Exploring the influencing factors on stochastic codynamics for nonlinear fractional epidemic model with control strategies

Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2), responsible for the COVID-19 pandemic, primarily affects the respiratory system. Co-infections involving malaria and COVID-19 (M-COV) have been documented across multiple countries, making it crucial to understand the underlying mechanisms of such interactions. To address this, we aim at developing a continuous-time fractional M-COV co-infection model. The framework incorporates white noise and Brownian motion to examine the interactions among twelve compartments, which are formulated through a system of twelve-dimensional partial differential equations. The model’s biophysical validity is established by proving the positivity and boundedness of its solutions. Equilibrium points and their respective existence criteria are determined, ensuring a comprehensive understanding of the system’s dynamics. Additionally, we analyze the stabilization conditions for both Plasmodium falciparum (malaria) and COVID-19-exclusive sub-models. Notably, under certain conditions, when the reproduction number of the sub-model falls below unity, a backward bifurcation in the malaria-only population may occur. Despite this, the broader M-COV system maintains local asymptotic stability, though the presence of backward bifurcation limits global stability. Furthermore, the robustness of the proposed framework is validated using stochastic Lyapunov functional analysis. Under specific conditions, we explore the stationary distribution and the potential for co-infection eradication. A deterministic-probabilistic modeling strategy is implemented in MATLAB to investigate the long-term behavior of the system. The study also highlights the advantages of piecewise differential techniques, which allow researchers to incorporate distinct characteristics across different time-period stages.