The Mathematics of Coronavirus COVID-19

Pre reading

This case study focuses on the economic impact of the surging Coronavirus and uses economic models both for dealing with preventions and handling the economic fallout.

The origin of viruses

The 1918 Spanish Flu

Case study of Minneapolis St Pauls in Spanish Flu

The case of Gunneson Clorado

Prevention and Treatment

Models

Springer Nature

PLOS Mathematical Models of infectious diseases

Los Alamos Models

Sponsored by TurboCASH Accouting

"Nature teaches Beasts to know their friends". Coriolanis

Philip Copeman, Mohammed Cassim, Benjamin Napier

philip@pinksoft.co.za

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Data

John Hopkins in one Spreadsheet

John Hopkins dataviz

Github repository

kaggle

Introduction

Avoid being taken down the conspiracy theories that the Coronavirus is a man-made biological weapon or comes from outer space. It is highly likely that COVID-19 is a very worldly organism, that has been here in other spiecies and is only now getting recognised by us because it has jumped to human infection. How this happened is not as important as how we deal with its expansion.

Media is calling it an "infodemic"- an overflow of info on the Coronavirus. This case study focuses on the mathematics and strategies for South Africa and Texas. We view this not as a health issue but as an exercise in mathematical economics. Priority is dealing with isolation and containment. This study focuses on macro data. The CDC is a good source for detailed mico behavior.

COVID-19 is easily transmitted, but low mutating. (a priori assumption needs substantiation)

This means that it is easy to transmit (with proximity) and once the host recovers it build an immunity to reinfection. (a priori assumption needs substantiation) The recovered cases act as a firewall. The Virus cannot get past these immune hosts and eventually dies ou or subsides to very low levels, has jumped to human infection. How this happened is not as important as how we deal with its expansion.

COVID-19 is easily transmissable but low mutating. This means that it is easy to transmit (with proximity) and once you recover you build an immunity to reinfection. The recovered cases act as a firewall. The Virus cannot get past these immune hosts and eventually dies out or subsides to very low levels, firewalled by recovered cases.

Our Proposals

States of infection

Much has been written about Viruses, but what is particularly interesting is the extreme cases that have a two scenario outcome. The Virus kills the host or the host kills the virus. This has shaped our evolutionary history for two Billion years and today we have evolved highly developed immune systems.

The Host has four states: not infected, confirmed, dead, recovered and each of these states affects the outcome of how me of the virus progresses.

In stage one, not infected. We have not encountered the virus.

In stage two, confirmed it is transmitted and starts to multiply. It keeps on doing so unless it is stopped by the host.

Stage 3A, death. In the event that the host cannot stop the virus spread, death occurs.

Stage 3B, recovery. The host defeats the virus and becomes recovered. It is much harder for the host to be reinfected.

There is a real need to build a working model of the Virus. Right now everyone is speculating.

Strategies

Isolation

The virus needs proximity to transmit from host to host. This is complicated by the fact that transmission is possible even without the host showing symptoms.

Containment begins first at a national level, then once this has failed at a regional level, a suburban level, household level and at the individual.

Isolation is the cheapest economic means of dealing with the virus. However, it takes a huge will and in a zero confirmed environment, there is no sense of urgency to contain the virus.

Containment

Once the virus has been detected, it s usually because there are already other cases and the community spread has already started.

Containment measures require data system for tracing contact and putting suspected cases into quarantine. This is more expensive than isolation.

Modeling the speed of infection is most important because we should be trying to get recovered patients faster that new infections. It is the total amount infections that put the health system under pressure and predjudices treatment. t.

Modeling the speed of infection is most important because we should be trying to get recovered patients faster that new infections. It is the total amount infections that puts the health system under pressure and predjudices treatment.

Treatment

Treatment is to continue containment, boost the immune system and deal with secondary infections (which is what actually kills the host). People with weak immune systems (Due to age or other conditions) have a higher death rate. This is a specialist health area and not the focus of this case study. What is of interest is modeling what happens when resources are put under pressure.