Seasonal variability and stochastic branching process in malaria outbreak probability

Area of Science:

• Epidemiology
• Mathematical Biology
• Parasitology

Background:

• Malaria, a fatal parasitic disease transmitted by mosquitoes, poses a significant threat, particularly in Bangladesh due to its geographical location.
• Vector-host models are essential for understanding disease dynamics and predicting outbreaks.
• Stochastic behavior and seasonal variability are key factors influencing malaria transmission.

Purpose of the Study:

• To analyze the dynamics of malaria transmission using vector-host models.
• To investigate the impact of seasonal variability on disease outbreaks.
• To calculate the probability of malaria outbreaks using stochastic modeling.

Main Methods:

• Developed a continuous-time Markov chain (CTMC) representation for malaria transmission.
• Incorporated seasonal variability into a time-varying stochastic vector-host model.
• Utilized phase plane analysis and branching process approximation to study disease characteristics and outbreak probability.

Main Results:

• Disease outbreak probability is dependent on the number of infected hosts and vectors.
• Periodic transmission rates significantly influence the likelihood of an outbreak.
• The basic reproduction number (R0) was derived, providing a basis for analyzing epidemic dynamics.

Conclusions:

• Seasonal variability critically affects malaria transmission dynamics.
• The probability of a malaria outbreak is influenced by time-dependent factors and initial infection counts.
• Branching process approximation is effective for large populations with a basic reproduction number below 1, aiding in disease prevention planning.