Search

This paper deals with the non-linear Susceptible–Infected–Hospitalized–Recovered model with Holling type II incidence rate, treatment with saturated type functional response for the prevention and control of disease with limited healthcare facilities. The well-posedness of the model is ensured with the help of the non-negativity and boundedness of the solution of the system. The feasibility of the model with DFE (Disease-free equilibrium) and EE (endemic equilibrium) is analysed. The local and global stability are discussed with the help of the computed basic reproduction number R 0. At R 0 = 1 , we use the Centre manifold theory to analyse the transcritical bifurcation exhibited by the system. It is found that the disease is not eradicated even if R 0 < 1 due to the occurrence of backward bifurcation. The occurrence condition of Hopf bifurcation is obtained. The optimal control theory is used to analyse the effects of the minimum possible medical facilities, hospital beds, and awareness creation on the population dynamics. The Hamiltonian function is constructed with the extended optimal control model and solved by Pontryagin's maximum principle to get the minimum possible expenditure. Different types of control strategies are shown by numerical simulation. The sensitivity analysis is discussed with the help of a crucial parameter that depends on the reproduction number. Further, the model is simulated numerically to support the theoretical studies. This paper emphasizes the significance of treatment intensity, the total number of hospital bed available and their occupancy rate as vital parameters for prevention of disease prevalence. • A nonlinear model is proposed to study the spread and control of infectious diseases with limited healthcare facilities. • Due to backward bifurcation, R 0 < 1 is insufficient to eliminate the disease, and the system exhibits periodic oscillation due to the emergence of Hopf bifurcation. • Using Pontryagin's maximum principle, effects of the limited medical facilities, hospital beds, and awareness-building initiatives are examined to determine the minimum possible expenses. • Sensitivity analysis is used to determine the appropriate control parameter and cost-effectiveness analysis is used for finding most optimal strategy. [ABSTRACT FROM AUTHOR]

The present study assumes that infectious disease among prey classifies them as susceptible (S) and infected (I) prey. When strong (susceptible) prey forms a herd to defend against the predator, it can reverse their role. This paper focuses on spotlighting the impact of disease, generalized herd shape, predator mortality due to prey group, the attack rate for healthy prey, and time delay. These factors crucially govern the system's dynamics like Hopf-bifurcation, transcritical bifurcation, and chaos. The sketch of the maximum Lyapunov exponent confirms the chaotic nature. Extensive theoretical and numerical analysis reveals the existence and stability of steady-states in the presence or absence of delay. This study finds out that disease spread in prey can enhance the chances of predator survival. Furthermore, sensitivity analysis demonstrates the influence of some epidemic and ecological parameters on the reproduction numbers of the proposed eco-epidemic system. [ABSTRACT FROM AUTHOR]