Malaria, a parasite based infectious disease spread by anopheles mosquitos, is widespread, affecting people of all ages. Malaria blood-borne pathogens cause approximately 110 million clinical cases of malaria and between one and two million deaths associated with Plasmodium falciparum each year worldwide, including Bangladesh. In this paper, we develop a human–mosquito transmission dynamics malaria model and analyse of the system properties and solutions. Both analytical and numerical results suggest that if the basic reproduction number R0<1, the disease-free equilibrium is asymptotically stable, meaning malaria naturally dies out. Further, if R0>1, the malaria disease persists in the population. We also provide the model calibration to estimate parameters with year-wise malaria incidence data from 2001 to 2014 in Bangladesh. Sensitivity analysis also performs to identify the most critical parameters through the partial rank correlation coefficient method. We found that the contact rate of both humans and mosquitoes had the most extensive influence on malaria prevalence. Finally, the impacts of progression rate, disease-related death rate, recovery rate and the rate of losing immunity are examined through numerical simulations and graphical analysis.