Vaccination impact on impending HIV-COVID-19 dual epidemic with autogenous behavior modification: Hill-type functional response and premeditated optimization technique.

An HIV-COVID-19 co-infection dynamics is modeled mathematically assimilating the vaccination mechanism that incorporates endogenous modification of human practices generated by the COVID-19 prevalence, absorbing the relevance of the treatment mechanism in suppressing the co-infection burden. Envisaging a COVID-19 situation, the HIV-subsystem is analyzed by introducing COVID-19 vaccination for the HIV-infected population as a prevention, and the "vaccination influenced basic reproduction number" of HIV is derived. The mono-infection systems experience forward bifurcation that evidences the persistence of diseases above unit epidemic thresholds. Delicate simulation methodologies are employed to explore the impacts of baseline vaccination, prevalence-dependent spontaneous behavioral change that induces supplementary vaccination, and medication on the dual epidemic. Captivatingly, a paradox is revealed showing that people start to get vaccinated at an additional rate with the increased COVID-19 prevalence, which ultimately diminishes the dual epidemic load. It suggests increasing the baseline vaccination rate and the potency of propagated awareness. Co-infection treatment needs to be emphasized parallelly with single infection medication under dual epidemic situations. Further, an optimization technique is introduced to the co-infection model integrating vaccination and treatment control mechanisms, which approves the strategy combining vaccination with awareness and medication as the ideal one for epidemic and economic gain. Conclusively, it is manifested that waiting frivolously for any anticipated outbreak, depending on autogenous behavior modification generated by the increased COVID-19 prevalence, instead of elevating vaccination campaigns and the efficacy of awareness beforehand, may cause devastation to the population under future co-epidemic conditions.

Bifurcation analysis of autonomous and nonautonomous modified Leslie-Gower models.

In ecological systems, the predator-induced fear dampens the prey's birth rate; yet, it fails to extinguish their population, as they endure and survive even under significant fear-induced costs. In this study, we unveil a modified Leslie-Gower predator-prey model by incorporating the fear of predators, cooperative hunting, and predator-taxis sensitivity. We embark upon an exploration of the positivity and boundedness of solutions, unearthing ecologically viable equilibrium points and their stability conditions governed by the model parameters. Delving deeper, we unravel the scenario of transcritical, saddle-node, Hopf, Bogdanov-Takens, and generalized-Hopf bifurcations within the system's intricate dynamics. Additionally, we observe the bistable nature of the system under some parametric conditions. Further, the nonautonomous extension of our model introduces the intriguing interplay of seasonality in some crucial parameters. We establish a set of sufficient conditions that guarantee the permanence of the seasonally driven system. By conducting a numerical study on the seasonally forced model, we observe a myriad of phenomena manifesting the predator-prey dynamics. Notably, periodic solutions, higher periodic solutions, and bursting patterns emerge, alongside intriguing chaotic dynamics. Specifically, seasonal variations of the predator-taxis sensitivity and hunting cooperation can lead to the extinction of prey species and even the control of chaotic (higher periodic) solutions through the generation of a simple periodic solution. Remarkably, the seasonal forcing has the capacity to govern the chaotic behavior, leading to an exceptionally quasi-periodic arrangement in both prey and predator populations.

Stability switches and chaos induced by delay in a reaction-diffusion nutrient-plankton model.

In this paper, we investigate a reaction-diffusion model incorporating dynamic variables for nutrient, phytoplankton, and zooplankton. Moreover, we account for the impact of time delay in the growth of phytoplankton following nutrient uptake. Our theoretical analysis reveals that the time delay can trigger the emergence of persistent oscillations in the model via a Hopf bifurcation. We also analytically track the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions. Our simulation results demonstrate stability switches occurring for the positive equilibrium with an increasing time lag. Furthermore, the model exhibits homogeneous periodic-2 and 3 solutions, as well as chaotic behaviour. These findings highlight that the presence of time delay in the phytoplankton growth can bring forth dynamical complexity to the nutrient-plankton system of aquatic habitats.

A mathematical model for the impact of disinfectants on the control of bacterial diseases.

Here, we investigate a mathematical model to assess the impact of disinfectants in controlling diseases that spread in the population via direct contacts with the infected persons and also due to bacteria present in the environment. We find that the disease-free and endemic equilibria of the system are related via a transcritical bifurcation whose direction is forward. Our numerical results show that controlling the transmissions of disease through direct contacts and bacteria present in the environment can help in reducing the disease prevalence. Moreover, fostering the recovery rate and the death rate of bacteria play significant roles in disease eradication. Our numerical observations convey that reducing the bacterial density at the source discharged by the infected population through the use of chemicals has prominent effect in disease control. Overall, our findings manifest that the disinfectants of high quality can completely control the bacterial density and the disease outbreak.

A delay non-autonomous model for the combined effects of fear, prey refuge and additional food for predator.

In this paper, we investigate the combined effects of fear, prey refuge and additional food for predator in a predator-prey system with Beddington type functional response. We observe oscillatory behaviour of the system in the absence of fear, refuge and additional food whereas the system shows stable dynamics if anyone of these three factors is introduced. After analysing the behaviour of system with fear, refuge and additional food, we find that the system destabilizes due to fear factor whereas refuge and additional food stabilize the system by killing persistent oscillations. We extend our model by considering the fact that after sensing the chemical/vocal cue, prey takes some time for assessing the predation risk. The delayed system shows chaotic dynamics through multiple stability switches for increasing values of time delay. Moreover, we see the impact of seasonal change in the level of fear on the delayed as well as non-delayed system.

Bifurcations, chaos, and multistability in a nonautonomous predator-prey model with fear.

Classical predator-prey models usually emphasize direct predation as the primary means of interaction between predators and prey. However, several field studies and experiments suggest that the mere presence of predators nearby can reduce prey density by forcing them to adopt costly defensive strategies. Adoption of such kind would cause a substantial change in prey demography. The present paper investigates a predator-prey model in which the predator's consumption rate (described by a functional response) is affected by both prey and predator densities. Perceived fear of predators leads to a drop in prey's birth rate. We also consider both constant and time-varying (seasonal) forms of prey's birth rate and investigate the model system's respective autonomous and nonautonomous implementations. Our analytical studies include finding conditions for the local stability of equilibrium points, the existence, direction of Hopf bifurcation, etc. Numerical illustrations include bifurcation diagrams assisted by phase portraits, construction of isospike and Lyapunov exponent diagrams in bi-parametric space that reveal the rich and complex dynamics embedded in the system. We observe different organized periodic structures within the chaotic regime, multistability between multiple pairs of coexisting attractors with intriguing basins of attractions. Our results show that even relatively slight changes in system parameters, perturbations, or environmental fluctuations may have drastic consequences on population oscillations. Our observations indicate that the fear effect alters the system dynamics significantly and drives an otherwise irregular system toward regularity.