Cost-effectiveness analysis is a mode of determining both the cost and economic health outcomes of one or more control interventions. In this work, we have formulated a non-autonomous nonlinear deterministic model to study the control of COVID-19 to unravel the cost and economic health outcomes for the autonomous nonlinear model proposed for the Kingdom of Saudi Arabia. We calculated the strength number and noticed the strength number is less than zero, meaning the proposed model does not capture multiple waves, hence to capture multiple wave new compartmental model may require for the Kingdom of Saudi Arabia. We proposed an optimal control problem based on a previously studied model and proved the existence of the proposed optimal control model. The optimality system associated with the non-autonomous epidemic model is derived using Pontryagin’s maximum principle. The optimal control model captures four time-dependent control functions, thus, $u_1$-practising physical or social distancing protocols; $u_2$-practising personal hygiene by cleaning contaminated surfaces with alcohol-based detergents; $u_3$-practising proper and safety measures by exposed, asymptomatic and symptomatic infected individuals; $u_4$-fumigating schools in all levels of education, sports facilities, commercial areas and religious worship centres. We have performed numerical simulations to investigate extensive cost-effectiveness analysis for fourteen optimal control strategies. Comparing the control strategies, we noticed that; Strategy 1 (practising physical or social distancing protocols) is the most cost-saving and most effective control intervention in Saudi Arabia in the absence of vaccination. But, in terms of the infection averted, we saw that strategy 6, strategy 11, strategy 12, and strategy 14 are just as good in controlling COVID-19.

Maize is one of the most extensively produced cereals in the world. The maize streak virus primarily infects maize but can also infect over 80 other grass species. Leafhoppers are the primary vectors of the maize streak virus. When feeding on plants, susceptible vectors can acquire the virus from infected plants, and infected vectors can transmit the virus to susceptible plants. However, because maize is normally patchy and leafhoppers are mobile, leafhoppers will always be foraging for food. Therefore, we want to look at how leafhoppers interact on maize farms using Holling’s Type III functional response in a Caputo fractal-fractional derivative sense. We show that the proposed model has unique positive solutions within a feasible region. We employed the Newton polynomial scheme to numerically simulate the proposed model to illustrate the qualitative results obtained. We also studied the relationship between the state variables and some epidemiological factors captured as model parameters. We observed that the integer-order versions of the model exaggerate the impact of the disease. We also observe that the increase in the leafhopper infestation on maize fields has a devastating effect on the health of maize plants and the subsequent yield. Furthermore, we noticed that varying the conversion rate of the infected leafhopper leads to a crossover effect in the number of healthy maize after 82 days. We also show the dynamics of varying the maize streak virus transmission rates. It indicates that when preventive measures are taken to reduce the transmission rates, it will reduce the low-yielding effect of maize due to the maize streak virus disease.

The main objective of this paper is to formulate an epidemiological model using fractional order derivatives which has an advantage over the classical integer order models due to its memory effect property. Our mathematical formulation of the non-integer order initial value problem will be based on the famous fractional order Caputo derivative. We discuss and show the existence of non-negative solutions of the mathematical model. We further investigate local asymptotic stability analysis of model equilibria. Finally, numerical solutions are presented using Adams-type predictor-corrector method to illustrate fractional model trajectories.

The present paper deals with a fractional-order mathematical epidemic model of malaria transmission accompanied by temporary immunity and relapse. The model is revised by using Caputo fractional operator for the index of memory. We also recommend the utilization of temporary immunity and the possibility of relapse. The theory of locally bounded and Lipschitz is employed to inspect the existence and uniqueness of the solution of the malaria model. It is shown that temporary immunity has a great effect on the dynamical transmission of host and vector populations. The stability analysis of these equilibrium points for fractional-order derivative α and basic reproduction number $\mathcal{R}_{0}$R 0 is discussed. The model will exhibit a Hopf-type bifurcation. The two control variables are introduced in this model to decrease the number of populations. Mandatory conditions for the control problem are produced. Two types of numerical method via Laplace Adomian decomposition and Runge–Kutta of fourth order for simulating the proposed model with fractional-order derivative are presented. To validate the mathematical results, numerical simulations, sensitivity analysis, convergence analysis, and other important studies are given. The paper is finished with some conclusions and discussion.