A mathematical model of tuberculosis and COVID-19 coinfection with the effect of isolation and treatment

Abstract

In this research, we developed a coinfection model of tuberculosis and COVID-19 with the effect of isolation and treatment. We obtained two equilibria, namely, disease-free equilibrium and endemic equilibrium. Disease-free equilibrium is a state in which no infection of tuberculosis and COVID-19 occurs. Endemic equilibrium is a state in which there occurs not only the infection of tuberculosis and COVID-19 but also the coinfection of tuberculosis and COVID-19. We assumed that the parameters follow the uniform distribution, and then, we took 1,000 samples of each parameter using Latin hypercube sampling (LHS). Next, the samples were sorted by ranking. Finally, we used the partial rank correlation coefficient (PRCC) to find the correlation between the parameters with compartments. We analyzed the PRCC for three compartments, namely, individuals infected with COVID-19, individuals infected with tuberculosis, and individuals coinfected with COVID-19 and tuberculosis. The most sensitive parameters are the recovery rate and the infection rate of each COVID-19 and tuberculosis. We performed the optimal control in the form of prevention for COVID-19 and tuberculosis. The numerical simulation shows that these controls effectively reduce the infected population. We also concluded that the effect of isolation has an immediate impact on reducing the number of COVID-19 infections, while the effect of treatment has an impact that tends to take a longer time.

A Systematic Literature Review of Mathematical Models for Coinfections: Tuberculosis, Malaria, and HIV/AIDS

“…19 This model divides the population into different compartments based on certain assumptions and characteristics. 20 Model can also serve to depict the occurrence of epidemic events involving interactions between two diseases. Using this model enables the estimation of individuals who are infected.…”

Tuberculosis experience in possible respiratory infectious disease outbreaks with lessons learned during the COVID-19 pandemic

“…Среди других неудач в борьбе со вспышкой вируса стало ясно, что многие медицинские учреждения плохо оборудованы и не готовы справиться с наплывом пациентов, а также имеют неадекватные медико-эпидемиологические подготовки для надлежащего ухода за пациентами, что привело к повышенной заболеваемости и смертности медицинских работников от коронавирусной инфекции. Типичной моделью аэрогенной инфекции, для проведения профилактических «учений» по подготовке системы здравоохранения к очередным пандемиям, является противотуберкулезная служба [1,2,5]. Данная служба имеет большинство схожих этио-патогенетических механизмов с коронавирусной инфекцией [3,4].…”

Mathematical Modeling and Sensitivity Analysis of COVID-19 and Tuberculosis Coinfection with Vaccination

“…Lockdown has hampered tuberculosis patient services, resulting in an increase in tuberculosis dissemination and COVID-19 tuberculosis co-infection [37]. In terms of the influence of the COVID-19 pandemic on TB, the analysis shows that people infected with COVID-19 cause an increase in the number of people infected with tuberculosis and slow down the cure rate [38].…”