Mathematical Analysis of the Ross–Macdonald Model with Quarantine

Abstract

People infected with malaria may receive less mosquito bites when they are treated in well-equipped hospitals or follow doctors' advice for reducing exposure to mosquitoes at home. This quarantine-like intervention measure is especially feasible in countries and areas approaching malaria elimination. Motivated by mathematical models with quarantine for directly transmitted diseases, we develop a mosquito-borne disease model where imperfect quarantine is considered to mitigate the disease transmission from infected humans to susceptible mosquitoes. The basic reproduction number R 0 is computed and the model equilibria and their stabilities are analyzed when the incidence rate is standard or bilinear. In particular, the model system may undergo a subcritical (backward) bifurcation at R 0 = 1 when standard incidence is adopted, whereas the disease-free equilibrium is globally asymptotically stable as R 0 ≤ 1 and the unique endemic equilibrium is locally asymptotically stable as R 0 > 1 when the infection incidence is bilinear. Numerical simulations suggest that the quarantine strategy can play an important role in decreasing malaria transmission. The success of quarantine mainly relies on the reduction of bites on quarantined individuals.

Modelling the Dynamics of Endemic Malaria Disease with Imperfect Quarantine and Optimal Control

“…In this paper, a deterministic compartmental model is formulated and analyzed. The model is formulated based on the assumptions of [17] by incorporating imperfect quarantine that is, we classify the infectious human as Exposed quarantined individuals with no disease clinical symptoms for the time being, but sharing common environment or home with these may have continuous opportunities of bite from malaria parasite carrier denoted by , Infected quarantined with disease clinical symptoms denoted by and Hospitalized (infected isolated individuals these are already getting treatment) and denoted by .…”

“…Erdem et al studied the impact of imperfect quarantine on the dynamics of an SIR-type model [16]. X. Jin et al, mathematical analysis of the Ross-Macdonald malaria model with quarantine using SIQ-SI model type [17]. K. O.…”

Dynamical models of acute respiratory illness caused by human adenovirus on campus

“…Arino et al [31] and Wang et al [32] developed dynamic model on asymptomatic infected individuals and estimated the importance of the proportional parameter representing symptomatic infected for the pandemic. Jin et al [33] considered the impact of quarantine strategy, and the results suggest that quarantine has a significant role to reduce malaria transmission.…”

Global stability of a time-delayed malaria model with standard incidence rate

“…In recent years, many scholars further revised the classical Ross-Macdonald model (see, e.g., [1,16,24]). Subsequent studies have extended the revised models to higher dimensions (see, e.g., [5,9,14,15,20,25]). For example, in 2015, Safan and Ghazi [20] proposed a fourdimensional ODEs model of malaria with standard incidence rates, and analyzed the local and global stability of equilibria of the model.…”