Investigating the Effects of Intervention Strategies on Pneumonia and HIV/AIDS Coinfection Model

HIV/AIDS and pneumonia coinfection have imposed a major socioeconomic and health burden throughout the world, especially in the developing countries. In this study, we propose a compartmental epidemic model on the spreading dynamics of HIV/AIDS and pneumonia coinfection to investigate the impacts of protection and treatment intervention mechanisms on the coinfection spreading in the community. In the qualitative analysis of the model, we have performed the positivity and boundedness of the coinfection model solutions; the effective reproduction numbers using the next-generation operator approach; and both the disease-free and endemic equilibrium points' local and global stabilities using the Routh-Hurwiz and Castillo-Chavez stability criteria, respectively. We performed the sensitivity analysis of the model parameters using both the forward normalized sensitivity index criteria and numerical methods (simulation). Moreover, we carried out the numerical simulation for different scenarios to investigate the effect of model parameters on the associated reproduction number, the effect of model parameters on the model state variables, and the solution behavior and convergence to the equilibrium point(s) of the models. Finally, from the qualitative analysis and numerical simulation results, we observed that the disease-spreading rates, protection rates, and treatment rates are the most sensitive parameters, and we recommend for stakeholders to concentrate and exert their maximum effort to minimize the spreading rates by maximizing the protection and treatment rates.

Quantitative Assessment of a Dual Epidemic Caused by Tuberculosis and HIV in the Philippines

Tuberculosis (TB) and human immunodeficiency virus (HIV) are the two major public health emergencies in the Philippines. The country is ranked fourth worldwide in TB incidence cases despite national efforts and initiatives to mitigate the disease. Concurrently, the Philippines has the fastest-growing HIV epidemic in Asia and the Pacific region. The TB-HIV dual epidemic forms a lethal combination enhancing each other's progress, driving the deterioration of immune responses. In order to understand and describe the transmission dynamics and epidemiological patterns of the co-infection, a compartmental model for TB-HIV is developed. A class of people living with HIV (PLHIV) who did not know their HIV status is incorporated into the model. These unaware PLHIV who do not seek medical treatment are potential sources of new HIV infections that could significantly influence the disease transmission dynamics. Sensitivity analysis using the partial rank correlation coefficient is performed to assess model parameters that are influential to the output of interests. The model is calibrated using available Philippine data on TB, HIV, and TB-HIV. Parameters that are identified include TB and HIV transmission rates, progression rates from exposed to active TB, and from TB-latent with HIV to active infectious TB with HIV in the AIDS stage. Uncertainty analysis is performed to identify the degree of accuracy of the estimates. Simulations predict an alarming increase of 180% and 194% in new HIV and TB-HIV infections in 2025, respectively, relative to 2019 data. These projections underscore an ongoing health crisis in the Philippines that calls for a combined and collective effort by the government and the public to take action against the lethal combination of TB and HIV.

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.