Assessing the Effects of Holling Type-II Treatment Rate on HIV-TB Co-infection

Impact of saturated treatments on HIV-TB dual epidemic as a consequence of COVID-19: optimal control with awareness and treatment

In this study, we propose an HIV-TB co-infection model by considering the treatment provision limitation induced by recent COVID-19 pandemic that impacts this dual epidemic immensely, assimilating the significance of educational attempts. We analyze the model and its submodels with single infections individually. We obtain the awareness-induced basic reproduction numbers and discuss the global stability of disease-free equilibrium when provision limitation is zero. We observe that the submodels exhibit forward as well as backward bifurcations under provision restriction. Further, we derive thresholds for resource limitations regulating the dynamical behavior of the systems while analyzing the stability of endemic equilibrium of the models with single infections. Sophisticated simulation approaches are implemented to discover the influences of provision-restricted medication and awareness on dual epidemic. Our findings convey the persistence of co-infection though the basic reproduction number is below unity, if the provision restriction remains uncurbed. An observable insight is that, in spite of having epidemic threshold less than unity and no limitation in TB treatment, co-infection relapses and persists in the population, when there is no awareness attempt. Numerical findings emphasize the urgent need of increased treatment accessibility and importance of awareness in the current situation. Moreover, an optimization problem incorporating treatment and awareness controls is formulated and solved to find the ideal strategy to manage HIV-TB co-epidemic that recommends to diminish the medical resource limitation to get the enormous impact in dominating the adversity caused by COVID-19.

Optimal control strategies on COVID-19 infection to bolster the efficacy of vaccination in India

The Novel Coronavirus which emerged in India on January/30/2020 has become a catastrophe to the country on the basis of health and economy. Due to rapid variations in the transmission of COVID-19, an accurate prediction to determine the long term effects is infeasible. This paper has introduced a nonlinear mathematical model to interpret the transmission dynamics of COVID-19 infection along with providing vaccination in the precedence. To minimize the level of infection and treatment burden, the optimal control strategies are carried out by using the Pontryagin's Maximum Principle. The data validation has been done by correlating the estimated number of infectives with the real data of India for the month of March/2021. Corresponding to the model, the basic reproduction number [Formula: see text] is introduced to understand the transmission dynamics of COVID-19. To justify the significance of parameters we determined the sensitivity analysis of [Formula: see text] using the parameters value. In the numerical simulations, we concluded that reducing [Formula: see text] below unity is not sufficient enough to eradicate the COVID-19 disease and thus, it is required to increase the vaccination rate and its efficacy by motivating individuals to take precautionary measures.

A fractional order HIV-TB co-infection model in the presence of exogenous reinfection and recurrent TB

In this article, a novel fractional order model has been introduced in Caputo sense for HIV-TB co-infection in the presence of exogenous reinfection and recurrent TB along with the treatment for both HIV and TB. The main aim of considering the fractional order model is to incorporate the memory effect of both diseases. We have analyzed both sub-models separately with fractional order. The basic reproduction number, which measures the contagiousness of the disease, is determined. The HIV sub-model is shown to have a locally asymptotically stable disease-free equilibrium point when the corresponding reproduction number, R H , is less than unity, whereas, for R H > 1 , the endemic equilibrium point comes into existence. For the TB sub-model, the disease-free equilibrium point has been proved to be locally asymptotically stable for R T < 1 . The existence of TB endemic equilibrium points in the presence of reinfection and recurrent TB for R T < 1 justifies the existence of backward bifurcation under certain restrictions on the parameters. Further, we numerically simulate the fractional order model to verify the analytical results and highlight the role of fractional order in co-infection modeling. The fractional order derivative is shown to have a crucial role in determining the transmission dynamics of HIV-TB co-infection. It is concluded that the memory effect plays a significant role in reducing the infection prevalence of HIV-TB co-infection. An increment in the number of recovered individuals can also be observed when the memory effect is taken into consideration by introducing fractional order model.