Impact of Travel on Spread of Infection

Impact of Travel on Spread of Infection

Chapter in a book

In this paper, we are concerned with a generalization of the classical SIR model describing the dynamics of an infectious disease. Two distinctive features of the proposed model are: (i) the split of the cohort of susceptible into two sub-cohorts, frequent travelers running higher risks of being infected and individuals who do not travel with a lower infection rate, and (ii) lack of immunity to disease with the possibility of re-infection after recovery. These modifications reflect recent experience from Covid-19 epidemics when countries were introducing quarantine measures or travel restrictions and multiple cases of repeated reinfection of individuals were reported. Numerical simulations demonstrate that the ratio between the infection rates of mobile and non-mobile susceptible significantly impacts the dynamics of the disease. Higher infection rates for a smaller sub-cohort of active travelers lead to earlier epidemics outbreaks and affect a larger proportion of individuals.

In this paper, we are concerned with a generalization of the classical SIR model describing the dynamics of an infectious disease. Two distinctive features of the proposed model are: (i) the split of the cohort of susceptible into two sub-cohorts, frequent travelers running higher risks of being infected and individuals who do not travel with a lower infection rate, and (ii) lack of immunity to disease with the possibility of re-infection after recovery. These modifications reflect recent experience from Covid-19 epidemics when countries were introducing quarantine measures or travel restrictions and multiple cases of repeated reinfection of individuals were reported. Numerical simulations demonstrate that the ratio between the infection rates of mobile and non-mobile susceptible significantly impacts the dynamics of the disease. Higher infection rates for a smaller sub-cohort of active travelers lead to earlier epidemics outbreaks and affect a larger proportion of individuals.

Mathematical epidemiology; compartmental models; SIR-type model; system of nonlinear differential equations; disease-free equilibrium; endemic equilibrium; asymptotic stability; mobile susceptible; non-mobile susceptible; travel patterns; positive solutions; Routh-Hurwitz criterion; next generation method; basic reproduction number; transition between discrete and continuous systems; rates of transfer between compartments; numerical simulations; epidemic outbreak; impact of travel on the spread of infection.

Mathematical epidemiology; compartmental models; SIR-type model; system of nonlinear differential equations; disease-free equilibrium; endemic equilibrium; asymptotic stability; mobile susceptible; non-mobile susceptible; travel patterns; positive solutions; Routh-Hurwitz criterion; next generation method; basic reproduction number; transition between discrete and continuous systems; rates of transfer between compartments; numerical simulations; epidemic outbreak; impact of travel on the spread of infection.

HOLM, K.; REBENDA, J.; ROGOVCHENKO, Y.

2024

09.12.2023

Springer Cham

Cham, Switzerland

978-3-031-42688-9

Computational and Mathematical Models in Biology

Nonlinear Systems and Complexity book series, volume 38

183

211

29

https://link.springer.com/chapter/10.1007/978-3-031-42689-6_8