Mathematical model of pertussis and pneumonia co-infection in infants with maternally derived immunity

• Main Authors: Yakubu, Aisha Aliyu, Farah Aini Abdullah, Yazariah Mohd Yatim
• Format: Article
• Language: English
• Published: Penerbit Universiti Kebangsaan Malaysia 2022
• Online Access: http://journalarticle.ukm.my/20248/1/21.pdf; http://journalarticle.ukm.my/20248/; https://www.ukm.my/jsm/malay_journals/jilid51bil7_2022/KandunganJilid51Bil7_2022.html
• Institution: Universiti Kebangsaan Malaysia

The transmission dynamics of a pertussis-pneumonia co-infection model is analyzed. The model takes into account temporary immunity of infected infants and includes a maternally derived immunity compartment. The basic reproduction number of the co-infected model is obtained using the next generation matrix, and stability analysis is carried out. The model exhibits four equilibria, namely, the pertussis-free equilibrium, the pneumonia-free equilibrium, the co-infection-free equilibrium and co-infection endemic equilibrium. Subsequently, the local stability of the co-infection-free equilibrium is analyzed and is shown to be locally asymptotically stable. Similarly, by constructing a suitable Lyapunov function, the co-infection endemic equilibrium is shown to be globally asymptotically stable. Numerical simulations are carried out to illustrate the validity of these results.