Analysis of a competitive respiratory disease system with quarantine: epidemic thresholds and cross-immunity e ects
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Extending the body of research on co-infection dynamics, we conducted an investigation using a deterministic epidemic model involving a single host population and two competitive strains, denoted as -c and -i, to gain insights into co-infection dynamics under the influence of quaran- tine measures. Our study involved an examination of the conventional epidemic threshold and the establishment of possible conditions for controlling each pathogen based on their quarantine reproduction numbers, denoted as R ̃qk. We also explored the role of cross-immunity in confer- ring protection against specific pathogens. Our findings illuminated several key insights. In the context of perfect quarantine, the disease-free equilibrium (DFE) within the single-strain model consistently exists and is globally asymptotically stable (GAS). However, under specific condi- tions related to imperfect quarantine, an endemic equilibrium can stably emerge when R ̃qk > 1. Furthermore, our model displayed a forward bifurcation occurring at R ̃qk = 1, indicating that it is influenced by the interplay between the transmission rate and the likelihood of individu- als remaining asymptomatic after exposure. In the two-strain model, the strain with a higher reproduction number, exceeding one, competitively dominates the other, potentially leading to the extinction of the less competitive strain. In scenarios where both R ̃qk > 1, the coexistence of multiple endemic states becomes a possibility. The persistence of co-infection hinges on the co- infected quarantine reproduction number exceeding one, but co-infection diminishes otherwise. Notably, cross-immunity, as represented by parameters ηc and ηi, exerts a substantial influence by reducing susceptibility to the other pathogen. The extent of cross-immunity plays a pivotal role, expanding the region where co-infection can be sustained, with lower and higher values of ηc and ηi, respectively.