tetano
Editor, Senior Moderator
Math Biosci. 2017 Dec 19. pii: S0025-5564(17)30512-6. doi: 10.1016/j.mbs.2017.12.002. [Epub ahead of print]
[h=1]A Filippov model describing the effects of media coverage and quarantine on the spread of human influenza.[/h] Chen C[SUP]1[/SUP], Chong NS[SUP]2[/SUP], Smith R[SUP]3[/SUP].
[h=3]Author information[/h]
[h=3]Abstract[/h] Mass-media reports on an epidemic or pandemic have the potential to modify human behaviour and affect social attitudes. Here we construct a Filippov model to evaluate the effects of media coverage and quarantine on the transmission dynamics of influenza. We first choose a piecewise smooth incidence rate to represent media reports being triggered once the number of infected individuals exceeds a certain critical level [Formula: see text] . Further, if the number of infected cases increases and exceeds another larger threshold value [Formula: see text] ( [Formula: see text] ), we consider that the incidence rate tends to a saturation level due to the protection measures taken by individuals; meanwhile, we begin to quarantine susceptible individuals when the number of susceptible individuals is larger than a threshold value S[SUB]c[/SUB]. Then, for each susceptible threshold value S[SUB]c[/SUB], the global property of the Filippov model with regard to the existence and stability of all possible equilibrium and sliding-mode dynamics is performed, as we vary the infected threshold values [Formula: see text] and [Formula: see text] . We show generically that the Filippov system stabilizes at either the endemic equilibrium of the subsystem or the pseudoequilibrium on the switching surface or the endemic equilibrium [Formula: see text] depending on the choice of the threshold values. The findings suggest that proper combinations of infected and susceptible threshold values can maintain the number of infected individuals either below a certain threshold level or stabilize at a previously given level.
[h=4]KEYWORDS:[/h] Filippov model; Influenza; Media coverage; Quarantine; Sliding mode; Threshold policy
PMID: 29273381 DOI: 10.1016/j.mbs.2017.12.002
[h=1]A Filippov model describing the effects of media coverage and quarantine on the spread of human influenza.[/h] Chen C[SUP]1[/SUP], Chong NS[SUP]2[/SUP], Smith R[SUP]3[/SUP].
[h=3]Author information[/h]
[h=3]Abstract[/h] Mass-media reports on an epidemic or pandemic have the potential to modify human behaviour and affect social attitudes. Here we construct a Filippov model to evaluate the effects of media coverage and quarantine on the transmission dynamics of influenza. We first choose a piecewise smooth incidence rate to represent media reports being triggered once the number of infected individuals exceeds a certain critical level [Formula: see text] . Further, if the number of infected cases increases and exceeds another larger threshold value [Formula: see text] ( [Formula: see text] ), we consider that the incidence rate tends to a saturation level due to the protection measures taken by individuals; meanwhile, we begin to quarantine susceptible individuals when the number of susceptible individuals is larger than a threshold value S[SUB]c[/SUB]. Then, for each susceptible threshold value S[SUB]c[/SUB], the global property of the Filippov model with regard to the existence and stability of all possible equilibrium and sliding-mode dynamics is performed, as we vary the infected threshold values [Formula: see text] and [Formula: see text] . We show generically that the Filippov system stabilizes at either the endemic equilibrium of the subsystem or the pseudoequilibrium on the switching surface or the endemic equilibrium [Formula: see text] depending on the choice of the threshold values. The findings suggest that proper combinations of infected and susceptible threshold values can maintain the number of infected individuals either below a certain threshold level or stabilize at a previously given level.
[h=4]KEYWORDS:[/h] Filippov model; Influenza; Media coverage; Quarantine; Sliding mode; Threshold policy
PMID: 29273381 DOI: 10.1016/j.mbs.2017.12.002