Transmission Dynamics of Malaria in Ghana

Abstract

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

Simulating the council-specific impact of anti-malaria interventions: A tool to support malaria strategic planning in Tanzania

“…WHO) [2,35,36]. Mathematical models have been applied in various studies at high resolution in all sub-Saharan African (SSA) countries [29,30,37,38], or more local levels, for example in Kenya [39][40][41][42][43], Nigeria [31,32,44], South Africa [45,46], Ghana [41,47,48], Uganda [41], Mozambique [49], and Tanzania [41], and modelling is also being done in Asia [50][51][52]. Previous country specific model predictions were either generalised based on archetypical settings at regional level (admin 1) [31], at 5x5 km 2 level [29], or applied for a specific sub-area of the country [33,[53][54][55].…”

Applied mathematical modelling to inform national malaria policies, strategies and operations in Tanzania

“…Mathematical models have been applied for various countries at varying resolutions, examples include sub-Saharan African (SSA) countries [15,[20][21][22], Ghana [23,24], Kenya [25,26], Mozambique [27,28], Nigeria [16,17,29], Uganda [30], South Africa [31], Zambia [32][33][34][35], and the Asia-Pacific Region [36,37]. In those examples, modelling was used to investigate relevant transmission dynamics, intervention effectiveness or for stratification.…”

Towards malaria control and elimination in Ghana: challenges and decision making tools to guide planning

“…The focus of these models was on investigating the basic reproductive number, conducting stability analyses and simulation studies to determine when Ghana could achieve malaria free status. [25] The second model, with same structure, sought to test the impact of interventions on malaria transmission in Ghana. [26] These two models were developed and parameterised using country-wide annually aggregated health facility reported malaria incidence data.…”

“…While some models [26] aim at Ghana in general, they do not consider the varying epidemiological settings accounting for transmission variability due to local factors such as climatic and environmental factors. Other models [25,27,31,52–54] were developed on a smaller scale and more tailored to data from specific districts. Almost all the models developed in Ghana, as mentioned above, used data from communities located in either the forest or coastal ecological zones.…”