A study on mathematical modeling and control of leptospirosis transmission dynamics during a hurricane with asymptomatic measures

Abstract

In order to examine the dynamics of disease transmission across human, animal, and environmental compartments, this study creates a unique fractal-fractional leptospirosis model utilizing the Mittag-Leffler kernel. Important memory effects and hereditary characteristics of illness transmission are included in the model. Lyapunov functions is used to examine global stability and fixed-point theory to prove the existence and uniqueness of solutions. Finding equilibrium points, calculating the basic reproduction number R0, and doing a thorough parameter sensitivity analysis are examples of analytical outcomes. The importance of memory effects in transmission dynamics is shown by numerical simulations that show that reduced fractional order ξ and transmission rates β considerably impede illness progression. Flip bifurcation analysis is performed and it has been verified that model behaviour is bounded and flip bifurcation does not exist. According to our findings, R0 may be successfully decreased by strategically reducing contact rates ψ,ρ and environmental contamination kθ, as well as by improving recovery rates bθ,ωθ and sanitation measures πθ. The visual confirmation of endemic equilibrium stability and compartmental interactions is provided by the 3D phase space analysis. This fractal-fractional architecture gives a strong mathematical basis for creating focused leptospirosis control techniques, as well as improved forecasting power.