Understanding the Role of Environmental Transmission on COVID-19 Herd Immunity and Invasion Potential

Abstract

COVID-19 is caused by the SARS-CoV-2 virus, which is mainly transmitted directly between humans. However, it is observed that this disease can also be transmitted through an indirect route via environmental fomites. The development of appropriate and effective vaccines has allowed us to target and anticipate herd immunity. Understanding of the transmission dynamics and the persistence of the virus on environmental fomites and their resistive role on indirect transmission of the virus is an important scientific and public health challenge because it is essential to consider all possible transmission routes and route specific transmission strength to accurately quantify the herd immunity threshold. In this paper, we present a mathematical model that considers both direct and indirect transmission modes. Our analysis focuses on establishing the disease invasion threshold, investigating its sensitivity to both transmission routes and isolate route-specific transmission rate. Using the tau-leap algorithm, we perform a stochastic model simulation to address the invasion potential of both transmission routes. Our analysis shows that direct transmission has a higher invasion potential than that of the indirect transmission. As a proof of this concept, we fitted our model with early epidemic data from several countries to uniquely estimate the reproduction numbers associated with direct and indirect transmission upon confirming the identifiability of the parameters. As the indirect transmission possess lower invasion potential than direct transmission, proper estimation and necessary steps toward mitigating it would help reduce vaccination requirement.

Keywords: COVID-19; Identifiability; Indirect transmission; Mathematical modeling; Vaccination.

Fig. 1

Flowchart. The squares represent the compartments, solid lines show the flow between the compartments, and dotted line demonstrates the inducing effect of the compartment on the respective flow rate (color figure online)

Fig. 2

Role of direct $(R_{0}H)$ and indirect $(R_{0}F)$ transmission in outbreak (color figure online)

Fig. 3

Comparison of the $R_0$ and $T_H$. For the same combination of $R_{0H}$ and $R_{0F}$, we compared the value of $R_0$ (thick lines) and $T_H$ (thin lines) using a contour plot (color figure online)

Fig. 4

Extinction probability. Approximate extinction probabilities for different combinations of $R_{0H}$ and $R_{0F}$ corresponding to the same $T_H$ have been shown. The figure on the left is for $0\ge R_{0F},R_{0H}\ge 1.1$, whereas the figure on the right is for $0\ge R_{0F},R_{0H}\ge 1.2$ (color figure online)

Fig. 5

Data fitting with Likelihood profile. Graphs showing data fitting and likelihood profiles of the estimated parameters for the early days of COVID-19 outbreak in Nigeria, Bangladesh, and USA, respectively (color figure online)

Fig. 6

Estimated vaccination threshold. Graph showing the vaccination thresholds for USA, Nigeria, and Bangladesh as a function of $R_{0F}$. Early COVID-19 data from Nigeria, Bangladesh, and USA were used for the estimation. Data are available online on Worldometer at https://www.worldometers.info. The estimated vaccination thresholds for these countries are 0.539, 0.306, and 0.360, respectively. However, these could be further decreased to a minimum of 0.353, 0.191, and 0.130, respectively, by reducing $R_{0F}$, i.e., preventing indirect transmission (color figure online)