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#### Models

Modeling of infectious diseases is an integration of many disciplines - data science, mathematics, epidemiology and an understanding of public health policy and human behaviors.  There are many models and their variants that have been developed to predict the spread and containment of infectious diseases.  The following Nature Publication www.nature.com/articles/s41592-020-0822-z has a good overview of modeling infectious diseases. The Videos and Publications pages on this site also have links to several good resources for mathematical epidemiology.

An Excel based simple SIR  model can be downloaded from the link below. This is a great starting point to understand factors that contribute to the shape of a typical epidemic curve.

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EXCEL SIR Model | Western Kentucky University (wku.edu)

One of the key parameters for modeling infectious diseases is R0  (R not) - a measure of how many persons are infected by an infected person.

R0  is dependent upon 3 main factors:

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• Duration of infectiousness(how long an infected person is able to transmit the virus to others) - varies depending on the state the person is infected

• The probability of infection being transmitted during contact between an infected person and susceptible person(depends on type of contact and transmission). For example: Droplet/aerosol transmission could result in a higher R0, while body fluid transmission means a lower R0 value

• Average rate of contact between infected and susceptible individuals(depends on family structure, who you meet with outside of the house and how long, work environment, social/community service etc.)

For  R0  > 1, there is an outbreak of a given disease, and for R0  < 1, the number of cases will diminish over time and the virus will not be very contagious.

Herd immunity is obtained at (1 - 1/R0 ).  So for R0 of 4, herd immunity is reached when 80% of the population is immune or has been vaccinated.

The charts below shows the  R0  for various infectious diseases.

“‘When Will It Be over?": An Introduction to Viral Reproduction Numbers, R0 and Re .” The Centre for Evidence-Based Medicine, May 20, 2020. https://www.cebm.net/covid-19/when-will-it-be-over-an-introduction-to-viral-reproduction-numbers-r0-and-re/.

McGinty, Jo Craven. “How Many People Might One Person With Coronavirus Infect?” The Wall Street Journal. Dow Jones & Company, February 17, 2020. https://www.wsj.com/articles/how-many-people-might-one-person-with-coronavirus-infect-11581676200.

Wealth and socio-economics of a country also have a profound impact

The effectiveness of reducing infectious diseases is also based upon the socio-economic wealth of a country and the resources used in order to achieve a lower rate of infection, as described by this Nature Article by Alvarez et al."The gap between developed and developing countries may explain some of the differences in the scale of the responses that we are observing. Countries that are better equipped than others in terms of high-end scientific development, diagnostics technology, and health care infrastructure may respond more efficaciously to a pandemic scenario."

Furthermore, the use of mathematical modeling can provide insight as to the methods needed to enable change in various health-care related departments."Friendly and widely available mathematical modeling will enable rational planning (i.e., prediction of hospital bed occupancy, design of testing campaigns, and reinforcement/redirection of social distancing strategies). Moreover, the use of simple/user-friendly models to evaluate in (practically) real-time the effectiveness of containment strategies or programs may be a powerful tool for analyzing and facing epidemic events."

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Source: Alvarez, Mario Moisés, Everardo González-González, and Grissel Trujillo-de Santiago. “Modeling COVID-19 Epidemics in an Excel Spreadsheet to Enable First-Hand Accurate Predictions of the Pandemic Evolution in Urban Areas.” Nature News. Nature Publishing Group, February 22, 2021. https://www.nature.com/articles/s41598-021-83697-w.

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The US National Library of Medicine, better known as the PMC also stresses the importance of mathematical modeling for infectious diseases. "Only towards the end of the twentieth century did mathematical modeling come into more widespread use for public health policy making. Modeling approaches were increasingly used during the first two decades of the AIDS pandemic for predicting the further course of the epidemic and for trying to identify the most effective prevention strategies."

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Source: Kretzschmar, Mirjam, and Jacco Wallinga. “Mathematical Models in Infectious Disease Epidemiology.” Edited by Alexander Krämer, Mirjam Kretzschmar, and Klaus Krickeberg. Modern Infectious Disease Epidemiology: Concepts, Methods, Mathematical Models, and Public Health. U.S. National Library of Medicine, July 28, 2009.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7178885/

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