Modelling COVID-19 transmission in the United States through interstate and foreign travels and evaluating impact of governmental public health interventions

Abstract

Background: The first case of COVID-19 was reported in Wuhan, China in December 2019. The disease has spread to 210 countries and has been labelled as a pandemic by the World Health Organization (WHO). Modelling, evaluating, and predicting the rate of disease transmission is crucial in understanding optimal methods for prevention and control. Our aim is to assess the impact of interstate and foreign travel and public health interventions implemented by the United States government in response to the COVID-19 pandemic. Methods: A disjoint mutually exclusive compartmental model was developed to study transmission dynamics of the novel coronavirus. A system of nonlinear differential equations was formulated and the basic reproduction number $R_0$ was computed. Stability of the model was evaluated at the equilibrium points. Optimal controls were applied in the form of travel restrictions and quarantine. Numerical simulations were conducted. Results: Analysis shows that the model is locally asymptomatically stable, at endemic and foreigners free equilibrium points. Without any mitigation measures, infectivity and subsequent hospitalization of the population increased. When interstate and foreign travel was restricted and the population placed under quarantine, the probability of exposure and subsequent infection decreased significantly; furthermore, the recovery rate increased substantially. Conclusion: Interstate and foreign travel restrictions, in addition to quarantine, are necessary in effectively controlling the pandemic. The United States has controlled COVID-19 spread by implementing quarantine and restricting foreign travel. The government can further strengthen restrictions and reduce spread within the nation more effectively by implementing restrictions on interstate travel.

Keywords: Covid-19; Public health; Transmission; Travel.

Fig. 1

Compartmental diagram showing movement of individuals from one compartment to another compartment.

Fig. 2

Trajectories of each compartment showing flow of individuals in respective compartment.

Fig. 3

Scatter plotting between different compartment combination is observed showing the behaviour of respective combinations.

Fig. 4

We plot phase diagram of interstate class when exposed to COVID-19 observing again and again exposure of interstate population to COVID-19.

Fig. 5

This indicates phase plot of foreigner class when exposed to COVID-19. Here we observe convergent behaviour of respective classes making it stable.

Fig. 6

Behaviour of interstate class with quarantine class (a) and Phase plot of quarantine with foreigners (b).

Fig. 7

Transition diagram of interstate and foreigner population. Here the movement of individuals between respective classes is observed.

Fig. 8

Shows directional plot of Interstate population infected with COVID-19 indicating the infectiousness of interstate population.

Fig. 9

Depicts behaviour of Foreigner population infected with COVID-19. Here we observe that foreign travellers are getting infection at large.

Fig. 10

Directional plot of hospitalization of interstate population (a) and foreigner (b).

Fig. 11

Here we observe continuous fluctuation in all the compartments which very well depicts the scenario of COVID-19 among interstate and foreign travellers.

Fig. 12

Effect of controls applied to the system (1) is observed on each compartment. Here it can be seen that after control is applied, population of each compartment decreases.

Fig. 13

Represents chaotic diagram showing mortality rate of 2019-nCoV.

Fig. 14

Percentage wise distribution of interstate (a) and foreigner population in COVID-19 scenario (b). In Fig. 14 a, we observe out of 26% of interstate population 17% is infected and from Fig. 14 b, among 19% of foreigners we have 18% infected population.

Fig. 15

Figure indicates percentage wise distribution of all the compartments of the system (1). Here we have 21% of interstate population, 14% of foreign population out of which 13% gets the infection with 15% getting hospitalised.