**2. Model and methods**

We use a deterministic model of ordinary differential equations (ODE):

$$\frac{d\mathbb{S}}{dt} = -\beta(\mathbb{1} - \mathbb{x})(A + I)\text{ S} \tag{1}$$

$$\frac{dE}{dt} = \beta(\mathbf{1} - \mathbf{x})(A + I)\,\,\mathbf{S} - aE \tag{2}$$

$$\frac{dA}{dt} = a(\mathbf{1} - p)E - \mu\_A A \tag{3}$$

$$\frac{dI}{dt} = apE - \mu\_I I - \mu\_H I - \mu\_D I \tag{4}$$

$$\frac{dH}{dt} = \mu\_H \left[ 1 - \mu\_R \left| H - \mu\_D \right| H \right] \tag{5}$$

$$\frac{dD}{dt} = \mu\_D \, I + \mu\_D \, H \tag{6}$$

$$\frac{dR}{dt} = \mu\_A A + \mu\_I I + \mu\_R H \tag{7}$$

$$\frac{d\mathbf{x}}{dt} = r\mathbf{x}(\mathbf{1} - \mathbf{x})(c\_1 I + c\_2 D - c\_3(K\_0 - k)/K\_0)) - \xi\,\mathbf{x} \tag{8}$$

$$\frac{dk}{dt} = \sigma \left( (\mathbf{S} + A + R)((\mathbf{1} - \mathbf{x}) + q\mathbf{x}) \right)^{\gamma} k^{1-\gamma} - \delta k - c\_h H, \mathbf{0} < q < \mathbf{1}.\tag{9}$$

with seven states/compartments: susceptible (*S*), exposed but not infectious (*E*), infected but asymptomatic (*A*), infected and symptomatic (*I*), isolated or hospitalized (*H*), dead (*D*), and recovered (*R*) (see **Figure 4**). The same letters (*S, E, A, I, H, R,* and *D*) are used notations for the variables that represent the proportion of individuals in each compartment. In this model, the effective transmission rate *β*ð Þ 1 � *x* is dependent on the proportion practicing social isolation *x* whose complement modulates the disease transmission rate *β*. See **Table 1** for definitions of parameters and their values.

We also use a population behavior dynamical Eq. (8) to model the dynamical changes of *x* in which people abiding to social isolation compare the risks of infection and fear of death to the relative economic loss. They can also break out of isolation after an average of 1/*ξ* days due to fatigue from social isolation. We postulate that the rate of fatigue *ξ* is dependent on the six cultural dimensions of Hofstede (see **Figure 1**); especially, individualism, long-term orientation, and indulgence. The constants *c*1, *c*2, and *c*<sup>3</sup> reflect also perceptions of risk of infection, fear of death and degree of damage due to the relative drop in GDP. Those factors are also related to cultural, social, and economical characteristics of the society. For instance, the perception of risk of infection might be related to uncertainty

#### **Figure 4.**

*Schematic illustration of the COVID-19 SEAIHRD model showing the force of infection β*ð Þ 1 � *x* ð Þ *A* þ *I . Parameters α, μA, μI*, *μH*, *μ<sup>R</sup> and μ<sup>D</sup> are the rates of transition between the compartments. The fraction p is the probability of becoming symptomatic and infectious. The proportion of those who choose to maintain the social isolation is given by x. The pandemic fatigue rate is ξ.*


#### **Table 1.**

*Parameters, their definitions, values and references.*

avoidance, whereas the economic damage might be related to long-term orientation, masculinity, and socioeconomic status.

The population economic growth/decline is modeled using the Solow economic model of the per-capita GDP (*k* ¼ *GDP=N*) in \$1000 with Cobb–Douglas functional form of investment and production. We assume an initial per-capita GDP of *K*0. The per-capita GDP suffers from lack of labor due to isolation except for a fraction *q* who are working from home. Also, it decreases due to the hospitalization burden that costs *ch* per patient-day.

*Human Cultural Dimensions and Behavior during COVID-19 Can Lead to Policy Resistance… DOI: http://dx.doi.org/10.5772/intechopen.96689*

We use the method of Next-generation matrix [40] to find the basic reproduction number *R*<sup>0</sup> for the disease model without social isolation (in the beginning of the epidemic). The basic reproduction number is given by

$$R\_0 = \beta \left[ \frac{1 - p}{\mu\_A} + \frac{p}{\mu\_I + \mu\_H + \mu\_D} \right]. \tag{10}$$

We use this formula for the basic reproduction number to calibrate some of the disease model's parameters at *R*<sup>0</sup> ¼ 2*:*5 [41].
