $0.2$ ${\rm{day}}^{-1}$ $\alpha$ $0.00001$ ${\rm{day}}^{-1}$ $d$ $0.00004$ ${\rm{day}}^{-1}$ $r$ $0.006$ ${\rm{day}}^{-1}$ $r_0$ $0.005$ ${\rm{day}}^{-1}$ $\theta$ $0.0005$ $\omega$ $6000$ $p$ $1200$ $M_0$ $500$
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