20.2 Viruses as Pathogens

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Fig. 20.3 Results from the Markovian realization of the SIRD model. Horizontal axes: iteration

number (number of days elapsed). Green points (colour online), susceptible fraction; red, infected

fraction; blue, recovered fraction; black, dead fraction (in all panels except the lower right, at the

extreme right of the graphs the order of the colours from top to bottom is blue, green, red; the lower

right panel has order green, blue, red). Parameters are given in Table 20.1 (from J.J. Ramsden,

COVID-19. Nanotechnol. Perceptions 16 (2020) 5–15; reproduced with permission)

Table 20.1 Parameters for the SIRD modelSuperscript normal a^a

PositionSuperscript normal b^b

betaβ

rhoρ

muμ

lamdaλ

d Subscript normal infinityd∞

Figure 20.3 UL

0.3

0.1

0.001

0.0

0.008736945

Figure 20.3 UR

0.3

0.1

0.001

0.01

Superscript normal c^c

Figure 20.3 LL

0.3Superscript normal d^d

0.1

0.001

0.0

0.007497489

Figure 20.3 LR

0.3Superscript normal d^d

0.1

0.001

0.0

0.008179990

Superscript normal a Baseline i 0^ai0 was invariably 0.0000015

Superscript normal b^bUR denotes “upper right” etc.

Superscript normal c^cIncreasing linearly by about 330,703 deaths per day in the UK

Superscript normal d^dChanged to 0.1 on day 80

be almost 566,000, or about 0.87% of the UK population (to put this in perspective,

in 2018 there were 616,014 deaths in the UK). Allowing recovery with a probability

lamda equals 0.01λ = 0.01 yields a much higher steady level of susceptible people and a significantly

lower fraction of recovered people. Hence, the infection never completely dies out

and the number of deaths keeps rising—see Table 20.1 for the parameters.

Two important instruments of public health policy are lockdowns and mass vac-

cination. On 24 March 2020 lockdown was enacted in the UK, whereby people

were essentially confined to their homes. At a stroke, the number of daily contacts