<p>This study develops and analyzes a mathematical model for the co-infection dynamics of malaria and typhoid fever in humans, explicitly incorporating waning immunity and enhanced susceptibility due to prior infection. Co-infection arises because both diseases are driven by similar environmental and socio-economic factors, increasing the likelihood that individuals exposed to one disease become susceptible to the other. We derive the basic reproduction numbers for malaria-only, typhoid-only, and the coupled co-infection systems and investigate their stability properties, including the possibility of backward bifurcation. An optimal control framework is formulated and analyzed using Pontryagin’s Maximum Principle to identify cost-effective intervention strategies. Model parameters are estimated using least-squares fitting to reported case data from Delhi, India, and sensitivity analysis is performed to quantify the influence of one disease on the other. Our results indicate that malaria infection significantly increases susceptibility to typhoid, whereas typhoid infection has a comparatively weaker effect on malaria acquisition.</p>

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Exploring the Co-dynamics of Malaria and Typhoid: An In-Depth Analysis of a Mathematical Model and Cost-Effectiveness Optimal Control

  • Padmaja Tripathi,
  • Harish Chandra,
  • Ram Keval,
  • Vinod Baniya

摘要

This study develops and analyzes a mathematical model for the co-infection dynamics of malaria and typhoid fever in humans, explicitly incorporating waning immunity and enhanced susceptibility due to prior infection. Co-infection arises because both diseases are driven by similar environmental and socio-economic factors, increasing the likelihood that individuals exposed to one disease become susceptible to the other. We derive the basic reproduction numbers for malaria-only, typhoid-only, and the coupled co-infection systems and investigate their stability properties, including the possibility of backward bifurcation. An optimal control framework is formulated and analyzed using Pontryagin’s Maximum Principle to identify cost-effective intervention strategies. Model parameters are estimated using least-squares fitting to reported case data from Delhi, India, and sensitivity analysis is performed to quantify the influence of one disease on the other. Our results indicate that malaria infection significantly increases susceptibility to typhoid, whereas typhoid infection has a comparatively weaker effect on malaria acquisition.