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Reproduction Number of Infectious Diseases

The recurring questions in the mind of medical officials and other scientists whenever a new infectious disease, just like the case of Covid-19 comes to light is “will this disease ever be eradicated from the population or will it become an epidemic?” To answer this question George Macdonald (1952) was able to derive a number called quantity basic reproduction rate which was used to determine if malaria will become an epidemic or it will die out. As time pass on mathematicians and epidemiologist continue to use the reproduction number to predict how a disease will act in a population. 

What are Reproduction Numbers? 

Reproduction numbers are generally of two types, the basic reproduction number and the effective reproduction number.

Basic reproduction Number: 

Basic reproduction number () according to Rahman B et al (2020) in the World Health Organization (WHO) bulletin, defined basic reproduction numbers as ‘an indication of the initial transmissibility of the virus, i.e., the average number of secondary infections generated by each infected person.’ In other words, it can be said to be the number of secondary infections caused by a single infected individual in a population assuming that all the population are susceptible to the disease without any herd immunity. For example, if the basic reproduction number for a disease is 20 it means that any infected individual is most likely going to infect 20 people with the disease.

Effective reproduction number

In this kind of reproduction number, The population is most likely not all going to be susceptible to a disease due to either some people having natural immunity, been vaccinated or gain immunity as a result of recovery from the disease or previous immunization. Hence the effective reproduction number can be defined as the average number of secondary cases per infectious case in a population made up of both susceptible and non-susceptible. The effective reproduction number is usually less than the basic reproduction number. 

Factors affecting the Reproduction number

The reproductive number is affected by several factors which include:

  • How frequent the populations are in contact: the more the contact between the population the higher the reproduction number and vice versa. 
  • How contagious is the disease: If the disease is highly contagious the reproduction number is likely going to be higher compared to a less contagious disease.
  • How long is the disease infectious: disease with a higher duration of infectiousness will have a higher reproduction number than those with lower infectiousness.

The interpretation of the reproduction number

Generally, the value of the reproduction number is used to determine if the disease will eventually die out of the population with time or will become endemic to the population. If the reproduction number  then the disease will become endemic in the population but if the  then the disease will eventually die out after some time.


Macdonald G (1952). “The analysis of equilibrium in malaria”. Tropical Diseases Bulletin. 49 (9): 813–29. PMID 12995455.

Rahman B, Aziz I.A, Khdhr F.W & Mahmood D.F.D. (2020). Preliminary estimation of the basic reproduction number of SARS-CoV-2 in the Middle East. [Preprint]. Bull World Health Organ. E-pub: 1 May 2020. doi:

Rothman K.J, Lash T, Greenland S. (2013). Modern Epidemiology, Lippincott Williams & Wilkins.


Mr. Agada Apeh Andrew is a Lecturer II at the Department of Mathematical Sciences in Skyline University Nigeria (SUN). He has completed his MSc in Mathematics from the Modibbo Adama University of Technology, Yola.

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