In this paper, we present and analyze predator-prey system where prey population is linearly harvested and affected by fear and the prey population has grown logistically in the absence of predators. The predator population follows hunting cooperation, and it predates the prey population in the Holling type II functional responses. Based on those assumptions, a two-dimensional mathematical model is derived. The positivity, boundedness, and extinction of both prey and predator populations of the solution of the system are discussed. The existence, stability (local and global), and the Hopf bifurcation analysis of the biologically feasible equilibrium points are investigated. The aim of this research is to explore the effect of fear on the prey population and hunting cooperation on the predator population, and both prey and predator populations are harvested linearly and taken as control parameters of the model. If the values of , then both prey and predator populations are extinct and also fear parameter has a stabilizing effect on system 4. From the numerical simulation, it was found that the fear effect, hunting cooperation, prey harvesting, and predator harvesting change the dynamics of system 4.

The membranes that encompass the brain and spinal cord become inflamed by the potentially fatal infectious disease called pneumococcal meningitis. Pneumonia and meningitis “coinfection” refers to the presence of both conditions in a single host. In this work, we accounted for the dynamics of pneumonia and meningitis coinfection in communities by erroneously using a compartment model to analyze and suggest management techniques to stakeholders. We have used the next generation matrix approach and derived the effective reproduction numbers. When the reproduction number is less than one, the constructed model yields a locally asymptotically stable disease-free equilibrium point. Additionally, we conducted a sensitivity analysis to determine how different factors affected the incidence and transmission rate, which revealed that both the pneumonia and meningitis transmission rates are extremely sensitive. The performance of our numerical simulation demonstrates that the endemic equilibrium point of the pneumonia and meningitis coinfection model is locally asymptotically stable when max R 1 , R 2 > 1 . Finally, as preventative and control measures for the coinfection of pneumonia and meningitis illness, the stakeholders must concentrate on reducing the transmission rates, reducing vaccination wane rates, and boosting the portion of vaccination rates for both pneumonia and meningitis.

In this study, we analyzed the effect of mother-to-child transmission (MTCT) of hepatitis B virus (HBV) and human immunodeficiency virus (HIV) on the transmission dynamics of their coinfection to make a recommendation based on reasons to public health sector, policy makers, and programme implementers. We proved that the solutions of the sub and full models are positive and bounded. The effective reproduction numbers of the models are derived using the next generation matrix method. The disease-free and endemic equilibria of the submodels and the coinfection model are computed, and the stability of those equilibria is analyzed using Routh-Hurwitz criteria after computing the associated effective reproduction numbers. We performed a sensitivity analysis to show the influence of different parameters on the effective reproduction number of HBV-HIV/AIDS coinfection model, and we identified the most sensitive parameters are τ 2 and α 1 , which are the rate of MTCT of HIV and treatment rate for HBV infected class, respectively. The numerical simulation of the model is done using MATLAB and the findings from the simulations are discussed. From the results of numerical simulations, we observed that an increase in the rates of MTCT of HBV and HIV exacerbated HBV-HIV/AIDS coinfection, while a decrease in the rates of MTCT of these infections would decline the number of cases, minimize the spread, and help to eliminate HBV-HIV/AIDS coinfection from the society gradually.

In this paper, we present and analyze a spatio-temporal eco-epidemiological model of a prey predator system where prey population is infected with a disease. The prey population is divided into two categories, susceptible and infected. The susceptible prey is assumed to grow logistically in the absence of disease and predation. The predator population follows the modified Leslie-Gower dynamics and predates both the susceptible and infected prey population with Beddington-DeAngelis and Holling type II functional responses, respectively. The boundedness of solutions, existence and stability conditions of the biologically feasible equilibrium points of the system both in the absence and presence of diffusion are discussed. It is found that the disease can be eradicated if the rate of transmission of the disease is less than the death rate of the infected prey. The system undergoes a transcritical and pitchfork bifurcation at the Disease Free Equilibrium Point when the prey infection rate crosses a certain threshold value. Hopf bifurcation analysis is also carried out in the absence of diffusion, which shows the existence of periodic solution of the system around the Disease Free Equilibrium Point and the Endemic Equilibrium Point when the ratio of the rate of intrinsic growth rate of predator to prey crosses a certain threshold value. The system remains locally asymptotically stable in the presence of diffusion around the disease free equilibrium point once it is locally asymptotically stable in the absence of diffusion. The Analytical results show that the effect of diffusion can be managed by appropriately choosing conditions on the parameters of the local interaction of the system. Numerical simulations are carried out to validate our analytical findings.

Fasciola hepatica is a parasitic flatworm that causes fascioliasis, a significant disease in livestock leading to substantial economic losses in agriculture. This paper develops and analyzes a mathematical model that incorporates optimal control strategies to manage the transmission of F. hepatica . The model includes four control measures: pasture management, anthelmintic treatment, isolation, and snail control. Stability analysis demonstrates that the disease‐free equilibrium is locally and globally stable when the effective reproduction number ( R ₀ ) is less than 1. The model exhibits a forward bifurcation at R ₀ = 1. Sensitivity analysis identifies key parameters that influence F. hepatica transmission. The use of muscicides is a highly influential parameter in the transmission of the disease. Pontryagin′s maximum principle was applied to determine optimal time‐dependent control strategies for cattle fascioliasis. Cost‐effectiveness analysis, using the incremental cost‐effectiveness ratio, shows that combining all four control measures is the most cost‐effective strategy.