




































Ecology, Economy and Society–the INSEE Journal 4 (1): 31–43, January 2021 

 
THEMATIC ESSAY  
 

Mobility Restrictions and the Control of COVID-19 
 

Charles Perrings and Baltazar Espinoza  
 
Abstract: A recent study on the impact of mobility controls on the final size of 
epidemics by Espinoza, Castillo-Chavez, and Perrings (2020) found that mobility 
restrictions between areas experiencing different levels of disease risk and with 
different public health infrastructures do not always reduce the final epidemic size. 
Indeed, restrictions on the mobility of people from high-risk to low-risk areas can 
increase, not reduce, the total number of infections. Since the first response of 
many countries to the COVID-19 pandemic was to implement mobility 
restrictions, it is worth bearing in mind the implications of the Espinoza result 
when considering the effectiveness of such restrictions. 

Keywords: Mobility Restrictions; COVID 19; Diseases Risk; Health Infrastructure. 

 

1. INTRODUCTION 

Most governments‘ first response to the COVID-19 pandemic was to 
introduce mobility restrictions. These took many forms, spanning selective 
restrictions on national and international travel and trade; closure of 
schools, museums, and cultural and social centres; restrictions on non-
essential local travel; local stay-at-home orders; and area quarantines. By the 
end of May 2020, 220 countries had imposed a total of over 62,000 
restrictions on international travel (International Organization for Migration 
2020). As a result, trade in services involving proximity between suppliers 
and consumers, especially services involving travel or the temporary 
movement of people, has since been ‗paralyzed‘ (World Trade Organization 

                                                        
 School of Life Sciences, Arizona State University, P.O. Box 874501, Tempe, AZ 85287-

4501, USA; Charles.Perrings@asu.edu.  

 Biocomplexity Institute and Initiave, University of Virginia, P.O. Box 400298, 
Charlottesville, VA 22904-4298, USA; baltazar.espinoza@virginia.edu. 

Copyright © Perrings and Espinoza 2021. Released under Creative Commons Attribution-
NonCommercial 4.0 International licence (CC BY-NC 4.0) by the author.  

Published by Indian Society for Ecological Economics (INSEE), c/o Institute of Economic 
Growth, University Enclave, North Campus, Delhi 110007.  

ISSN: 2581-6152 (print); 2581-6101 (web). 

DOI: https://doi.org/10.37773/ees.v4i1.344  

https://doi.org/10.37773/ees.v4i1.344


Ecology, Economy and Society–the INSEE Journal [32] 

2020a). Internally, public curfews, domestic travel restrictions, and 
lockdowns of varying severity have had similar effects.  

A recently published paper by Espinoza, Castillo-Chavez, and Perrings 
(2020) analysed the effectiveness of mobility restrictions in controlling 
infectious diseases such as COVID-19. The paper particularly considered 
the impact of mobility restrictions between areas experiencing different 
levels of infection risk and having different access to healthcare. The main 
result reported in the paper (hereafter ‗the Espinoza result‘) was that 
mobility restrictions between low- and high-risk areas do not always reduce 
the final epidemic size. Indeed, in some cases, restrictions can have the 
opposite effect. Restricting people in high-risk areas from moving to low-
risk areas can increase, not reduce, the total number of infections. In some 
cases, allowing mobility out of high-risk areas can be sufficient to control an 
outbreak. In this paper, we discuss the implications of the Espinoza result 
for the effectiveness of COVID-19 disease control. 

The problem modelled by Espinoza, Castillo-Chavez, and Perrings (2020) is 
one in which mobility restrictions limit movement between areas that differ 
not just in the level of infection risk but also in their capacity to treat those 
who are infected. It is assumed that the low- and high-risk areas are 
distinguished by differences in income, nutrition, health status, and health 
infrastructure. It follows that they will also differ in terms of outcomes 
associated with the same number of cases. While theoretical studies on the 
impact of mobility restrictions on epidemiological dynamics in a multi-
patch system suggest little impact on the final epidemic size if restrictions 
permit some movement between patches (Arino et al. 2007), the Espinoza 
result finds that restrictions on movement between high- and low-risk areas 
can have a substantial impact on both the area-specific and global final 
epidemic size.  

In all recent epidemics affecting multiple countries—the 2003 SARS 
epidemic, the 2009 H1N1 influenza pandemic, and the 2014 Ebola 
epidemic—the speed, direction, and extent of spread of the disease were 
determined by pre-existing patterns of trade and travel. These patterns 
determined both the routes along which the disease spread and the 
frequency with which it was introduced (Sirkeci and Yucesahin 2020). In all 
cases, the response to the outbreak included travel restrictions, international 
border closures, and area quarantines (cordons sanitaires). Broadly similar 
measures have been deployed in the management of infectious diseases for 
hundreds of years (McNeill 1977; McNeill 2003). 

The motivation for the study by Espinoza, Castillo-Chavez, and Perrings 
(2020) was evidence that mobility restrictions have not always succeeded in 



[33] Charles Perrings and Baltazar Espinoza 

controlling the size of epidemics. In the 2014 Ebola epidemic, for example, 
quarantining an area that later contained about 70% of all cases led to a 
perfect storm within the area. Food supply was disrupted, the healthcare 
system was overwhelmed, infection risk increased, and both, the number of 
cases and the case mortality rate, increased over time. The final epidemic 
size—around 29,000 cases leading to around 11,000 deaths—was larger 
than it would have been with no quarantine (Towers et al. 2014; Castillo-
Chavez et al. 2015; Espinoza et al. 2016). In the following sections, we first 
summarize the Espinoza result and then consider the implications it has for 
the spread of COVID-19 and for the wellbeing of people in regions with 
varying degrees of development. 

 

2. A MODEL OF MOBILITY RESTRICTIONS AND DISEASE 
DYNAMICS 

The model developed by Espinoza, Castillo-Chavez, and Perrings (2020) 
describes infectious disease transmission between two communities 
connected through the movement of people. Specifically, it models the time 
spent by individuals in each community using a residency time matrix. In a 
two-community world, time not spent in one community is assumed to be 
spent in the other community. Individuals either spend all of their time in a 
single community or they divide their time between two communities. Their 
location is tracked over time, making it possible to understand the impact 
of mobility and mobility restrictions on disease dynamics in each 
community and on a global scale (Bichara  et al. 2015). The risk of infection 
in a given community is assumed to be proportional to the time spent there, 
weighted by a community-specific infection likelihood. This makes it 
possible to model the impact of mobility restrictions on disease dynamics in 
communities. The model is parameterized for COVID-19.  

Intuitively, one would expect people‘s mobility away from the outbreak 
location to increase both the rate at which the disease is spread and the final 
epidemic size. What the Espinoza result shows, however, is that if the two 
communities differ in population density, disease risk, and standards of 
healthcare, outcomes may be quite different. Specifically, if infected 
individuals in a high disease risk community move to a less densely 
populated region with better sanitary conditions, then the increase in the 
number of secondary infections in that region may be offset by the 
reduction in the number of secondary infections in the high-risk 
community. 

 



Ecology, Economy and Society–the INSEE Journal [34] 

The dynamics of COVID-19 in two communities with distinct infection 
risks is described by the following system of differential equations: 


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jjii

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11

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iii I)(EI  1
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iii J)(IJ  2
  

iii JIR 21   

  ji,,j,i  21  

For the thi community, the compartments comprise susceptible, iS , 

exposed and potentially infectious, iE , symptomatic infectious and 

undiagnosed individuals, iI ; diagnosed cases, iJ ; and recovered individuals, 

iR . Individuals move between compartments, depending upon: i , the 

community-specific transmission rate per day;  , the progression rate to 
symptomatic infectious;  , the progression rate from infectious to 

quarantine; 1 , the infectious individuals‘ recovery rate; 2 , the diagnosed 

individuals‘ recovery rate; q , the reduced infectiousness of the exposed 

class; l , the reduced infectiousness of diagnosed cases; and,  , the 
COVID-19-induced mortality rate per day. Transmission rates in the 

thi community are weighted by the average proportion of time spent in that 

community, and it  refers to residency time in the community.  

It is assumed that different conditions in the two communities drive 
differences in the community-specific values of the basic reproduction 

number, 0R . For the case where the disease dies out in the low-risk 

community (when the 0R for that community is less than one), the 

Espinoza result shows that strong mobility restrictions can increase the final 
global epidemic size while weak restrictions can reduce it.  

To illustrate this result, Figure 1 shows the community-specific and global 

final epidemic sizes, measured on the y axis, as functions of the average 

proportion of time that people from the high-risk community spend in the 

low-risk community, denoted by 1t and measured on the x axis. The first 



[35] Charles Perrings and Baltazar Espinoza 

threshold, 1



t , reflects the trade-off involved in mobility from the high-risk 
to the low-risk community—the reduction in the number of secondary 
infections in the high-risk community against the increase in the number of 

secondary infections in the low-risk community. The second threshold, 1



t , 
gives the level of mobility between the high-risk and low-risk communities 
required for the global basic reproduction number to fall below 1. 
Espinoza, Castillo-Chavez, and Perrings (2020) then test the sensitivity of 
this result to variations in population density ratios and community-specific 
risks of infection. 

Figure 1: Patch-specific, global final size in the presence of mobility 

 

Source: Espinoza, Castillo-Chavez, and Perrings (2020) 

Figure 1 shows the community-specific and total final epidemic size with 

unidirectional mobility from the high-risk community, 1t ( 2t = 0). The 

thresholds 1



t  and 1



t denote the level of mobility required to reduce the 
total final epidemic size below that reached by applying the most extreme 
mobility restrictions (area quarantine), and the level of mobility needed to 
control a disease outbreak in the whole system, respectively. 

 

3. COVID-19 AND THE 2020 RECESSION 

Estimating the cost of disease control measures is complicated by the fact 
that the pandemic coincided with an expected downturn in the economy. 
COVID-19 proved to be the trigger for a widely anticipated recession, 
making it hard to identify the excess costs due to disease control measures. 



Ecology, Economy and Society–the INSEE Journal [36] 

In mid-April 2020, the International Monetary Fund (IMF) estimated that 
government measures to sustain economic activity amounted to USD 3.3 
trillion and that loans, equity injections, and guarantees totalled an 
additional USD 4.5 trillion—most of which were at least formally tied to 
COVID-19. They projected the increase in public-sector borrowing to 
finance this to be equal to 6.2% of the global gross domestic product 
(GDP). In the US, the IMF expects the fiscal balance to GDP ratio to rise 
from 5.8% in 2019 to 15.7% in 2020. France, Germany, Italy, Japan, and 
the United Kingdom all have public sector support measures exceeding 
10% of their GDPs (International Monetary Fund 2020). In terms of GDP 
growth, the IMF‘s April 2020 estimate was that the global economy would 
decline by 3.0% in 2020 but that the impact would be significantly different 
for developed (-6.1%) and developing economies (-1.0%) (Table 1).  

Table 1: Projected Change in World GDP 

 
2019 2020 (Projected) 

World  2.9  –3.0  

Advanced economies  1.7  –6.1  

United States  2.3  –5.9  

Euro Area  1.2  –7.5  

Japan  0.7  –5.2  

Other advanced economies  1.6  –5.2  

Emerging market and developing economies  3.7  –1.0  

Regional groups  
  Emerging and developing Asia  5.5  1.0  

Emerging and developing Europe  2.1  –5.2  

Latin America and the Caribbean  0.1  –5.2  

Middle East and Central Asia  1.2  –2.8  

Sub-Saharan Africa  3.1  –1.6  

Source: International Monetary Fund (2020) 

In terms of trade, a similarly timed estimate by the World Trade 
Organization (WTO) was that the decline in world merchandise trade 
would be between 12.9% and 31.9% in 2020 (Table 2).  

In these projections, the differences between developed and developing 
economies are less pronounced. World trade was already declining in 2019, 
and this was expected to become worse in 2020. Detecting the impact of 
the COVID-19 response in the data is hard. Mobility restrictions primarily 
affect trade in services, which are not included in merchandise trade. 
However, the WTO makes the point that there are tight connections 
between trade in goods and trade in services (since transport is a service). 
They also note that there are no inventories of services. It is not possible to 



[37] Charles Perrings and Baltazar Espinoza 

draw down on a service in one year and restock it in another. The 
implication is that any decline in services in 2020 cannot be recouped later 
(World Trade Organization 2020b).  

Table 2: Projected Change in World Merchandise Trade 

  

Optimistic 
Scenario 

Pessimistic 
Scenario 

 
2019 2020 2020 

Volume of world merchandise trade  -0.01 -12.9 -31.9 

Exports 
   North America 1 -17.1 -40.9 

South and Central America  -2.2 -12.9 -31.3 

Europe 0.1 -12.2 -32.8 

Asia 0.9 -13.5 -36.2 

Other regions -2.9 -8.0 -8.0 

Imports 
   North America -0.4 -14.5 -33.8 

South and Central America  -2.1 -22.2 -43.8 

Europe 0.5 -10.3 -28.9 

Asia  -0.6 -11.8 -31.5 

Other regions 1.5 -10.0 -22.6 

Source: World Trade Organization (2020b) 

Note: Other regions comprise Africa, Middle East, and Commonwealth of 
Independent States (CIS) including associate and former member states. 

In the case of COVID-19, the social cost of the disease includes the cost of 
the morbidity and mortality it induces along with the cost of treatment. The 
social cost of disease control includes all direct and indirect consequences 
of disruptions to trade and travel, social distancing, industry closures, 
domestic market restrictions, and financial measures to compensate firms 
and households for the effect of such restrictions. Backward and forward 
supply chain linkages mean that disease control measures in one location 
have consequences for employment and output elsewhere. Just as private 
contact decisions may generate external effects, so also disease control 
measures may have external consequences for both disease transmission 
and economic disruption elsewhere in the trade network. 

 

 

 

 



Ecology, Economy and Society–the INSEE Journal [38] 

4. IMPLICATIONS FOR EFFICIENCY 

While the result reported in Espinoza is strictly epidemiological, in that it 
concerns the impact of mobility restrictions on the final size of the 
epidemic only, it does have implications for the efficiency of mobility 
restrictions as a disease control measure. First, trade and travel decisions 
both affect disease transmission through their effects on contact between 
infectious and susceptible individuals (Jones  et al. 2008; Daszak 2012). For 
private individuals, the potential disease risks of contact are included in the 
costs of both trade and travel decisions and are weighed against the benefits 
of those decisions. Disease dynamics are thus sensitive both to the cost of 
disease and the cost of disease avoidance (the forgone benefits of contact). 
If the cost of disease is low, there is little incentive to avoid it. If the cost of 
disease is high, people will do more to avoid it. Understanding the trade-
offs involved can therefore strengthen our capacity to predict disease 
dynamics (Fenichel et al. 2011).  

At the same time, unless private individuals confront the full social cost of 
their actions, the level of disease avoidance may be less than socially 
optimal. This is the motivation for interventions designed to limit contact—
for example, mobility restrictions and social distancing measures. The test 
for whether such interventions are socially efficient is whether they 
minimize the social cost of disease and disease control. If the health 
authorities implementing disease control measures neglect the cost of those 
measures for people elsewhere, their actions are unlikely to be cost-
minimizing (Perrings et al. 2014).  

The Espinoza result assumes that the public health authority responsible 
for imposing mobility restrictions weighs disease prevalence in each 
community equally. If we do not consider the economic costs of disease 
control, it then follows that mobility restrictions should be increased up to 
the point that the global final epidemic size is minimized. The reason that 
mobility restrictions fail to minimize the global epidemic size is that 
individual communities generally place a greater weight on containing their 
own risk than on reducing risk overall. They focus on community-specific 
epidemic size rather than the global epidemic size. Multiple public health 
authorities, each representing a different community or a different 
jurisdiction, have little incentive to coordinate their responses to the 
pandemic to assure the lowest global epidemic size (Espinoza et al. 2020). 

Including the economic cost of disease control complicates the calculus. In 
the current COVID-19 pandemic, most disease control interventions are 
made at the national level. Indeed, efforts to coordinate control 
interventions across nation states have been frustrated by efforts to weaken 



[39] Charles Perrings and Baltazar Espinoza 

the World Health Organization. In several countries, control has devolved 
to even lower levels. In the US, for example, most disease control measures 
have devolved to individual states, while some measures have devolved to 
individual counties or cities. While it may be motivated by the subsidiarity 
principle, the devolution of disease control to local authorities is 
problematic when the consequences of control are realized over a much 
wider area. For the individual authority, the incentive is to increase disease 
control up to the point where only the local costs of disease and disease 
control are minimized irrespective of global costs. If this results in higher 
overall costs than could be achieved through a cooperative approach, the 
outcome is socially inefficient.  

For any given public health authority, their actions involve two possible 
sources of inefficiency. First, the adoption of specific disease control 
measures in one location may have a direct impact on both morbidity and 
mortality in other locations, but this impact may be ignored. The Espinoza 
result described above indicates why. Second, disease control measures that 
affect either labour or transport potentially have effects either up or down 
the supply chain, and these effects may occur at a distance from the place 
where the measures are enforced. A recent study on the short-term 
economic impacts of sector-specific transport and labour supply constraints 
imposed in response to the COVID-19 pandemic found that even countries 
that are not directly affected by the virus would face large losses (greater 
than 20% of their GDP) due to the disruption of supply chains. They also 
found that low- and middle-income countries are more vulnerable to supply 
chain-mediated effects than high-income countries (Guan et al. 2020). 

 

5. IMPLICATIONS FOR EQUITY 

An additional issue with a public health control strategy that privileges 
individual communities is that the outcome may not only be inefficient 
from a social perspective, it may also be inequitable. In the long history of 
area quarantines, the question of whether quarantining people is ethical 
and/or equitable has seldom been raised. In the COVID-19 pandemic, 
however, the question is being discussed in ways not been seen before. 
Countries have different approaches to it. In China, the imposition of a 
cordon sanitaire around Wuhan, the epicentre of the pandemic, was not 
questioned. In the US, by contrast, much milder social distancing measures 
that limit the behaviour of individuals have been challenged as a violation 
of individual rights.  

Because mobility restrictions differentially affect the health and welfare of 
those who are restricted and those who are not, they have distributional 



Ecology, Economy and Society–the INSEE Journal [40] 

implications. The Espinoza result implies that the people who are 
constrained to remain in high-risk areas face an increased risk to their 
health. If they also face increased losses due to the disruption of supply 
chains, lost access to product or labour markets, the collapse of public 
services, and so on, they are twice harmed. The evidence currently suggests 
that low-income countries, and low-income communities within developed 
countries, are most affected by the disease. This is in part due to the state of 
their public health infrastructures. Limited healthcare personnel (especially 
anaesthesiologists), hospital beds, intensive care units, oxygen, ventilators, 
infusion pumps, and even water and power supply mean that low-income 
countries have a more limited capacity to handle a large number of cases 
compared to high-income countries (see, for example, Sonenthal  et al. 
2020). This is partially because most surgeries are urgent and non-elective 
(such as caesarean deliveries). They cannot be postponed (Bong et al. 2020). 
But it is also because people with low incomes have fewer options to avoid 
infection, whether by changing work habits, social distancing, or moving to 
safer environments.  

In New York, the city most affected by the pandemic in the US, evidence 
indicates (a) that residents from high-income neighbourhoods were more 
likely to move away from the city than residents from low-income 
neighbourhoods, (b) that residents in low-income Black and Hispanic 
neighbourhoods exhibit the most high-risk work activity during working 
hours, and (c) these residents are least likely to ‗shelter in place‘ outside of 
working hours (Coven and Gupta 2020). The evidence also indicates that 
COVID controls affect women more than men. The closure of schools and 
day-care centres has impacted child care and hence working mothers (Alon 
et al. 2020). In East and South East Asia, travel restrictions have restricted 
the availability of employment for female foreign domestic workers 
traveling between the Philippines, Indonesia, Hong Kong, and Singapore 
(Wenham, Smith, and Morgan 2020). 

The central point here is that mobility restrictions evidently limit the 
capacity of those in less safe environments to move to more safe 
environments, whether within a country or between countries. This raises 
the cost of disease in less safe environments and lowers it in more safe 
environments. Just as this has implications for epidemiology, so does it 
have implications for equity.  

 

 

 



[41] Charles Perrings and Baltazar Espinoza 

6. CONCLUDING REMARKS 

The emergence of COVID-19 shares many similarities with the emergence 
of other novel zoonotic diseases over the last 50 years. The first appearance 
of the disease in the wet markets of Wuhan mirrors the first appearance of 
many other emerging zoonoses. An interface between humans and wildlife 
at forest margins is the likely origin of the disease, and local markets for 
wildlife products are the likely mechanisms for transmission from the forest 
margin to the urban centre. As with other emerging zoonoses, its 
transmission from one country to another was due to patterns of travel and 
trade. Where it differs from other recently emerged zoonoses is in the 
characteristics that make it especially difficult to contain—the high 
proportion of people infected who are asymptomatic but infectious. In 
these circumstances, mobility restrictions appear to be an effective means of 
slowing spread between communities, although a recent study concluded 
that airline travel restrictions would not have been sufficient to prevent the 
spread of the virus (Shi et al. 2020).  

What makes the Espinoza result interesting is that the same mobility 
restrictions can, conversely, increase transmission within restricted 
communities. When communities are differentiated in terms of population 
density, health infrastructure, and the resources that susceptible individuals 
have to avoid infection, restrictions that limit the capacity of people in high-
risk areas to leave can lead to higher rates of infection in those areas. Not 
only does this increase the number of cases in high-risk communities, but it 
also increases the probability that health infrastructures will fail, that case 
mortality rates will rise, and that the disease will not be contained. Aside 
from the ethical issues this raises, it also risks prolonging the pandemic. 
Despite the lack of a coordinated response to COVID-19, it is still an 
infectious disease and its control is still a public good of a very particular 
kind. As with other infectious diseases, control of COVID-19 is a weakest 
link public good (Sandler 2004). The benefits of disease control to all are, 
ultimately, only as effective as the benefits of disease control offered by the 
least effective provider. As long as there are any countries where public 
health authorities are unable to contain the disease, no country is safe.  

An immediate implication of this is that the interests of all are best served 
by strengthening the capacity of the weakest links in the chain. As it 
happens, we have seen resources being diverted away both from health-
oriented development assistance and from intergovernmental organizations 
set up to protect global interests. Indeed, the US has announced its 
intention to withdraw from the World Health Organization at the very 
moment it is most needed. We have also seen the use of mobility 
restrictions that are certain to increase the stress on already stretched health 



Ecology, Economy and Society–the INSEE Journal [42] 

infrastructures in low-income countries. There is certainly scope for 
collaborative action within the Global South to fill the void, but there is 
also little clear indication that this will happen.  

 

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