Mitigating the transmission of infection and death due to SARS-CoV-2 through non-pharmaceutical interventions and repurposing drugs

Abstract

The Covid-19 pandemic has put the world under immeasurable stress. There is no specific drug or vaccine till now that can cure the infection or protect people from the infection of coronavirus. It is therefore prudent to use the existing resources and control strategies in an optimal way to contain the virus spread and provide the best possible treatments to the infected individuals. Use of the repurposing drugs along with the non-pharmaceutical intervention strategies may be the right way for fighting against the ongoing pandemic. It is the objective of this work to demonstrate through mathematical modelling and analysis how and to what extent such control strategies can improve the overall Covid-19 epidemic burden. The criteria for disease elimination & persistence were established through the basic reproduction number. A case study with the Indian Covid-19 epidemic data is presented to visualize and illustrate the effects of lockdown, maintaining personal hygiene & safe distancing, and repurposing drugs. It is shown that India can significantly improve the overall Covid-19 epidemic burden through the combined use of NPIs and repurposing drugs though containment of spreading is difficult without serious community participation.

Keywords: Basic reproduction number; Control strategy; Data fitting; Local & global stability; Mathematical model for Covid-19.

Fig. 1

Schematic diagram of the disease progression mechanism considered in the system (2).

Fig. 2

Actual cumulative values (red colour) of confirmed, recovered and death cases in India for the study period March 1 to March 24, 2020 (before lockdown period) are fitted by the solution (green colour) of the system (3) with $u_1=u_2=u_3=0$ . (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 3

Actual cumulative data (red colour) of confirmed, recovered and death cases in India for the study period March 25 to May 31, 2020 (lockdown period) are fitted by the solution (green colour) of the system (3) with fixed controls $u_1=0.3$, $u_2=0.1$ and $u_3=0$. (For interpretation of the references to colour in this figure legend, thereader is referred to the web version of this article.).

Fig. 4

Actual cumulative values (red colour) of confirmed, recovered and death cases in India for the study period 1st June to 27th August, 2020 (unlock period) are fitted by the solution (green colour) of the system (3) with fixed controls $u_1=0.15$, $u_2=0.35$ and $u_3=0$ . (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 5

Predicted cumulative Covid-19 confirmed, recovered and death cases in India for the next one month (August 28 to September 26) for different values of the control $u_3$. Here 180 days implies August 27, 2020, and 210 days implies September 26, 2020. The predicted results with $u_3=0$ is represented by the green dashed line in each figure. The red, brown and blue colours represent the same for $u_3=0.2$, $u_3=0.3$ and $u_3=0.4$, respectively. The cumulative number of deaths as of September 26 when $u_3=0$ are 97,243 and the same for $u_3=0.3$ are 92.449, implying 4794 fewer deaths in one month. Parameters are as in Table 2 (unlock period) . (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 6

(a) Variation in the basic reproduction number, $R_0$, of the Covid-19 epidemic in India for the study period March 1 to August 27, 2020. It shows that $R_0$ decreases from its value 1.8723 as of March 24 to 1.1180 as of August 27. March 24 is the lockdown starting date and May 31 is the lockdown ending date for India. The daily positive cases will decline from its current value once $R_0$ goes below the dashed line $R_0=1$. (b) The curve $R_0=1$ separates the infection-free state ($R_0<1$) from the endemic state ($R_0>1$) in the plane of control parameters $u_1$, $u_2$. The present estimated values of $u_1$ and $u_2$ are marked with a red dot. Parameters are as in Table 2 with unlock case . (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 7

Percentage change in the projected numbers of positive, recovered and death cases as of September 26 due to the use of repurposing drug therapy with different control efficacies. The change is calculated with their corresponding values of August 27. It shows that the use of repurposing drugs will reduce the projected deaths by 2.39%, 4.93% and 7.51% when $u_3$ takes values 0.2, 0.3 and 0.4, respectively. Similar changes may be observed in the cumulative infected cases ($I_h+I_c$). An increase in the recovery class ($R$) is also observed and the percentage change is indicated by a positive sign.