The post-Covid-19 era requires maximum urban resilience

This paper reviews the low-resilience problem in many cities, poor designs of cities to cope with disasters, and the need for tolerance of urban constructions. It explores answers concerning the question of how shall we build cities resiliently? The method of this applied research is a multiphase process that considers all physical and socioeconomic elements of a city. It introduces six indicator groups of urban management (M), economy (E), built environments (U), Infrastructures (I), natural environments (N), and health protection (H). The groups include 55 indicators as variables in the mathematical calculations in this paper. This paper builds a mathematical model to maximize the profitability of resilient buildings by optimizing investments in the required projects. The projects will upgrade the firmness and tolerance of cities against nature-based and human-made dangers and risks. There is linear programming in 55 variables to select optimal solutions from fifty-five factorial alternatives. Then, the programming will develop into non-linear programming. The unique innovation of this paper is its linear programming interpretation by non-linear to give optimal solutions for the problem. Applying the Lagrange function in the Kuhn-Tucker conditions proves the accuracy of the hypothesis that post-COVID urbanization requires maximum resilience. Only in this way, the urban economies will be free of risks. Outcomes in this paper will assist in the pre-planning, design, and building of built environments everywhere resilient and sustainable.


Introduction
The economic, social, technological, and political systems of cities are intertwined with radical changes (Ye et al., 2017). The history of human life reveals cities, which have been destroyed completely or partially by natural disasters, epidemics, and wars. In contrast, many cities demonstrated an astounding resilience by preparation for response to and recovering from natural and conflict disasters. For some time now, modern urbanization has realized that we must make cities resilient to threats and risks (Vale & Campanella, 2005, Timmerman, One major topic in urban resilience studies is the contradictory urban processes of growth and shrinkage that constitute the overall pattern of growing urbanization worldwide. Multiple functions of urban vacant land have been rudimentary and subjective (Song et al., 2020).
The necessity of strengthening cities exists when the COVID-19 global disaster devastates all communities economically and biotic. The need to redesign cities exists when the Coronavirus attack all communities economically and biotic. The pandemic revealed the need for urban spaces with different sizes and fewer crowds. The COVID-19 required new architectural and building standards and regulations.
We are aware of the danger is not only the killer viruses but also climate change. Floods, flu, animal diseases, locust infestations on farms and groves, sheltering farmers and ranchers in dilapidated cities, and those displaced by the urban economic network are natural or social crises. When faced with these threats, we need a new model for future planning and the physical planning of cities. We shall find new ways to protect urbanization against all possible present and coming threats. Therefore, we ought to find answers to the following question: Who shall we plan and design cities better to help people cope with disasters, shocks, and risks? In other words, what projects shall we plan and implement to construct a resilient city?
This research increases the measurable ability of the urban system and its inhabitants to maintain a continuous life and safe, comfortable, and fair activities against all-natural or human-made shocks and pressures. Therefore, a city will be resilient when urban management has conducted the necessary assessment, planning, and measures to prevent, prepare and respond to natural, human-made, sudden, gradual, and unexpected hazards.
Every city must be strong enough and flexible to protect and strengthen inhabitants' lives.
Engineers shall use structural systems and building materials to meet the maximum stress tolerance.
Our research methods to achieve the goal are both theoretical and workshops. We review the ideas of scholars and the experiences of pragmatic engineers on building cities resilient and sustainable. Simultaneously, this research is an experimental study, and we benefit from our tests in urban planning and development workshops. From a practical perspective, we introduce indicators to assess the degree of resilience of cities. The indicator groups lead the city and setting its strategic goals concerning urban society and economy, urban built environment and infrastructure, the natural environment and hygiene, and citizens' health protection.
Outcomes of this research in the shape of a feasible model assist relevant actors in building cities resiliently.

Methods and materials
We rebuild a city resiliently in the process. The first step in the process is to clarify the current situation in rigidity and decision making. At this stage, we introduce some indicators to identify the risks, shocks, and disasters that threaten the city. The second step is to determine an optimal resilience situation that the city wants to achieve. The third step is to explain how it achieves that vision of resistance. This step requires definition, planning, and implementation of projects, which we shall perform. The scope of our field study is global, as the epidemic of Covis-19 disease swept across the globe, and all cities more or less acknowledged the need for sustainability. Scientists have developed indicators to measure the resilience of cities to disasters. But as many experts declared, and in our opinion, those indicators did not cover all aspects of a city (Tan et al., 2017, Gutter, 2016and Copeland, 2020. Using the opinions of scholars and scientists by structural interviews and our field and workshop experiences, we extract indicators to guide our measurement and practice in the three steps of this process. Table 1 introduces indicators that assist us in measuring the rate of the resilience of a given city. linear plan and determine the amount of investment in each indicator group to achieve the best economic profit by the maximum resilience of the city. By setting strategic policies for the socio-economic and physical development of the city, we will illustrate a model that makes the city resilient. The work is possible with classic methods, experiments, and forecasting techniques to picture the future.
We build a general mathematical program to show the resilient model every city will apply to respect its particular characteristics.
Our mathematical model begins with an allocation method that is a linear programming technique for determining an optimal allocation of funds. This technique is an optimal allocation schedule. With this simple linear programming technique, we improve n indicators by one of the n projects. Each project is for only one indicator. We exhibit the condition results in a square matrix, where the number of projects and indicators is equal. The above square matrix has eleven columns and rows. The first left side column shows the M i group of indicators. Other columns exhibit alternative investment amounts in projects to upgrade the resiliently of the city. For example cell of F 11 $ shows the amount of investment in the project related to the indicator of 'Selecting competent, qualified, and specialized managers to lead the city', M 1 . Similarly, the cell of F 1111 $ is the investment in projects on the 'Transparent and comprehensive processes for approving urban programs', M 11 . This matrix with 11indicators and 11 alternatives of project investment has 11!equal to 39916800 solutions. For determining optimal investment in projects of M i group indicators, we try all 39916800 possibilities and select the best for every project to meet maximal urban resilience.
Here, we are writing our simplex method for the solution of the matrix.
Therefore, we set up a matrix for all indicators in (7) to be upgraded and suitable for a resilient city. In equation (7), our variables are unstable, which varies in different situations.
We have 55 indicators in Table 4. In the above matrix, 55! solutions exist, but we find only 55 optimal investments in the projects related to the improvement of 55 indicators.
From We have quantified our parameters in terms of monetary gain for the city through its resilience. In objective equation of (8) Pr ofit R is the profit caused by resilient building of a given city per $ and OPI is the optimal projects' investment to improve the indicators. In maximization equation (8): 1≤i and j≤55.
In the third step, to achieve the maximum profit produced by making the city resilient, it is necessary to prepare a comprehensive program that includes projects to improve the indicators. The program with underlying projects brings the city to its goal of maximum resilience and economic benefits.

Experiences and results
We experienced many cities in the world are unable to protect their residents from potential risks such as flood, earthquake, tsunami, sandstorm, drought, famine, etc. (Shahraki, 2020, World Health Organization, 2017, and Siegel, 2018. Most of the world's inhabitants are now defenceless even against predictable events such as rain, sandstorms, cold and extreme heat.
The goal of resilience in the city is to protect it against such threats.
In the first step, we shall clarify the current situation and recognize the shocks and disasters that threaten it. For this reason, we analyze the components of each city. The following are generic elements of a city:  Built environments, including the skeleton and physics of the city, in terms of quantitative and qualitative standards applied in homes and urban spaces.  An economy includes the diversity of economic sectors and stability and efficient marketing. Additionally, the development of unique capacities of the city and emphasis on strengthening its economic potentials is a way to sustainable development.
Knowing the physical and characteristics of every city is possible with field research tools.
Case studies and experiences assist us in risks, shocks, and disasters that threaten the city. Table 5 shows some dangers that threaten cities.

Name of risks Line
Failure consequences of macro-socio-economic programs. 1 Consequences of non-realized urban development prediction and national plans of previous decades. 2 The migration of unemployed farmer migration. Similarly, the fisher moved to the city that increases the residential density. 3 The collapse of the labor market, the increase in unemployment, and the homeless phenomenon resulted in social unrest.

4
The problem caused by an unlicensed population and children in war-torn cities. 5 The growing crisis of the expansion of suburban areas in cities 6 Crisis of expansion of worn-out areas of cities 7 An increasing number of people are losing their homes in the current economic crisis. 8 The crisis of poor, unemployed, and oppressed women 9 The growing crisis of working and sexually abused children 10 The crisis caused by climate change and the expansion of unsuitable constructions with the climate of the city 11 Drought crisis 12 Danger of sudden and devastating floods 13 Tsunami risk 14 Risk of volcanic activity overlooking the city 15 Risk of collapse of unstable and nonresistant buildings 16 Risk of landslides and landslides and slopes and landslides 17 Earthquake risk 18 Risk of sandstorm attacks 19 The danger of disconnection of unstable water sources that comes from a distance 20 Industrial, hospitals, and household sewage flows and surface water in the city that help spread infectious diseases.

21
Risk of interruption of transport networks and suburban traffic 22 The problem of the narrowness of passages, stations, and offices of transportation and traffic and high population density in these places

23
The problem of interruption in electronic communications and telecommunications due to their inefficiency or the decisions of the rulers of the countries 24 Risks of shortage and improper distribution of fossil fuels such as oil, gas, diesel, and gasoline 25 Risks of power outages 26 Risk of epidemic diseases in the city 27 Lack of hospitals, clinics, laboratories, nurses and doctors 28 Risk of epidemic diseases in livestock and poultry 29 Lack of veterinarian and equipment and medicines for livestock 30 Risk of epidemic diseases in plants and trees and lack of pesticides 31 The danger of locust infestation, and pests. Lack of aircraft and spraying equipment. 32 Risks of food shortages and famines and food insecurity 33 Shocks by military action, war, and the lack of any shelter for civilians. 34 Lack of adequate firefighting equipment and assistance to the injured 35 Short knowledge, technologies, and machinery to fight natural disasters 36 Poor regional and interregional collaboration networks with peripheral cities 37 Characteristics of cities based on our observation and experiences prove the existence of risks listed in Table 5. During recent decades, cities have experienced numerous economic, demographic, social, cultural, climate, physical, environmental, and exosystemic changes. Table 5 shows the changes that risks make in cities. The increase in the population of cities has caused the need for more urban spaces and streets, and passages. In densely populated cities, people are now fleeing from each other and distance themselves physically from others to escape the coronavirus, but to no avail. All bus stops, trains, and vehicles are crowded.
In parallel, the physical expansion of cities destroyed their natural and organic systems.
Research shows that the Coronavirus has lived in the glaciers located in the poles for billions of years (Taillant, 2021). But by destroying the environment and melting glaciers, humans destroyed the invasive viruses and brought it into his life (Kumar et al., 2021 andEpstein &Mills, 2005). Some scholars highlighted the risks associated with viruses hidden in permafrost, and the risks arising out of ecological destruction (Dash et al., 2021).
The destruction of ecosystems by increasing urbanization is not the only current problem, but also the increasing populations in cities reduces vegetation and increases carbon, waste and sewage production, and soil erosion. Poor inhabitants spread infectious viruses through running sewers ( Shahraki, 2021). COVID-19's one-year experience revealed that cities were helpless against the coronavirus despite their arrogant medical and pharmaceutical advances over the centuries. Hospitals do not have enough space for patients and medical facilities. We agree with Narwhal & Jain that recently said "Build resilient health systems" (Narwal & Jain, 2021). We observed the relationship between individuals and general health indices with environmental and ecosystem factors. Other experiences show the same relationship as Mapar et al., who wrote "The results showed that safety theme and environmental themes are important in the municipal sustainability performance" (Mapar et al., 2020).

The second step determines what model of resilience is pertinent to the city.
We suggested the resilience model by setting strategic policies for economic, social, and physical development with classic and experienced models of forecasting and scenarios. We are aware that cities are complex and dynamic systems. They operate to link the natural and built environments with human processes. Therefore, the suggested mode to make cities resilient is complex.
By learning from the experiences and knowledge of a given city, we plan and design it resiliently. The World Health Organization has particular urban settings in health, social services, transport, housing and energy, education, water supply, and distribution, etc. The settings prepare cities against COVID-19 (World Health Organization, 2020). The United Nations Office for Disaster Risk Reduction, UNDRR, with lessons learned from the hurt cities, suggested ten essentials for making cities resilient (Schofield & Twigg, 2019). They organize disaster resilience, identifying, understanding, and using current and future risk scenarios. They recommended financial capacity for resilience, pursue resilient urban development and design, and safeguard natural buffers to enhance ecosystems' protective functions. They recommend strengthening the institutional capacity for societal resilience, improvement of infrastructure, effective response to disaster, and expedite build back better.
The actions should be part of the disaster resilience and urban development planning model.
Other scientists also suggested resilient models for cities. "Scientists proposed rigorous models of urban resilience with multidisciplinary and integrated approaches based on humane perspectives" (OECD, 2020). Scientists proposed rigorous models of urban resilience by multidisciplinary and integrated approaches based on human perspectives (Bozza et al., 2015). Our workshops were on effective management and public participation. We worked to integrate the planning of the urban economy with the physical development of the city.
Transparent management is necessary to know and cooperate with effective actors in the development of the city. Here, we supply a generic list of effective actors, but every city shall consider its own needs. Table 6 a generic list of forces and actors influencing matters related to urban resilience Line Name of force/ organization/ influential factor 1 Representatives of government departments, who are representatives of the executive branch in the city 2 Representatives of the judiciary in the city in the form of the judiciary, courts, judges, and lawyers 3 Representatives of the legislature in the form of representatives of the people of the city in parliament 4 Representatives of the city council 5 Representatives of the Guild Council 6 Representatives of employers' organizations 7 Representatives of existing banks in the city 8 Indigenous investors of the city and province 9 Representatives of investors from all over the country 10 Representatives of International Investors 11 Educated, specialists, and sympathizers of the city 12 Representatives of trade unions in democracies 13 Representatives of non-governmental organizations 14 Representatives of radio and television, national government newspapers 15 Representatives of local radio and television in democracies 16 Representatives of local and indigenous newspapers of the city 17 Representatives of international resilience organizations of world cities such as the World Bank Group Urban resilience is feasible by secure livelihoods and employment. It requires the provision of municipal services such as transportation infrastructure and reliable communications. The urban development model should reduce risk and harm to minimize human vulnerability, the lives and health of citizens, and comprehensive security and the rule of law.
Our model for urban resilience maximizes the benefits through optimal investment to upgrade 55 indicators. See Objective function (8). We think this generic model is feasible in every city after analyzing the risks and vulnerabilities of the city. The implementation of this model strengthens and sustains cities in six M, E, U, I, N, and H indicator groups. It also brings economic prosperity. We achieve this goal by implementing the projects that we define and implement in detail in the third step of the resilience process.
The third step explains how the city achieves the determined vision of resilience. This step reflects the present situation of the city and exhibits its future. In the third step, we introduce projects for every indicator, explain them in detail, and determine an optimal amount of investment in the projects. See equations (1)-(6). Table 7 suggests generic projects to upgrade the situation of the indicators briefly. Local planners and engineers shall explain every project in detail with an acting schedule and investment plan according to the characteristics of their cities.
Table 7 a list of required projects to build a city resilient Introducing projects to upgrade the city's resilient Indicator Line Projects of the urban management training program at the university with a number of elite volunteers.

M 1 1
Project to form decision-making groups by selecting people for urban areas and the whole city.

M 2 2
A project on integrated and coordinated planning and management plan consisting of representatives of all public and private sectors of the city. Project to prepare an emergency management plan for the city M 7 7 A project for public education and awareness of the people of the city to deal with possible dangers prepared by the city manager M 8 8 Project to prepare and define the mechanism of people interaction and management in times of crisis M 9 9 Project to set fair and efficient urban land policies M 10 10 Project to set up a comprehensive and transparent mechanism for the approval of urban development plans

M 11 11
Project for evaluating and feasibility of economic and commercial cooperation with cities and surrounding areas. Also, if possible, conclude trade agreements and economic partnerships.

E 1 12
Project to measure the unique economic capabilities of the city and plan to use these facilities E 2 13 Project to prepare business plans in various economic sectors E 3 14 Project to provide a mechanism for public access to judicial justice E 4 15 Project to provide a mechanism for influencing the opinion of inhabitants to determine the duties and behavior of the police.
Project to provide effective mechanisms for combating government corruption. E 6 17 Project for the preparation of social programs for crime prevention. E 7 18 Project for preparing mechanisms to increase the rate of social participation in economic and social activities of the city E 8 19 Project to integrate the identity and culture of the city in economic and social activities E 9 20 Project to provide mechanisms to guarantee the legal activities of democratic groups of the people.

E 10 21
Project to provide mechanisms for fair and meritorious access of people in the community to job opportunities and banking facilities.

E 11 22
Project to provide efficient and guaranteed mechanisms on the unemployed and the needy. The project also monitors that city administrations do not relinquish their duties under the pretext of helping compassionate people.

E 12 23
Projects to review previous land-use policies and setting new policies to design streets, sidewalks, stations and reduce population density in urban spaces.

U 1 24
Projects for standard housing to increase per capita housing in the city suitable for modern human needs.

U 2 25
Projects of standard housing for low-income groups to have access to housing. U 3 26 Projects to allocate sufficient land for constructing schools, stadiums, workshops, and commercial centers and reduce the population density.

U 4 27
Project for maintenance of urban spaces U 5 28 Project for the maintenance of the components of the city to provide services to the citizens U 6 29 Project to provide effective and efficient urban services to the people. U 7 30 Project to set guidelines, standards, and building codes for the sustainable physical development of the city.

U 8 31
Project to provide an efficient mechanism for enforcing construction regulations and preventing construction violations.

U 9 32
Project to prepare an atlas of accident-prone and unsafe parts of the city to prevent construction there.

U 10 33
Project for construction of flood dams, stress-bearing walls of buildings resistant to earthquakes, sewage collection networks, and anti-storm tree windbreaks I 1 34 Projects for constructing transport networks, including lines and stations, to reduce congestion.

I 2 35
Project for design and construction of digital infrastructure and smart city. I 3 36 Project for water supply, water distribution networks, regulation to prevent water losses, and reducing water consumption.

I 4 37
Project for gas distribution network infrastructure and construction of gas stations and distribution of fossil fuels.

I 5 38
Project to determine the mechanisms of fair access of people to electricity, gas, gasoline, and other energies I 6 39 Project to collect and treat the city's wastewater for reuse I 7 40 Project for soil protection by reducing construction, increasing the city's green spaces, and other soil conservation mechanisms.

N 1 41
Project to maintain existing water resources through water management methods and natural resource conservation.

N 2 42
Project to protect ponds, lakes, and pastures around the city to preserve wildlife and birds. N 3 43 Project to collect surface water and sewage for environmental cleanliness N 4 44 Project to improve water quality and purity and public access to safe drinking water. N 5 45 Project to reduce air pollutants and keep the air clean of toxins and carbon dioxide N 6 46 Project to reduce noise pollution from workshops and traffic, especially in residential and educational areas and hospitals.

N 7 47
Project to clean all components of the environment. N 8 48 Project to increase urban life-quality by standards of the World Health Organization and striving to achieve them.

H 1 49
Project to increase the public health rate of the city by health and products and reducing prices.

H 2 50
Project to evaluate the rate of public health care services and determine mechanisms to increase them.

H 3
Project to improve the quantity and quality of hospitals and medical centers. Additionally, increase beds, equipment, doctors, and nurses.

H 4 52
Project for monitoring the fair access rate of people to health services and insurance and ensuring these accesses.

H 5 53
Project to increase medical equipment and facilities by purchasing vital equipment and tools.

H 6 54
Project to determine the mechanism of safe access of people in the community to health goods and medicines.

H 7 55
The right-hand column of Table 7 lists the projects related to the city's 55 maximum resilience indicators with optimal investment. This list has been prepared using our workshop experiences and shows only the concept and purpose of the projects. However, it is necessary to plan and implement the mentioned projects according to the characteristics of the city in detail and prepare maps.
Here a question arises. How do the projects listed in Table 7 assist the cities resilience? The projects will support the municipality and other institutions related to urban development to make the city strong against risks. Every project has a task to eliminate a particular known vulnerability of the city. Projects together supply a safe and suitable place for all citizens. The results of the projects will significantly improve the city's capacity to withstand risks, stresses, and shocks. From this perspective, urban resilience has something in common with sustainable development.

Discussions
Substantial improvement of urbanism's situation considers a city as a whole and demonstrates a close relationship between urban land expansion and demographic urbanization (Song et al., 2021). The experiences show that cities need both planning and development. They also need protection plans against threats. Ignoring this need, even in the past, has led to the destruction of some cities or civilizations. We presented some risks that threaten unstable and unsustainable cities in Table 7. In the preceding section, we analyzed learnings and appropriations in the process of building cities resiliently. We introduced 55 indicators related to elements of the city that motivated an interconnected network with the ability to work collectively at the urban resilient differentiation.
Our linear program allocates the amount of investment to every indicator group optimally. It led the city to maximum resilience also economic profit. Equations 1-8 understand the relationship between networks, differentiation, and maximum urban hardness in our linear programming. Our model understood the principles of interactivity influence of the 55 projects introduced in table 7.
Efficient allocation of investments is the task of urban resilient building scholars.
Here, we interpret and develop our model with a non-linear procedure when considering our 55 projects as independent variables. Given a set of 55 projects in our target function with the capital limitations, we have: i=j.
Here, we write: We now address the question of how optimal allocation is accessible in maximum resilient building profit and write the Lagrange function for it (Abramowitz & Stegun, 1964).
Our Kuhn-Tucker conditions (Koopmans and Beckmann, 1957) for the optimal investment as a first derivation test of the model are in (10).
. In (10), are opportunity costs. denotes the time required to implement a given project i to allocate one unit of j's investment, p is the rate of profits (OPI) in the upgrading of projects.
In the maximization of the OPI by upgrading the p (in practice, we interpret the p to 55 projects) we have 55! = 1.269640335 ×1073 solution alternatives. The model finds exact 55 solutions from 1.269640335 ×1073. This situation is a linear allocation of the budgets for building the city resiliently.
We introduced a list of required 55 projects to build a city resilient. The projects upgrade the indicators and maximize the economic profits of the building city resiliently. A practical mechanism to realize the suggestions of our model is public participation, particularly the cooperation of the influencing factors. Table 6 introduced forces and actors influencing matters related to urban resilience.
We recognized the relationship between urbanization speed and quality, construction scale and management level, economic growth and social development, resource exploitation, and environmental protection. Scholars also noticed that the factors are crucial for urbanization (Guan et al., 2018). In the stages of the urban resilience process described in the previous sections, joint and integrated cooperation between all government departments is essential.
Our experience shows that such woven interaction is successful. We shall perform the operations under the responsibility of a competent, knowledge-based, and forward-looking management team. Cooperation between the private and public sectors and responsible international institutions will also advance the resilience of cities.

Conclusions
This applied research studied the need for urban resilient buildings. The relevance of urban resilience to the reopening of economies took more notice to analyze the dangers that threaten the cities everywhere in the world.
Our method was a multi-phased process of upgrading the indicators of urban resilience. We built a model of resilience with 55 required projects. Every project supported a large variety of solutions, but we learned to select one optimal investment with the help of the model in this paper. The model depended upon various forms of confidence-building tests: on risks.
The examinations in the Kuhn-Tucker conditions proved our hypothesis that maximum resilience supplies maximum economic profits.
We argued that these mechanisms replace the authorities integrated into urban management systems and supported rational, scientific, and problem-oriented strategies. This paper presented a procedure of urban building that can allow the six indicator groups to reach a maximum level of efficiency in the post-COVID era. We have suggested that such a building can also upgrade all indicator groups of M, E, U, I, N, and H. The ability of our model to simulate it in different urban systems will support the urban planners, engineers, entrepreneurs, and academicians to build their cities resiliently.