Abstract:HIV/AIDS and COVID-19 co-infection is a common global health and socio-economic problem. In this paper, a mathematical model for the transmission dynamics of HIV/AIDS and COVID-19 co-infection that incorporates protection and treatment for the infected (and infectious) groups is formulated and analyzed. Firstly, we proved the non-negativity and boundedness of the co-infection model solutions, analyzed the single infection models steady states, calculated the basic reproduction numbers using next generation mat… Show more
“…Using the criteria applied by references, 6 , 12 , 29 , 31 , 41 , 54 item (c) of Theorem 6 indicates bifurcation of the dynamical system ( 11 ) in the backward direction whenever . The basic requirement having the sub-model ( 11 ) effective reproduction number although is necessary, is not sufficiently enough to the complete control of the COVID-19 infection spreading in the community.…”
Section: Qualitative Analysis Of the Dynamical Systemmentioning
Different cross-sectional and clinical research studies investigated that chronic HBV infected individuals’ co-epidemic with COVID-19 infection will have more complicated liver infection than HBV infected individuals in the absence of COVID-19 infection. The main objective of this study is to investigate the optimal impacts of four time dependent control strategies on the HBV and COVID-19 co-epidemic transmission using compartmental modeling approach. The qualitative analyses of the model investigated the model solutions non-negativity and boundedness, calculated all the models effective reproduction numbers by applying the next generation operator approach, computed all the models disease-free equilibrium point (s) and endemic equilibrium point (s) and proved their local stability, shown the phenomenon of backward bifurcation by applying the Center Manifold criteria. By applied the Pontryagin’s Maximum principle, the study re-formulated and analyzed the co-epidemic model optimal control problem by incorporating four time dependent controlling variables. The study also carried out numerical simulations to verify the model qualitative results and to investigate the optimal impacts of the proposed optimal control strategies. The main finding of the study reveals that implementation of protections, COVID-19 vaccine, and treatment strategies simultaneously is the most effective optimal control strategy to tackle the HBV and COVID-19 co-epidemic spreading in the community.
“…Using the criteria applied by references, 6 , 12 , 29 , 31 , 41 , 54 item (c) of Theorem 6 indicates bifurcation of the dynamical system ( 11 ) in the backward direction whenever . The basic requirement having the sub-model ( 11 ) effective reproduction number although is necessary, is not sufficiently enough to the complete control of the COVID-19 infection spreading in the community.…”
Section: Qualitative Analysis Of the Dynamical Systemmentioning
Different cross-sectional and clinical research studies investigated that chronic HBV infected individuals’ co-epidemic with COVID-19 infection will have more complicated liver infection than HBV infected individuals in the absence of COVID-19 infection. The main objective of this study is to investigate the optimal impacts of four time dependent control strategies on the HBV and COVID-19 co-epidemic transmission using compartmental modeling approach. The qualitative analyses of the model investigated the model solutions non-negativity and boundedness, calculated all the models effective reproduction numbers by applying the next generation operator approach, computed all the models disease-free equilibrium point (s) and endemic equilibrium point (s) and proved their local stability, shown the phenomenon of backward bifurcation by applying the Center Manifold criteria. By applied the Pontryagin’s Maximum principle, the study re-formulated and analyzed the co-epidemic model optimal control problem by incorporating four time dependent controlling variables. The study also carried out numerical simulations to verify the model qualitative results and to investigate the optimal impacts of the proposed optimal control strategies. The main finding of the study reveals that implementation of protections, COVID-19 vaccine, and treatment strategies simultaneously is the most effective optimal control strategy to tackle the HBV and COVID-19 co-epidemic spreading in the community.
“…Analyses of mathematical modeling for real world situations have been the most important tool in understanding of different aspects of the real world phenomenon 22 , 23 . Different researchers have been formulated and analyzed a mathematical model for system dynamics in different research topics such as social sciences, natural sciences and other sciences, see scholars studies 24 – 54 .…”
In this study, we have formulated and analyzed the Tinea capitis infection Caputo fractional order model by implementing three time-dependent control measures. In the qualitative analysis part, we investigated the following: by using the well-known Picard–Lindelöf criteria we have proved the model solutions' existence and uniqueness, using the next generation matrix approach we calculated the model basic reproduction number, we computed the model equilibrium points and investigated their stabilities, using the three time-dependent control variables (prevention measure, non-inflammatory infection treatment measure, and inflammatory infection treatment measure) and from the formulated fractional order model we re-formulated the fractional order optimal control problem. The necessary optimality conditions for the Tinea capitis fractional order optimal control problem and the existence of optimal control strategies are derived and presented by using Pontryagin’s Maximum Principle. Also, the study carried out the sensitivity and numerical analysis to investigate the most sensitive parameters and to verify the qualitative analysis results. Finally, we performed the cost-effective analysis to investigate the most cost-effective measures from the possible proposed control measures, and from the findings we can suggest that implementing prevention measures only is the most cost-effective control measure that stakeholders should consider.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.