An optimal control model for COVID‐19, zika, dengue, and chikungunya co‐dynamics with reinfection

Abstract

The co‐circulation of different emerging viral diseases is a big challenge from an epidemiological point of view. The similarity of symptoms, cases of virus co‐infection, and cross‐reaction can mislead in the diagnosis of the disease. In this article, a new mathematical model for COVID‐19, zika, chikungunya, and dengue co‐dynamics is developed and studied to assess the impact of COVID‐19 on zika, dengue, and chikungunya dynamics and vice‐versa. The local and global stability analyses are carried out. The model is shown to undergo a backward bifurcation under a certain condition. Global sensitivity analysis is also performed on the parameters of the model to determine the most dominant parameters. If the zika‐related reproduction number is used as the response function, then important parameters are: the effective contact rate for vector‐to‐human transmission of zika ( , which is positively correlated), the human natural death rate ( , positively correlated), and the vector recruitment rate ( , also positively correlated). In addition, using the class of individuals co‐infected with COVID‐19 and zika ( ) as response function, the most dominant parameters are: the effective contact rate for COVID‐19 transmission ( , positively correlated), the effective contact rate for vector‐to‐human transmission of zika ( , positively correlated). To control the co‐circulation of all the diseases adequately under an endemic setting, time dependent controls in the form of COVID‐19, zika, dengue, and chikungunya preventions are incorporated into the model and analyzed using the Pontryagin's principle. The model is fitted to real COVID‐19, zika, dengue, and chikungunya datasets for Espirito Santo (a city with the co‐circulation of all the diseases), in Brazil and projections made for the cumulative cases of each of the diseases. Through simulations, it is shown that COVID‐19 prevention could greatly reduce the burden of co‐infections with zika, dengue, and chikungunya. The negative impact of the COVID‐19 pandemic on the control of the arbovirus diseases is also highlighted. Furthermore, it is observed that prevention controls for zika, dengue, and chikungunya can significantly reduce the burden of co‐infections with COVID‐19.

COVID-19 SIR model: Bifurcation analysis and optimal control

“…Recently, many researchers analyzed their COVID-19 model with backward [16] , forward–backward [17] , [18] , transcritical [19] , Hopf [20] bifurcations. With their model, they used optimal control variables to reduce COVID-19 [21] , [22] such as treatment, infection prevention, and vaccination.…”

Modelling the transmission of dengue, zika and chikungunya: a scoping review protocol

“…These mathematical and statistical models have even been widely used to study the spread of other diseases such as influenza, smallpox, HIV/AIDS and ebola, and have been used also in the context of healthcare-associated infections caused by antimicrobial resistance 13 33 34. Some VBDs studies have focused on measuring the impact of mathematical and statistical models, on the epidemiology of these diseases,13 35 the prediction of the number of cases,20 36 37 the climatic factors affecting the transmission of VBDs,38–44 whereas few of these studies have considered the coinfection and/or cocirculation between these and other diseases 17 45–51. Such modelling endeavours have contributed to the formulation of effective control strategies and interventions 2.…”

Mathematical Analysis of Fractal-Fractional Mathematical Model of COVID-19

“…A novel mathematical model has been created and analyzed to evaluate the interplay between COVID-19, Zika, chikungunya, and dengue co-dynamics. The aim is to determine the influence of COVID-19 on the dynamics of Zika, dengue, and chikungunya, as well as the reverse effect [2]. A proposed SEQAIHR model with saturated treatment is presented, and the biological feasibility of the model solutions is assessed, along with the calculation of the basic reproduction number (R0).…”