Seasonal variability and stochastic branching process in malaria outbreak probability

• Published in: Acta tropica 2024-09, Vol.257, p.107311, Article 107311
• Main Authors: Akhi, Asma Akter, Mohammad, Kazi Mehedi, Kamrujjaman, Md
• Format: Article
• Language: English
• Subjects: Animals; Bangladesh - epidemiology; Branching process; CTMC; Disease Outbreaks; Female; Humans; Malaria; Malaria - epidemiology; Malaria - transmission; Markov Chains; Mosquito Vectors - parasitology; Probability; Probability outbreak; Seasonality; Seasons; Stochastic Processes; Vector-borne disease
• ISSN: 0001-706X; 1873-6254; 1873-6254
• DOI: 10.1016/j.actatropica.2024.107311

•This study will introduce a malaria model and formulate its corresponding Continuoustime Markov chain (CTMC).•The number of infected vector and infected host populations of vector-borne diseases depends on seasonal variability.•The threshold quantity R0 is not same for the deterministic and periodic environments.•Seasonal variation influences the probability of disease outbreaks.•Random fluctuations in malaria modeling depend primarily on factors such as variations in mosquito biting rates, human mobility, and the efficacy of control interventions.•These stochastic elements introduce uncertainty into disease transmission dynamics and affect the accuracy of predictions and intervention planning. The best strategy for successfully controlling malaria transmission is suggested.•The analysis play the important role to understand the impact of various parameters and their stochastic behavior in the malaria model to prevent malaria outbreaks. Background: Malaria is the world’s most fatal and challenging parasitic disease, caused by the Plasmodium parasite, which is transmitted to humans by the bites of infected female mosquitoes. Bangladesh is the most vulnerable region to spread malaria because of its geographic position. In this paper, we have considered the dynamics of vector-host models and observed the stochastic behavior. This study elaborates on the seasonal variability and calculates the probability of disease outbreaks. Methods: We present a model for malaria disease transmission and develop its corresponding continuous-time Markov chain (CTMC) representation. The proposed vector-host models illustrate the malaria transmission model along with sensitivity analysis. The deterministic model with CTMC curves is depicted to show the randomness in real scenarios. Sequentially, we expand these studies to a time-varying stochastic vector-host model that incorporates seasonal variability. Phase plane analysis is conducted to explore the characteristics of the disease, examine interactions among various compartments, and evaluate the impact of key parameters. The branching process approximation is developed for the corresponding vector-host model to calculate the probability outbreak. Numerous numerical results are accomplished to observe the analytical investigation. Results: Seasonality and contact patterns affect the dynamics of disease outbreaks. The numerical illustration provides that the probability of a disease outbreak depends on the infected host or v