Analysis of an age-structured tuberculosis model with treatment and relapse

Abstract

A new tuberculosis model consisting of ordinary differential equations and partial differential equations is established in this paper. The model includes latent age (i.e., the time elapsed since the individual became infected but not infectious) and relapse age (i.e., the time between cure and reappearance of symptoms of tuberculosis). We identify the basic reproduction number for this model, and show that the determines the global dynamics of the model. If , the disease-free equilibrium is globally asymptotically stable, which means that tuberculosis will disappear, and if , there exists a unique endemic equilibrium that attracts all solutions that can cause the spread of tuberculosis. Based on the tuberculosis data in China from 2007 to 2018, we use Grey Wolf Optimizer algorithm to find the optimal parameter values and initial values of the model. Furthermore, we perform uncertainty and sensitivity analysis to identify the parameters that have significant impact on the basic reproduction number. Finally, we give an effective measure to reach the goal of WHO of reducing the incidence of tuberculosis by 80% by 2030 compared to 2015.

The influence of ambient air pollution on the transmission of tuberculosis in Jiangsu, China

“…Hence, C i ∼Poisson (mean = Z i ). And model fitting is performed by Markov Chain Monte Carlo (MCMC) method ( Guo et al., 2021 , 2022 ; Luo et al., 2019 ; Zhao et al., 2018 , 2019 ).…”

A tuberculosis model with early and late latency, imperfect vaccination, and relapse: An application to China

“…Indeed, some more realistic modifications can be made based on this work. For example, the heterogeneity factors of individuals from different ages and regions in population should be reflected in the TB dynamical model, in details, one possible modification would be to incorporate age structure into the ordinary differential equation model such as infection age and latency age (see previous studies [54,55]), another possible modification would be to research the dynamics for a reaction-diffusion model because frequent population mobility in different regions may promote TB transmission (see previous works [56,57]). We will leave these interesting and practically meaningful questions for future study to gain a deeper comprehension of TB transmission dynamics.…”

Analisis Model Epidemi Penyebaran Tuberkulosis Dengan Struktur Umur

“…Selama peyebaran tuberkulosis perlu diperhatikan bahwa setelah terinfeksi, beberapa individu akan segera mengembangkan penyakit tuberkulosis (dalam beberapa minggu), sebelum sistem kekebalan tubuh dapat melawan bakteri tuberkulosis tersebut. Meski demikian, banyak pula orang dengan infeksi tuberkulosis yang tidak pernah mengembangkan penyakit tuberkulosis disebut dengan individu laten [7]. Iannelli dan Milner [8] berpendapat bahwa struktur usia penting ketika memodelkan penyakit jangka panjang, karena kemungkinan individu yang terinfeksi menjadi individu yang menular dan sembuhnya pasien yang kambuh adalah variabel.…”

“…Penelitian tentang model SEIR pada penyakit pneumonia yang dibahas oleh Syarifuddin Side beserta rekannya tahun 2021 [11]. Penelitian tentang model tuberkulosis dengan pengobatan dan kekambuhan dibahas oleh Zhong-Kai Guo beserta rekannya [7]. Penelitian tentang dampak vaksinasi dalam penyebaran tuberkulosis menggunakan model matematis dibahas oleh Nkamba beserta rekanny [4].…”