Presentation Information
[MS07-02]Long-term Dynamics of Solutions to a Vector-borne Disease Model with Piecewise-constant Transmission Rates
*Destiny Lutero1,2, Timothy Robin Teng2, Mark Anthony Tolentino2 (1. University of the Philippines Los Baños (Philippines), 2. Ateneo de Manila University (Philippines))
Keywords:
vector-borne disease,switching transmission rates,mathematical analysis,non-autonomous systems,SEIRSEI model
Infectious diseases like dengue or malaria are often influenced by time-dependent conditions such as seasonality, which can lead to fluctuations in transmission rates. To capture these variations and understand how they influence disease spread over time, general and long-term patterns of disease transmission can be analyzed by using compartmental models that represent the dynamics of the disease. Here, we consider a general vector-borne disease (SEIRSEI) model consisting of differential equations describing the dynamics of susceptible, exposed, infected, and recovered individuals within the host population, and the susceptible, exposed, and infected vectors responsible for the disease transmission. The transmission rates in the model are assumed to be piecewise constant to reflect real-world scenarios since disease transmission can change abruptly, such as due to seasonal variations, environmental factors, or control interventions.
The disease-free equilibrium was found to be the only constant solution. Qualitative analysis was performed using switched systems theory. Threshold parameters Rhmax and Rvmax were determined using the next-generation matrix approach. It was established that solutions converge to the disease-free equilibrium whenever both Rhmax and Rvmax are less than 1. Even then, as exhibited by some simulations, disease eradication is still possible if at least one of Rhmax and Rvmax is greater than one. The results offer insights into optimal strategies for controlling vector-borne diseases, particularly in environments where transmission rates are not constant but vary over time.
The disease-free equilibrium was found to be the only constant solution. Qualitative analysis was performed using switched systems theory. Threshold parameters Rhmax and Rvmax were determined using the next-generation matrix approach. It was established that solutions converge to the disease-free equilibrium whenever both Rhmax and Rvmax are less than 1. Even then, as exhibited by some simulations, disease eradication is still possible if at least one of Rhmax and Rvmax is greater than one. The results offer insights into optimal strategies for controlling vector-borne diseases, particularly in environments where transmission rates are not constant but vary over time.