A DIFFERENT PARADIGM FOR EPIDEMIC MANAGEMENT

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EPIDEMIC, CONTROL POLICIES & VITAL HEALTH RESOURCES. OPTIMIZATION MODELING

https://www.dhirubhai.net/pulse/opchain-health-modelado-matemático-de-alta-para-la-toma-velasquez/

Spanish Version: https://www.dhirubhai.net/pulse/un-paradigma-diferente-para-la-gesti%25C3%25B3n-de-epidemias-jesus-velasquez/

LinkedIn Group Mathematical Modeling for Coronavirus Pandemic: https://www.dhirubhai.net/groups/12383318/

Version PDF: https://www.doanalytics.net/Documents/DW-Paradigm-Different-Epidemic-Management.pdf

Working Paper (Algebraic Formulation and Applications):

Management Epidemics using High Complexity Mathematical Modeling. Part I: Epidemic, Control Policies & Vital Health Resources

 https://www.doanalytics.net/Documents/DW-OPCHAIN-Health-Epidemic-Model.pdf 

INTELLECTUAL PROPERTY

THE INTELLECTUAL PROPERTY OF THIS DOCUMENT BELONGS TO JESúS VELáSQUEZ-BERMúDEZ. THE DOCUMENT, OR ITS PARTS, MAY NOT BE REPRODUCED, RECORDED IN STORAGE SYSTEMS, OR TRANSMITTED BY ANY PROCEDURE, WHETHER ELECTRONIC, MECHANICAL, REPROGRAPHIC, MAGNETIC OR ANY OTHER, WITHOUT EXPLICIT RECOGNITION AUTHORSHIP OF THIS DOCUMENT BY JESúS VELáSQUEZ-BERMúDEZ.

"the computer-based mathematical modeling is the greatest invention of all times"

Herbert Simon

Alfred Nobel Memorial Prize in Economic Sciences (1978)

"for his pioneering research into the decision-making process within economic organizations”

1.        INTRODUCTION

 This document presents a different approach to pandemic management based on the integration of epidemiological models, administration sciences and highly complex mathematical models. In order to maintain a limited frame of reference, the analysis is limited only to the minimization of deaths generated by the management of the epidemic, leaving aside any other consideration.

2.         HIGH COMPLEXITY MATHEMATICAL MODELING

 As a starting point it is convenient to clearly the concept of high complexity mathematical modeling, for this reference is taken the theoretical framework presented by Davenport & Harris in his book "Competing on Analytics" [2], who describe advanced analytics as composed of three types of analytics: descriptive, predictive and prescriptive. The following diagram, prepared by IBM from the original Davenport & Harris diagram describes in detail the level of complexity that different mathematical methodologies can handle, and puts in the dome, as the best of the breed, optimization, and more specifically optimization under uncertainty (which is not included in the original diagram of Davenport & Harris).

Based on the above, and to make clear the position of the author, it is considered as mathematical modeling of high complexity that is specifically related to optimization, and more specifically with stochastic programming and optimization robust, applied manifestations of optimization under uncertainty.

It is also made clear that these are not simulation models (deterministic or stochastic), which as stated by Davenport & Harris, and confirmed by IBM, the degree of complexity is not the same level as the one that manages optimization. The big difference between simulation and optimization is that the first iterates based on human computing capacity, and the second takes advantage of all the power that parallel computing gives today and optimization algorithms based on large-scale optimization methodologies.

3.        DEATHS IMPACT

In order to quantitatively estimate the impact of highly complex mathematical modelling, reference is taken of the results presented by Imperial College (IC, London, [1]) which has been used as a reference by governments in multiple countries.

 Table 4 of that report, which contains comparative results of four management strategies for COVID 19 pandemic. The strategies analyzed, with an IC simulation model, are:

1.      NOTH (DO NOTHING) 

2.      ZC-TP (Low/Zero Math Complexity), based on the "traditional practice" of total “quarantine” which can be considered as zero level of mathematical complexity. From mathematical point of view, it corresponds to a simulation of a TRADITIONAL PRACTICE

3.      MC-SM (Medium Math Complexity), it combines total social distancing control policy with mitigation based on prohibiting activities that generate crowds (colleges, universities). Medium level of complexity, it can be solved with MATH SIMULATION MODELS.

4.      HC-OM (High Math Complexity), it tries to determine the best mix of control policies. The IC used a simulation model to obtain this results, they may be optimal but, due to that it is high complexity mathematical problem, to solve it exactly it is necessary to use HIGH COMPLEX OPTIMIZATION ALGORITHMS. The IC results establish an upper bound for the minimum number of deaths.

This codification was made by the author, not by the IC that uses the codification rules that are showed in the header of the table 4. IC analyzed 20 experiments, combination of diffusion factor and entry speed (triggering).

The results (average values of 20 cases) are presented in the following table (produced by the author):

The following image visually presents the results

The following table (produced by the author) presents the comparative results in number of times more than high-tech mathematical models (in blue the code given by the author).

This can be summarized in:

1.      High complexity mathematical models (HC-OM) produce the least number of deaths (95.61% less than NOTH), which is equivalent to reducing the dead to 21.525 of a potential of 482.500.

2.      Decisions based on low mathematical complexity (ZC-MM), based on "traditional practices", produce 84.01% less than NOTH, implying that it produces 57.625 more deaths than HC-OM, or 168% more. But there are cases where the death ratio can be 1 to 9.77.

3.      Paradoxically, the highly complex strategy also produces the shortest confinement time: 81.35% ZC-MM, 78.84% MC-SM and 69.11% HC-OM.

Given that the value of human life is considered invaluable, the estimate of the cost of using an elementary decision model, and of low mathematical complexity, is 57.625 times humanly more expensive than using a formal mathematical model capable of solving problems of high complexity; in addition, to minimize the number of deaths, the highly complex methodology produces the least amount of time confined, implying a socio-economic benefit. Therefore, epidemic management policies obtained with a mathematical optimization model ensure that:

• Minimize the number of deaths
• Minimize confinement time
• Generate less socio-economic negative impact.

 Based on the above, it can be said that there is no rationality that justifies not using mathematical optimization to support the decision-making process. 

 4.        THE MANAGEMENT SCIENCES APPROACH

The problem of managing the peak demand of a good is well known by the Management Sciences (or Operations Research). We have two cases according to the types of goods:

1.      Storable: In this case (mostly industrial products) the problem is anticipated and occurs in advance, storing production to consume during peak demand. Mathematical models are responsible for managing production to establish the best way to meet the demand curve. Example, the demand for beer (or turkeys) that presents a very strong peak in demand in the holiday season, which causes production to anticipate.

2.      Non-Storable: In this case (mostly services) the only alternative is to try to change the demand curve to anticipate, or delay, the attention of the services considering the installed capacity. Mathematical models are responsible for establishing the best way to manage demand over time in order to meet it, hopefully 100%. Example: repairing vehicles that must go to a workshop with finite capacity.

Between these two extremes there are countless cases that can be faced by simultaneously managing demand and production, that is the power of highly complex mathematical models. The provision of services to address epidemics is in the second case. To address the problem, it is necessary to have a clear theory of how the epidemic spreads and how it generates demand for vital hospital services. To do this, we refer back to the study of the IC.

 The graph developed with the IC simulation models for Gran Britain presents three cases:

1.      DO NOTHING (CP-DN, black): this policy represents the natural behavior of the epidemic, a peak and the shortest duration of the epidemic process.

2.      CONFINEMENT (CP-CO, brown): total confinement applied for 5 months. This curve has a peak, to eliminate the peak the confinement should reach infinity, or until the region has a vaccine.

3.      MITIGATION (CP-MI, green): implementation of mitigation policy with partial confinement of 5 months. It has a peak with a shorter duration than the previous policy.

The red line indicates the installed capacity of vital hospital services.

Results will vary depending on region-specific data (country/state, city, province, ...). Below are the results for USA.

It is clear that the spikes of the epidemic depend on control policies and how they are implemented, the total effect will be the number of deaths at the end of the process. It is also clear that the temporary decline in the spread of the epidemic is not an indicator that the process is controlled and/or terminated.

If the pandemic is seen as an optimal resource management problem, two alternating periods can be visualized: (i) unused installed capacity and (ii) installed capacity deficit. In the following graph, the CP-MI policy (selected for contrasting reasons) has been referenced to visually analyze epidemic management.

It can be said that during:

1.      The first period (April to October) misuses the installed capacity which has a very low usage factor, if the green line could be approached to the level of installed capacity there would be fewer deaths (lives recovered). In this same period the CP-CO policy makes better use of installed capacity, greater use factor.

2.      The second period (November to January) accumulates demand for services, exceeding capacity and generating large numbers of deaths. The usage factor reaches 1., indicating low capacity of management the capacity.

The logical solution to the problem is:

1.      Anticipating the use of installed capacity in the first period, advancing the demand for hospital services (accelerating the spread of the pandemic) and

2.      Increase the use of installed capacity during the third period (stopping the spread of the pandemic during the second period.

The problem is that this which seems logical (smart) is easy to express in words, but very complex to quantify in real life. Perhaps that is why the last sentence of the IC report verbatim says:

 “However, we emphasise that is not at all certain that suppression will succeed long term; no public health intervention with such disruptive effects on society has been previously attempted for such a long duration of time. How populations and societies will respond remains unclear.”

The use of High Complexity Mathematical Programming methodologies can extend to other epidemic-related problems, for example, the optimization of:

• Epidemic control policies; goal: minimizing expected number of deaths
• Budget allocation and location of vital hospital resources, aim to ensure maximum utilization of resources in accordance with epidemic control policies
• Socio-economic impact oriented to maximize in the long-term quality of life indices of the society.
• Management of productive chains, maximizing the social welfare generated by the production chains during and after the epidemic
• Smart sampling, maximizing the information gained as a result of the measurement processes considering the scarcity of resources
• Vaccination programming, considering that this process should be extended throughout the period of supply of vaccines and that during it there is a likelihood of infection of the unvaccinated population.

All previous mathematical models (and others) make up the artificial hypothalamus of epidemic management [3].

 REFERENCES

 [1]  Ferguson N. M. et al. (2020) Impact of Non-Pharmaceutical Interventions (NPIs) to Reduce COVID-19 Mortality and Healthcare Demand, March 16/2020, DOI: https://doi.org/10.25561/77482).

 [2]  Davenport, T. and Harris J (2007). “Competing on Analytics: The New Science of Winning”. Harvard University Press.

 [3]  Velasquez-Bermudez, J. M. (2020). “High Complexity Epidemic Mathematical Modeling”. https://www.doanalytics.net/Documents/OPCHAIN-Health-English-Resume.pdf