Abstract
An S-Ic-I-R epidemic model is investigated for infectious diseases that can be transmitted through carriers, infected individuals who are contagious but do not show any disease symptoms. Mathematical analysis is carried out that completely determines the global dynamics of the model. The impacts of disease carriers on the transmission dynamics are discussed through the basic reproduction number and through numerical simulations.
Highlights
For certain infectious diseases, there are individuals who are able to transmit their illness but do not exhibit any symptoms
We propose a general mathematical model for infectious diseases with asymptomatic carriers to investigate the effects of carriers on the transmission dynamics
To prove the global asymptotic stability of P0 we use the method of Lyapunov functions
Summary
There are individuals who are able to transmit their illness but do not exhibit any symptoms. Asymptomatic carriers are believed to play an essential role in the evolution and global transmission of Typhi, and their presence greatly hinders the eradication of Typhoid fever using treatment and vaccination [13] Another major infectious disease that causes long-term asymptomatic carriage is hepatitis B, a liver disease caused by the HBV virus of the Hepadnavirus family. We propose a general mathematical model for infectious diseases with asymptomatic carriers to investigate the effects of carriers on the transmission dynamics. Rate of influx of susceptibles Natural death rates Death rates for Ic and I compartments, respectively, including both natural and disease-caused death Transmission coefficient for the carrier compartment Ic Transmission coefficient for the symptomatically infected compartment I Rate at which carriers develop symptoms Rate of recovery Probability of a newly infected individual is asymptomatic Vaccination rate bE.
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