The effect of demographic and environmental variability on disease outbreak for a dengue model with a seasonally varying vector population

• Published in: Mathematical biosciences Vol. 331; p. 108516
• Main Authors: Nipa, Kaniz Fatema, Jang, Sophia R.-J., Allen, Linda J.S.
• Format: Journal Article
• Language: English
• Published: United States Elsevier Inc 01.01.2021; Elsevier Science Ltd
• Subjects: Approximation; Branching (mathematics); Branching process approximation; Continuous-Time Markov Chain (CTMC); Demographics; Dengue fever; Dengue model; Differential equations; Environment models; Environmental effects; Epidemic models; Epidemics; Health risks; Infectious diseases; Itô stochastic differential equations (SDE); Markov chains; Mathematical analysis; Mosquitoes; Outbreaks; Periodicity; Probability theory; Rainfall; Seasonal variations; Stochastic models; Stochastic processes; Stochasticity; Variability; Vector-borne diseases; Vectors; Continuous-Time Markov Chain (CTMC); Itô stochastic differential equations (SDE); Dengue model; Branching process approximation
• ISSN: 0025-5564; 1879-3134
• DOI: 10.1016/j.mbs.2020.108516

Seasonal changes in temperature, humidity, and rainfall affect vector survival and emergence of mosquitoes and thus impact the dynamics of vector-borne disease outbreaks. Recent studies of deterministic and stochastic epidemic models with periodic environments have shown that the average basic reproduction number is not sufficient to predict an outbreak. We extend these studies to time-nonhomogeneous stochastic dengue models with demographic variability wherein the adult vectors emerge from the larval stage vary periodically. The combined effects of variability and periodicity provide a better understanding of the risk of dengue outbreaks. A multitype branching process approximation of the stochastic dengue model near the disease-free periodic solution is used to calculate the probability of a disease outbreak. The approximation follows from the solution of a system of differential equations derived from the backward Kolmogorov differential equation. This approximation shows that the risk of a disease outbreak is also periodic and depends on the particular time and the number of the initial infected individuals. Numerical examples are explored to demonstrate that the estimates of the probability of an outbreak from that of branching process approximations agree well with that of the continuous-time Markov chain. In addition, we propose a simple stochastic model to account for the effects of environmental variability on the emergence of adult vectors from the larval stage. •Single-serotype dengue models with seasonal forcing in the vector population.•Seasonality, demographic and environmental variability drive dengue dynamics.•Markov chain and stochastic differential equation models account for variability.•Branching process estimates obtained for periodic probability of a dengue outbreak.•Outbreaks depend on number of infected hosts and vectors and time of introduction.