A dynamic optimal control model for COVID-19 and cholera co-infection in Yemen

Abstract

In this work, we propose a new dynamic mathematical model framework governed by a system of differential equations that integrates both COVID-19 and cholera outbreaks. The estimations of the model parameters are based on the outbreaks of COVID-19 and cholera in Yemen from January 1, 2020 to May 30, 2020. Moreover, we present an optimal control model for minimizing both the number of infected people and the cost associated with each control. Four preventive measures are to be taken to control the outbreaks: social distancing, lockdown, the number of tests, and the number of chlorine water tablets (CWTs). Under the current conditions and resources available in Yemen, various policies are simulated to evaluate the optimal policy. The results obtained confirm that the policy of providing resources for the distribution of CWTs, providing sufficient resources for testing with an average social distancing, and quarantining of infected individuals has significant effects on flattening the epidemic curves.

A fractional-order model for COVID-19 and tuberculosis co-infection using Atangana–Baleanu derivative

“…Mathematical models have been formulated for the dynamics of COVID-19 and its co-infection with other diseases [13] , [14] , [15] , [16] . Omame et al.…”

“… [15] studied a fractional order model for COVID-19, comparing the behaviour of the model using different derivatives (Caputo, Caputo-Fabrizio and Atangana-Baleanu), and showed that Caputo presented better results in the form of stability as compared to the other two operators. Furthermore, in a related research, the authors in [16] showed that the policy of providing resources for the distribution of chlorine water tablets, sufficient equipments for testing with adequate compliance on social distancing rules as well as quarantining infected individuals has significant impact in reducing COVID-19 ad cholera co-infections in Yemen.…”

Modeling and dynamic analysis of novel coronavirus pneumonia (COVID-19) in China

“…With the continuous spread of COVID-19 around the world, many scholars established a series of COVID-19 models to simulate its spread according to different situations and considering different influencing factors [39][40][41][42][43][44][45][46][47]. Aba et al [39] developed a fractional mathematical model for the dynamics of COVID-19 by taking into account quarantine, isolation, and environmental viral load factors.…”

“…The best exit time of the blocking strategy is analyzed through experiments. Hezam et al [41] presented a new mathematical model of cotransmission of COVID-19 and cholera, and then fitted the data of coinfection outbreaks in Yemen between 1 January 2020 and 30 May 2020. The study took into account the preventive measures taken to contain the outbreak: social distance, lockdown, number of tests, etc.…”

Controlling COVID-19 spread in Jakarta, Indonesia, using quarantine, testing and medical treatment

“…Optimal control analysis allows evaluating various scenarios of pandemic management. In COVID-19 administration, some recent studies have been conducted in the framework of optimal control theory to assess different measures of control, such as the effect of lockdown, hand washing, side effect controling, and sanitising (Zamir et al 2021) quarantine and selfisolation (Araz 2021), public health education (Madubueze et al 2020), health support system (Silva et al 2021), and possibly with other disease coexistence (Hezam et al 2021). As the outcome of studies, the best strategies with respect to certain performance criteria are recommended in term of the timing and the degree of interventions.…”