**1. Introduction**

The WHO officially declared the COVID-19 pandemic more than a year ago, i.e., on 11 March 2020 [1]. COVID-19 is caused by the SARS-CoV-2 virus, which is thought to have originated in Wuhan, China. At the time of writing this paper, over 247,434,286 cases have been reported across 223 countries with a total of 5,014,576 people having died [2]. Since the announcement of the pandemic, almost every country has made a concerted effort to control the virus, but the number of COVID-19 infections is still climbing in many parts of the world. Although more than a year has passed, there remain some unwanted effects of the pandemic impacting almost every facet of human life. In terms of health, economy, and other human aspects, COVID-19 is still considered a very dangerous new disease. After more than a year since its first appearance, COVID-19 is still reoccurring in many parts of the world for multiple reasons including mutation of the virus into different variants. This is one of the reasons why most infected countries are failing in battling the disease.

Some works in the literature have shown that convalescent plasma transfusion (CPT) is currently being used as an alternative medical treatment method for COVID-19 patients. This treatment has been successfully implemented and has resulted, in particular, in increasing the number of survivors from the disease and reducing the number of deaths in moderate and severe cases. Convalescent plasma transfusion involves the use of blood

**Citation:** Husniah, H.; Ruhanda, R.; Supriatna, A.K.; Biswas, M.H.A. SEIR Mathematical Model of Convalescent Plasma Transfusion to Reduce COVID-19 Disease Transmission. *Mathematics* **2021**, *9*, 2857. https:// doi.org/10.3390/math9222857

Academic Editor: Arsen Palestini

Received: 13 October 2021 Accepted: 3 November 2021 Published: 10 November 2021

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plasma to assist COVID-19 patients with the process of recovery. Blood plasma is taken from people who have recovered from COVID-19 and who have antibodies against COVID-19 in their blood. Since there is currently no approved treatment for COVID-19, the US Food and Drug Administration has approved convalescent plasma therapy for people with COVID-19 [3]. Before blood can be transfused to a patient, it must be processed to produce plasma and antibodies through the removal of blood cells. Upon transfusion, this plasma has the ability to boost the attack rate of the body of its recipient against the virus. This treatment is commonly referred to as CPT [4,5]. It has been documented that many governments have already advocated for the use of this method to combat COVID-19. Among the governments that have implemented CPT in their countries are Indonesia, the United States, the United Kingdom, Australia, and India [6–8].

CPT is not a new concept. For more than a century, CPT has been used as a passive immunization strategy in the prevention and treatment of epidemic infections [9]. The first documented use of CPT dates back to at least 1918–1920, when it was used to treat Spanish influenza A (H1N1) pneumonia, but it could be even older [10]. This method is being used as a potential therapy for patients infected with COVID-19 [11]. Several studies have also shown that convalescent plasma can reduce the risk of mortality in a patient receiving CPT treatment [12,13]. Many works have shown that the result is a reduction in a patient's mortality risk as well as an increase in viral clearance [14].

Despite its increasing popularity as an alternative clinical treatment for COVID-19 patients, a recent finding [14] pointed out that "most clinical studies, in particular case reports and case series, were of poor quality. Only 1 RCT [randomized controlled trials] was of high quality". Hence, the authors argued that "future research is necessary to fill the knowledge gap regarding prevention and treatment for patients with COVID-19 with CP while other therapeutics are being developed". Currently, medical and epidemiological studies use not only clinical methods but include other forms or approaches such as mathematical modeling. The other shortcomings of studies on CPT are that, to date, the impacts of CPT applications on the population have remained unclear. The present study had the objective of filling in this gap via a mathematical approach in the hope that new insight could be gained regarding the effect of CPT applications, especially at the population level.

Only a few mathematical modeling papers (e.g., [15,16]) have addressed this issue mathematically. The authors of [16] performed preliminary work on this issue and presented mathematical models not specific to COVID-19 but that take the form of general discrete time SIR and SEIR models [16]. In the present paper, a mathematical modeling approach was used to answer an important question on the effect of convalescent plasma transfusion on the reduction of COVID-19 transmission at the population level. The assumptions used in the development of the model were taken from the literature, showing that the majority of patients who received CPT recovered and had lower mortality rates than patients who were not treated using CPT transfusion. In the developed model, we assumed that the effect of CPT would be to increase the rate of recovery. A continuous SEIR epidemic model was used to describe the transmission of COVID-19. The SEIR model can appear in the form of discrete models [17,18], but we used the continuous form here, since this is the most often used version in the literature.
