A periodic disease transmission model with asymptomatic carriage and latency periods

Abstract

In this paper, the global dynamics of a periodic disease transmission model with two delays in incubation and asymptomatic carriage periods is investigated. We first derive the model system with a general nonlinear incidence rate function by stage-structure. Then, we identify the basic reproduction ratio [Formula: see text] for the model and present numerical algorithm to calculate it. We obtain the global attractivity of the disease-free state when [Formula: see text] and discuss the disease persistence when [Formula: see text]. We also explore the coexistence of endemic state in the nonautonomous system and prove the uniqueness with constants coefficients. Numerical simulations are provided to present a case study regarding the meningococcal meningitis disease transmission and discuss the influence of carriers on [Formula: see text].

Threshold dynamics of a time-delayed epidemic model for continuous imperfect-vaccine with a generalized nonmonotone incidence rate

“…For further work, it will be interesting to consider the “asymptomatic carriers”. These carriers are individuals who have been infected and are able to transmit their illness without showing any symptoms [ 3 ]. For certain infectious diseases, asymptomatic carriers are a potential source for transmission such as Typhoid Fever, HIV and, most recently, the COVID-19.…”

“…Individuals in R may lose immunity at rate and become susceptible again, that is, they move to the class S (i.e., the vaccine is continuous). These assumptions lead to the following system of delay differential equations: The term represents the probability for individuals to survive the latent period , see e.g., [ 3 ]. The population flux among the five compartments is given in Fig.…”

A time-delayed SVEIR model for imperfect vaccine with a generalized nonmonotone incidence and application to measles

“…Theses assumptions lead to the following system of delay differential equations: The term represents the probability for individuals to survive the latent period see [19] . The population flux among the five compartments is given in Figure 1 and a description of the parameters is given in Table 1 .…”

“…In 1979, Cooke introduced a “time delay” to represent the disease incubation period in studying the spread of an infectious disease transmitted by a vector in [18] . Since then, many authors have incorporated time delays in epidemic models in different scenarios, such as incubation period or latent period [19] , [20] , [21] , [22] , [23] , vaccination period [24] , asymptomatic carriage period [19] and immune period [21] , [22] .…”

“…In [22] , the authors proposed an SEIRS disease transmission model with latent and temporary immune periods as a distributed delays. In [19] , a disease transmission model with two delays in incubation and asymptomatic carriage periods is investigated. In addition, many authors studied time delayed epidemic models with vaccination [2] , [25] , [26] , [27] .…”