On the delayed Ross-Macdonald model for malaria transmission

Area of Science:

• Epidemiology
• Mathematical Biology
• Vector-borne Disease Modeling

Background:

• Mosquito-borne diseases exhibit complex transmission dynamics involving feedback loops between human and mosquito populations.
• Significant time delays, primarily due to parasite incubation periods, complicate accurate modeling of disease spread.
• Understanding these delays is crucial for predicting disease prevalence and designing effective control strategies.

Purpose of the Study:

• To develop a mathematical model that explicitly incorporates incubation periods in both human and mosquito hosts.
• To analyze the impact of these time delays on the basic reproduction number (R0) of the disease.
• To assess the sensitivity of R0 to variations in incubation periods.

Main Methods:

• Development of a delayed Ross-Macdonald model to simulate disease transmission.
• Calculation of the basic reproduction number (R0) within the proposed delayed model.
• Sensitivity analysis to quantify the effect of incubation period durations on R0.

Main Results:

• The basic reproduction number (R0) was found to be a decreasing function of the incubation periods in both humans and mosquitoes.
• Increased incubation periods in either host population lead to a reduction in R0.
• Time delays significantly influence the overall transmission potential of the disease.

Conclusions:

• Extending incubation periods, through medical interventions or control measures, can effectively lower disease prevalence.
• The proposed delayed Ross-Macdonald model provides valuable insights into the role of incubation periods in disease dynamics.
• Targeting factors that prolong incubation periods represents a viable strategy for controlling mosquito-borne infections.