Is SARS-CoV-2 Extinct Without Immunity?

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), because the COVID-19 pandemic continues to kill thousands of people every day in different parts of the world. However, a recent study by researcher Bhavin S Khatri of Imperial College London has been published on the preprint server. medRxiv* The August 2020 SARS-CoV-2 virus suggests that if breeding numbers remain low, it may disappear faster than expected.

SIR model

The SIR (Susceptible-Infected-Recovered) model has continued to be one of the most commonly used models to understand the evolution of the epidemic since it was first introduced. SIR simplifies many of the factors associated with disease transmission over different populations, locations and periods. However, its strength lies in its ability to condense epidemics into several key parameters.

One of the most important factors in determining the course of an epidemic is the effective copy number or Re (R0, not to be confused with the basic copy number). It shows growth above 1 and contracts below 1. It also conveys the number of infections that occurred as a result of spread from the initial patient as 1/γ. Simple parameters can represent a broader outline of a more detailed model and provide a better idea of ​​how changing these parameters might affect an epidemic, but are more strictly parameterized. The quantitative accuracy provided by the model is sacrificed. Therefore, the combinatorial approach helps to more accurately predict the behavior of the epidemic.

Probability density of annihilation time for the same parameters as in Figure 1. However, it includes migration and subdivision into populations of the same size. Each histogram contains 1000 replicas of n = 5 regions connected by a uniform migration of probability φ. The gray bar corresponds to φ = 0 (complete separation), the blue corresponds to φ = 0.05, and φ = 0.1 is the red bar. For φ = 0, the solid gray line is exactly the same as the solid black line in Figure 2, indicating that the distribution of extinction times is the same for a single global mixed population of the same aggregate size. The solid blue and red lines fit the histogram using Eqn.7 with a single free parameter Re (with γ and I0 constrained to the values ​​used to run the simulation).

Individual discreteness

Current research deals with SIR models while incorporating individual discreteness. This differs from the deterministic model, where the number of infected individuals and their densities are treated as continuous, so density values ​​can actually be less than one. This may result in incorrect prediction of the second wave after the motion restrictions have been lifted. Instead, this model uses a low-density, complete stochastic description, keeping track of the course of development. In such a situation, the population population could be exactly 0. That is, if the number of infections is 0, the epidemic will be extinct. The second wave will not occur unless the case is imported.

This paper considers the current situation where herd immunity has not yet been achieved, but Re is less than 1. Therefore, although the epidemic is not widespread, each infected person is highly susceptible. Researchers are using a new threshold^† = 1 = (1-Re) represents the extinction time, and it can be shown that the average extinction time is significantly reduced compared to the deterministic model because Re is between 0.6 and 1.

Extinction time depends on date and time

To understand the impact of geographic variation and other differences, Khatri compared it to a more complex and simple model. He found that an exact distribution of extinction times could be reached by simply rescaling Re to include the effects of movement.

Using this theory, Khatri predicted that if Re was between 0.6 and 1, the extinction time would be years. At this interval, the deterministic model always overshoots the mark significantly. However, if you keep it below 0.5, it can drop to months within a year. If Re is less than this, there is not much merit in further reducing the disappearance time.

Finally, as the average infection duration 1/γ increases, so does the extinction time. Recent studies show a median duration of asymptomatic infection of 7 days, an average of 2 days presymptomatic and symptomatic, and a median of 13.4 days. According to initial studies, the average infection period is about 20 days. Of these, the duration of asymptomatic infection is probably the most important, as it is during this period that the infection is most likely to infect others.

UK and World Extinction Time

Therefore, the current model assumes an average infection duration of 7 days in terms of infectivity. Second, the UK model shows that if Re is less than 0.5, the epidemic can disappear in about 100 days. However, the UK Government estimates and the Cambridge MRC Biostatistics Unit estimate Re at the end of June as 0.9 in the UK. At this value, extinction would take almost two years.

The predicted annihilation time of the world population of 7.8 billion and the incidence rate of 0.05% is almost the same in 200 days (6 to 7 months) when Re is less than 0.5. However, if Re exceeds 0.6, it will take years to disappear. More specifically, if Re is 0.4 and the infection period is 7 days, we estimate that the extinction time will be approximately 177 days.

The simple model was evaluated by simulating the conditions using the realistic space fad simulator, GleamViz. Researchers have found that predicted extinction times for both methods are in close agreement. Khatri said, “Despite the heterogeneity of contact between different regions, the overall attenuation of infections is exponential and the stochastic variability is a good mixture of the stochastic SIR models presented here. According to the forecast.”

Implications and conclusions

Forecasting at the global level is considered a rough guide if all countries follow the same type of action plan. Researchers also warn that this may allow the virus to reinfect human populations, if there are non-human reservoirs that carry the virus. In this particular scenario, extinction is only a temporary condition. This can be explained in the same way as human imports, but if such a reservoir can be identified and investigated, this route can also be blocked.

Explaining his theory as providing a “useful and quick guide to estimating the time to extinction of an epidemic,” Khatri concludes: Or for less than half a year, the goal is to limit Re to a number less than 1, optimally in the region Re ≈ 0:4 → 0:5.

*Important Notices

medRxiv It publishes preliminary non-peer reviewed scientific reports and should not be considered conclusive and should not guide clinical practice/health-related behaviors or be treated as established information.