Mathematical modelling of malaria–typhoid co-infection: human–vector–environment dynamics and implications for integrated disease control

Malaria and typhoid fever remain major public health challenges across many low- and middle-income countries, where their overlapping clinical presentation frequently complicates diagnosis and management. Despite numerous epidemiological studies, relatively few mathematical models have jointly examined the transmission dynamics of malaria–typhoid co-infection while simultaneously accounting for vector transmission, environmental bacterial contamination, chronic carriers, treatment, and disease interaction. This study develops and analyzes a deterministic co-infection model to investigate the transmission dynamics of malaria and typhoid fever and to identify the epidemiological factors that most strongly influence disease persistence and control. A deterministic compartmental model consisting of human, mosquito, and environmental bacterial compartments was formulated and analyzed. The disease-free equilibrium was established, and the basic reproduction numbers for malaria ( \(R_{0M}\) ) and typhoid ( \(R_{0T}\) ) were derived using the next-generation matrix approach. Local stability, bifurcation behavior, and sensitivity analyses were performed to characterize disease dynamics. Local sensitivity indices and Latin Hypercube Sampling coupled with Partial Rank Correlation Coefficients (LHS–PRCC) were employed to identify the dominant transmission drivers, while numerical simulations were conducted to examine the temporal evolution of the epidemiological compartments and intervention contour analyses. The model admits a locally asymptotically stable disease-free equilibrium whenever the final reproduction threshold satisfies \(R_0<1\) , where \(R_0=\max \{R_{0M},R_{0T}\}\) . Numerical evaluation yielded \(R_{0M}=1.6556\) and \(R_{0T}=1.5909\) , indicating that malaria constitutes the dominant transmission pathway. Bifurcation analysis revealed backward bifurcation for the malaria subsystem and forward bifurcation for the typhoid subsystem, demonstrating that reducing \(\mathcal {R}_{0M}\) below unity alone may not guarantee malaria elimination, whereas typhoid elimination follows the classical threshold condition. Local and global sensitivity analyses consistently identified mosquito biting rate, mosquito mortality, malaria transmission probabilities, human recruitment, typhoid transmission rate, environmental sanitation, bacterial carrying capacity, and treatment-related parameters as the principal determinants of disease transmission. Numerical simulations showed rapid early epidemic growth followed by convergence to an endemic equilibrium, with the co-infected population remaining substantially lower than the mono-infected populations. Contour analyses further demonstrated that simultaneous vector control and environmental sanitation substantially enlarge the parameter regions where \(\mathcal {R}_0<1\) , emphasizing the importance of integrated intervention strategies. The proposed malaria–typhoid co-infection model demonstrates that sustained transmission is driven by distinct but interacting vector and environmental pathways. The coexistence of backward bifurcation in malaria and forward bifurcation in typhoid highlights the need for disease-specific control strategies, while the sensitivity and intervention analyses show that combining effective vector management, environmental sanitation, prompt treatment, and reduction of chronic bacterial carriage provides the greatest potential for reducing disease burden and interrupting transmission in endemic settings.