| Citation: |
Wei Yang, Chengjun Sun, Julien Arino. EFFECT OF MEDIA-INDUCED MODIFICATION OF TRAVEL RATES ON DISEASE TRANSMISSION IN A MULTIPLE PATCH SETTING[J]. Journal of Applied Analysis & Computation, 2020, 10(6): 2682-2703. doi: 10.11948/20200066
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EFFECT OF MEDIA-INDUCED MODIFICATION OF TRAVEL RATES ON DISEASE TRANSMISSION IN A MULTIPLE PATCH SETTING
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Abstract
A general SIS epidemic model is formulated that incorporates media-induced modification of travel rates. Basic local properties of solutions to the model are established. In particular, it is shown that the basic reproduction number does not involve parameters related to the effect of media on travel. The general model is subsequently specialised to two-patch models, with two different scenarios regarding patch population size. Qualitative analyses show that the basic reproduction number acts as a sharp threshold between disease persistence and extinction. The concept of uniform weak persistence is used to prove the existence of an endemic equilibrium and disease uniform strong persistence under a certain condition. Numerical investigations are carried out to gain insight into the analytically tractable and intractable cases, highlighting the importance of considering not only the basic reproduction number but also other measures of disease severity.-
Keywords:
- Epidemiology /
- metapopulations /
- media coverage /
- nonlinear travel rates /
- population sizes
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References
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Wei Yang, Chengjun Sun, Julien Arino. EFFECT OF MEDIA-INDUCED MODIFICATION OF TRAVEL RATES ON DISEASE TRANSMISSION IN A MULTIPLE PATCH SETTING[J]. Journal of Applied Analysis & Computation, 2020, 10(6): 2682-2703. doi: 10.11948/20200066
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Figure 1. Flow diagram of the SIS model in an isolated patch
$ p\in{\mathcal{P}} $ . - Figure 2. Flow diagram of the movement component of the SIS model, in the special case of two patches. Flows within patches are not shown for legibility.
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Figure 3. (a) Effect of media coverage on the time to extinction of an existing epidemic when
$ {\mathcal{R}}_{0}^{(4.1)}<1 $ . (b) Effect of media coverage on the prevalence of an existing epidemic when$ {\mathcal{R}}_{0}^{(4.1)}>1 $ . -
Figure 4. Equilibrium values of (a)
$ I_1^* $ and (b)$ I_2^* $ , as$ \sigma_1 $ and$ \sigma_2 $ are varied, with other parameters as in Table 1 such that$ {\mathcal{R}}_0^{(4.1)}>1 $ . -
Figure 5. Equilibrium values of (a)
$ I_1^* $ and (b)$ I_2^* $ , as$ \alpha_1 $ and$ \alpha_2 $ are varied, with other parameters as in Table 1 such that$ {\mathcal{R}}_0^{(4.1)}>1 $ . -
Figure 6. (a) Sensitivity of
$ {\mathcal{R}}_0^{(4.1)} $ to variations of parameters, for 10, 000 sample points in the parameter region indicated in the text. Sensitivity of$ {\mathcal{R}}_0^{(4.1)} $ to variations of individual parameters. In the absence of variation of any other parameters, (b)$ {\mathcal{R}}_0^{(4.1)}<1 $ and (c)$ {\mathcal{R}}_0^{(4.1)}>1 $ . -
Figure 7. Effect of population size on the prevalence of an existing epidemic when
$ {\mathcal{R}}_{0}^{(4.1)}, {\mathcal{R}}_{0}^{(5.1)}>1 $ .