Exploring Susceptible-Infectious-Recovered (SIR) Model for COVID-19 Investigation by Rahul Saxena & Mahipal Jadeja & Vikrant Bhateja

Author:Rahul Saxena & Mahipal Jadeja & Vikrant Bhateja
Language: eng
Format: epub
ISBN: 9789811941757
Publisher: Springer Nature Singapore

The magnitude of value fluctuates based on severity of a disease’s viral infection. Influenza epidemic of 1918 flu (Spanish flu) was predicted to have a value of 1.4–2.8 [3]. Similarly, Swine flu and H1N1 flu have value in the range of 1.4–1.6. In Sect. 5.​3, a more extensive comparison view is presented. According to the study reported in [9], the value considered for Covid-19 is in the range of 5.7–6.3 (based on the data of the first outbreak in Wuhan, China). The value of was formerly given 1.8–3.0; however, this range was later eliminated in [9].

The model’s analytical results are based on the disease’s value. It is ultimately determined by the number of contacts made and their frequency. The value for Covid-19 (5.7–6.3), as reported by [9], takes into account a variety of biological, socio-behavioural as well as environmental factors that influence virus transmission. However, because there is no direct metric for estimating the value of , it is given based on mathematical observations. The influence of the value, rather than how the value is calculated, makes more sense in the context of the reported simulations and analytical results.

As , the dependent parameters on which the value of depends are transmission rate (a) and recovery rate (b), where is a constant that represents the initial susceptible population. For different diseases, the ‘a’ and ‘b’ factors have varying values. Theoretically, and hold true because both the parameters are bound to have non-negative values. When , the value of is high, which explains the high rate of viral spread. If , it indicates that the epidemic is nearing its end. In practice, analysing the value of a and b parameters is difficult because these variables differ region-wise as well as country-wise. Furthermore, as per [6], they are dependent on several uncontrolled aspects such as people’s social distancing measures, regional immunity, temperature and weather conditions, and so on. However, given the transmission rate (a) and value, b is estimated to be about 1/15 based on the analysis in [10] and [8]. This suggests that if each individual is infected for 15 days, we can anticipate 1/15th of those infected to recover each day. The value varies from 1.1 to 3.8, with 0.073–0.2533 as the effective contact rate. On the contrary, in several other countries and regions, the effective contact rate ranges from 0.38 to 0.42, resulting in a value of 5.7–6.3.

The number for recovery rate is chosen as 1/15 for the sake of feasibility, and is assumed to be 6.0 as per [9]. The value of can change (can go up or down). The value is determined by the variation in infection and recovery rates. To illustrate this, the graph in Fig. 4.1 depicts how a generic SIR model will expand.

Fig. 4.1SIR model-based infection and recovery growth rate trends

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