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Modelling COVID-19 pandemic using Mathematics

1 Zulkifli  Mohd   Nopiah  (PhD)  2 Ramizi Bin Mohamed (PhD) 3 Raja  Affendi  Raja Ali ( M.Med.Sc ) 12 Faculty of Engineering and Built Environment, 3 Faculty of Medicine, UNIVERSITI KEBANGSAAN MALAYSIA.

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The COVID-19 pandemic can be modeled by using simple  S-I-R  or  S-E-I-R model . The letters stand for Susceptible, Exposed, Infectious and Removed.  Literatures can be found in many studies. The model developed was based on S-E-I-R  compartmental  model from Q. Lin et. al. 2020 and He et. al. 2013.   The developed model used THREE control parameters, earlier known as  Government Control Strategy, Early Detection Strategy and Public Response .

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S  – the number of  susceptible  individuals not yet infected with the disease. E  – is the compartment of population who have been  exposed  to the disease I  – denotes the individuals who have been  infected  with the disease. R   – is the compartment used for those have been infected and the  removed  from the disease.  This can be for those who have immunization ,  recovered   or due to  death .

Keyword :  Compartmental Meaning : Characterized by division into separate sections.

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Once the infected person gets into the healthy compartment, people start to get exposed. Where  Β (t)/N  is the strength factor

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The susceptible compartment is vulnerable and reducing number at rate

Expose within short period of time before totally infected,  the exposed person now becomes infected person.

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Infected persons gradually increase, hence infectivity rate increases.

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The plot of SEIR  and SIR are almost the same

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S-E-I-R Model  –  another representation

Susceptible
Exposed
Infectious
Removed
Recovered
Deaths

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R 0  =  represents the Reproduction Number. It is the number of cases, one case generates on average over the course of their infectious period, is a key measure of transmissibility and can be estimated in a number of ways from the data currently available (Fraser et al., 2009). Higher number of  R 0  would indicate that the outbreak could growth exponentially, and if the number falls down less than ONE (1) it has an indication that the disease can be controlled and eventually died out.

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The  behaviour  of the outbreak is similar to China’s experience since December 2019.   The strategy is to fit the  model with non-linear least square technique to the actual data from China, and use the parameter for Malaysian Covid-19 outbreak. The model does not consider for any emigration rate or even  zoonatic  cases.

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The estimation of the curve projection is based on current infected numbers.   The  objective  of the projection is to estimate the possible number of active cases and reproduction number R 0  (ref: WHO-China joint mission). We introduced step function,  β(t),  that consist of early transmission rate and control measure parameters to estimate for the next projection curve.  The step function is needed for future curve projection for any changes based on the current and previous number of active cases at any particular time (dates).

Note: R 0  represents the average number of people to which a single             infected person will transmit the virus

Modelling COVID-19 pandemic using Mathematics

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