A Host–Vector Compartmental Model for Malaria Transmission Dynamics in Sub-Saharan Africa: Vaccination, Clinical Staging, and Intervention Analysis

Source abstract

Background and Motivation: Malaria remains one of the most devastating vector-borne diseases globally, with over 240 million cases and approximately 600,000 deaths annually, disproportionately affecting children under five and pregnant women in sub-Saharan Africa. Nigeria alone contributes about 27 percent of global cases. Despite progress in control, transmission persists due to insecticide and drug resistance, incomplete intervention coverage, and the recent introduction of partially effective vaccines, creating an urgent need for mathematical frameworks that can evaluate integrated control strategies. Novelty and Objectives: This study develops an eleven-compartment host–vector model that simultaneously incorporates eight human disease stages (susceptible, vaccinated, exposed, asymptomatic, mildly infected, severely infected, treated, recovered) and three vector stages (susceptible, exposed, infectious). The model accounts for partial vaccination with explicit vaccine-failure dynamics, multi-stage clinical progression, waning immunity, treatment at every clinical stage, and re-infection. No previous classical ODE model calibrated to Nigerian data combines all of these features. Methodology: Positivity and boundedness of solutions are established. The disease-free equilibrium is derived in closed form and the basic reproduction number is obtained via the next-generation matrix method. Local asymptotic stability of the disease-free equilibrium is proved by the Routh–Hurwitz criterion; existence and local and global stability of the endemic equilibrium are analysed; and backward bifurcation is characterised using the Centre Manifold Theory of Castillo-Chavez and Song. Local and global (LHS–PRCC) sensitivity analyses identify the most influential parameters. The model is fitted to annual Nigerian malaria incidence data (2010–2022) from NCDC and WHO sources. Key Theoretical Findings: The disease-free equilibrium is locally asymptotically stable when the basic reproduction number is less than unity. The model exhibits backward bifurcation under biologically plausible conditions, implying that reducing the reproduction number below one may be insufficient for elimination. Sensitivity analysis ranks the mosquito biting rate and the human-to-vector and vector-to-human transmission probabilities as the dominant positive drivers, while treatment rates, vaccination coverage and recovery rates are the strongest negative (protective) drivers. Principal Numerical Results: Calibration yields a baseline reproduction number of approximately 2.47 for Nigeria, confirming an endemic state. Numerical simulations demonstrate that combining treatment coverage exceeding 80 percent, vaccination coverage exceeding 75 percent, and vector-density reduction exceeding 70 percent can reduce transmission by up to 85 percent. These quantitative thresholds provide concrete guidance for Nigeria’s National Malaria Elimination Programme.