In this paper, a deterministic mathematical model to investigate the transmission dynamics of malaria in Ghana is formulated taking into account human and mosquito populations. The model consists of seven non-linear differential equations which describe the dynamics of malaria with 4 variables for humans and 3 variables for mosquitoes. The state vector for the model is $(S_h, E_h, I_h, R, S_m, E_m, I_m,)$ where $S_h$, $E_h$, $I_h$, $R$, $S_m$, $E_m$ and $I_m$ respectively represent populations of susceptible humans, exposed humans, infectious humans, recovered humans, susceptible mosquitoes, exposed mosquitoes and infectious mosquitoes. Stability analysis of the model is performed and we make use of the next generation method to derive the basic reproduction number $R_0$. A mathematical analysis of the dynamic behaviour indicates that the estimated model has a unique endemic equilibrium point and malaria will persist in Ghana. The basic reproduction number for Ghana is found to be $R_0=0.8939$. Further, both the disease-free and endemic equilibria are locally asymptotically stable. Numerical simulations indicate that reducing current biting rate of female Anopheles mosquitoes by 1/16 could assist Ghana to achieve malaria free status by the year 2037. If, in addition, the number of days it takes to recover from malaria infection were reduced to three 3 days malaria free status could be achieved by the year 2029

A new dynamic model for the malaria disease has been developed for areas where the whole populace is at risk and exposure to the malaria infection is continuous throughout the year. In this model, the two vulnerable groups that is, infectious people those under 5years and pregnant women have been given separate compartments. The model has two equilibria, that is, disease-free and endemic equilibrium points. The basic reproduction number () for the model has been derived using the next-generation matrix approach. The local stability of two equilibria is investigated using matrix elementary row operations. However, global stability of disease-free equilibrium is investigated using theorem by Castillo-Chavez et.al (2002) and that of the endemic equilibrium is also investigated using Lyapunov's function. It is proven that disease-free equilibrium is locally asymptotically stable if < 1 and the endemic equilibrium exists if > 1. The endemic equilibrium is locally asymptotically stable when Α Α Φ > Φ and >. Sensitivity analysis has proved that malaria can be controlled or eliminated if the following parameters such as biting rates, recruitment rate and densitydependent natural mortality rate for mosquitoes and clinical recovery rates for humans are controlled.

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In this article, we apply the optimal control theory to a new age-structured malaria model with three infectious compartments for people under five years, over five years and pregnant women. The model is formulated for malaria endemic areas in the world and the following malaria control strategies ITN, IRS, Chemoprophylaxis and Improved Clinical Treatment were examined and analysed on the mode. The Cost-effectiveness Analysis points out that more attention should be given Insecticide -Treated bed nets (ITNs) in order to eliminate the malaria disease globally because the female Anopheles mosquitoes need human blood to lay their eggs. The expression for the effective reproduction number  has been derived by using the next-generation method. The impact of the controls on the was studied and it came out that all the four controls have a positive impact such that the ITNs can reduce to zero as the value of ITNs approaches one. Pontryagin’s Maximum Principle was applied to analyse the optimal control model theoretically and the optimality system was solved numerically through an iterative scheme. The optimal plots (Figs. 4-8) reveal that best control strategies for malaria elimination is the combination of ITN, Chemoprophylaxis and Improved Clinical Treatment. However, the Cost-effectiveness Analysis points out that ITN is economically best solution for fighting malaria in poor malaria endemic areas.