Modelling heterogeneity in host susceptibility to tuberculosis and its effect on public health interventions

Abstract

A tuberculosis (TB) model that accounts for heterogeneity in host susceptibility to tuberculosis is proposed, with the aim of investigating the implications this may have for the effectiveness of public health interventions. The model examines the possibility that recovered individuals treated from active TB and individuals treated with preventive therapy acquire different levels of immunity. This contrasts with recent studies that assume the two cohorts acquire the same level of immunity, and therefore both groups are reinfected at the same rate. The analysis presented here examines the impact of this assumption when designing intervention strategies. Comparison of reinfection rates between cohorts treated with preventive therapy and recovered individuals who were previously treated for active TB provides important epidemiological insights. It is found that the reinfection rate of the cohort treated with preventive therapy is the one that plays the key role in qualitative changes in TB dynamics. By contrast, the reinfection rate of recovered individuals (previously treated from active TB) plays a minor role. Moreover, the study shows that preventive treatment of individuals during early latency is always beneficial regardless of the level of susceptibility to reinfection. Further, if patients have greater immunity following treatment for late latent infection, then treatment is again beneficial. However, if susceptibility increases following treatment for late latent infection, the effect of treatment depends on the epidemiological setting. That is: (i) in (very) low burden settings, the effect on reactivation predominates and the burden declines with treatment; (ii) in moderate to high burden settings the effect of reinfection predominates and burden increases with treatment. The effect is most dominant between the two reinfection thresholds, RT2 and RT1, respectively associated with individuals being treated with preventive therapy and individuals with untreated late latent TB infection.

Impact of media information and reinfection in a COVID-19 dynamical model: emergence of periodic orbits through Hopf bifurcation

“…Consequently, as  0 increases or decreases while remaining greater than unity, infections will persist at a stable equilibrium until they reach the endpoint of the unstable branch E 4 , at which point they will transition to another stable branch. These findings align with observations made in [56,57]. To assess the stability of these endemic equilibrium points, we have generated plots depicting the real parts of the eigenvalues of the Jacobian matrix associated with each equilibrium point, as illustrated in figure 16.…”

Optimal control analysis of a tuberculosis model with exogenous re‐infection and incomplete treatment

“…A number of mathematical models have been developed to analyze the dynamical spread of TB in human population (see, eg, References 3‐11 and some of the references therein). In Reference 7, the authors presented a mathematical model for TB with exogenous re‐infection, which allows for the possibility of a subcritical bifurcation at a certain critical value of the basic reproduction number.…”

Modeling the Effects of Vaccination and Treatment on Tuberculosis Transmission Dynamics

“…ese models apply to di erent types of populations such as a city or country, a school, prison, or refugee camp, see for instance, [8,9] Also, di erent models would focus on various factors such as progression rate, treatment, vaccination, immigration, etc. see [10][11][12].…”