I thank the two anonymous referees for useful comments that have led to
additional simulations and discussions in the paper. Below is my detailed
response to the individual comments. The resulting changes to the paper
have been marked in blue.

> Referee: 1
> 1. In this model, the recovered individuals get reinfected with a
> probability γ. It appears more logical that a recovered individual first
> becomes susceptible and then gets reinfected. The SIRS model captures
> this possibility. Is there any reason behind reinfecting a recovered
> person directly? Do these two models produce similar results? If this is
> the case, the author should mention it. If not, the direct reinfections
> (R → I) should be justified.

I have now done the comparison and it turns out that in all the cases
presented in the paper, the differences are small. A direct comparison
is shown and discussed in Fig.10. Another comparison is given by Fig.6(c)
and Fig.8(a), where everything is the same, except that in the latter,
gamma'=0.1 has been used instead of gamma=0.1; see page 8.

> 2. The values of µ and γ used to generate Figure 3 should be mentioned
> in the caption.

This has now been done: both values were zero. This figure corresponds
now to Figure 4; see page 6.

> 3. The value(s) of t used for Figure 5(a), 5(b), and 5(c) should be
> mentioned in the caption.

This has now been done; t=500 in all cases. This figure corresponds now
to Figure 6; see page 7.

> 4. The case of µ = 0.1 and γ = 0.1 may be discussed a little more. The
> curve (c) of Figure 6 shows that the spread continues due to reinfections
> (unlike curve (a) with γ = 0). However, Figure 5(c) seems to indicate
> otherwise. The straight line portions of the curves (a) and (c) of Figure
> 6 are almost parallel even though they have very different values of
> µ. A discussion on this point could further demonstrate the impact
> of reinfections.

The fact that they are nearly parallel is because the spreading speed is
mainly determined by the diffusivity. To clarify this better, we have now
added Figs. 8 and 9, were we consider three different values of kappa.
This point has now been discussed on page 7, column 1, at the end of
Sec. 2.4.

> Referee: 2
> 1. There appears to be an error in the references (question mark in
> the second paragraph of the Introduction; some citations are incorrect).

This was probably a temporary problem during the submission, which was no
longer present in the arXiv submission.

> 2. The source of the data used in Figure 1 and Table 1 should be
> clearly cited.

This has now been stated on the left column of Page 2, where we quote
www.worldometers.info/coronavirus in the footnote.

> 3. Figure 2 is identical to a figure in Ref.[13], and should therefore
> be removed.

I have now addressed this point by using instead a new figure where I
show the emergence of three separate islands. I have now also added a
corresponding graph of <I>.  The remaining figure numbers have therefore
shifted by one.

> 4. In the statement of the conservation law S + I + R = const. it
> should be mentioned that this refers to spatial integrals of the fields.

This is now stated and explained on the right column of page 3.

> 5. I find the concluding statements "Subsequent variations in the number
> of cases and deaths can be explained by variations in the reinfection
> rate....The level of reinfections can easily be fluctuating because of
> seasonal and other effects, which explains the long period of growth with
> piecewise different slopes" a bit vague. According to Fig. 1 and Table 1,
> the prefactor of the growth law has been decreasing systematically since
> day 50. Can the model explain this trend, or not?

To address this point how to explain the systematic decline in the slope,
I now discuss two different possibilities: smaller diffusivities or smaller
reinfection rates. The latter appears to be the more plausible avenue, because
smaller diffusivities would correspond to stronger containment efforts,
which is not what happened. This is now discussed in the new Sect.2.6