Modeling the Co-Infection Dynamics of COVID-19 and Dengue: Well-posedness, Analysis of Equilibrium Properties and Numerical Simulations

Abstract

COVID-19 is an infectious disease primarily transmitted to individuals through direct contact with respiratory droplets. The infection, caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), continues to spread globally infecting around 776 million confirmed cases, including over 7 million deaths. Meanwhile, dengue is a vector-borne disease caused by the Flaviviridae virus and is transmitted through bites from female mosquitoes, primarily Aedes aegypti and Aedes albopictus. It is estimated that 390 million dengue virus infections occur per year caused by four distinct virus serotypes?DENV-1, DENV-2, DENV-3, and DENV-4. The COVID-19 pandemic has further strained public health systems, particularly in tropical and subtropical regions where dengue is endemic. The overlapping presence of these infectious diseases heightens the risk of co-infection, posing additional diagnostic and treatment challenges. Co-infection of COVID-19 and dengue cases were already reported and confirmed in several countries. In this study, an 11-compartmentalized deterministic mathematical model was developed to understand the transmission dynamics of COVID-19 and dengue co-infection. This modeling approach was described by a system of ordinary differential equations (ODEs), examining disease progression over time, offering insights into potential co-infection scenarios and
control strategies to help guide public health interventions. The well-posedness of the model was verified, ensuring the existence and uniqueness of its solutions based on continuity, local Lipschitz conditions, and invariance over a compact feasible region. The basic reproduction number (R0), a significant indicator of disease transmission, was calculated using the Next Generation Method (NGM). Four equilibrium points were identified: the disease-free, COVID-19-only, dengue-only, and COVID-19-dengue co-infection equilibrium points. Threshold values of the basic reproduction number were calculated to establish the conditions for the existence and stability of the equilibrium points. These equilibrium points and threshold values provide critical insight into the conditions necessary for eradicating or controlling each disease, serving as a guide for developing interventions during different stages of an epidemic or pandemic. Furthermore, a phase diagram of two parameters sensitive to R0 (COVID-19 transmission ?c and dengue vector-to-human transmission Cvh) was established which presented six distinct regions of existence and stability states of the equilibrium points. These regions described different stable epidemiological scenarios whenever the parameter values were varied. Numerical simulations were conducted to verify the stability results and to analyze the effects of varied parameter values on the model solution. The simulations illustrated the positive impacts of reducing the recovery period on the spread of infections even with increasing transmission rates. This demonstrates the effectiveness of timely interventions, such as accelerated recovery through early diagnosis and treatment, in mitigating the severity of outbreaks. All the algebraic calculations, analysis, and numerical simulations were conducted with the aid of MATLAB R2023b and Maple software.