_applied_  
_sciences_  
_Impact of Quarantine and Vaccination Policies on Viral Load_  
[PERSON] 1, [PERSON] 2, [PERSON] 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 3  
model was shaped to its current compartmental forms in 1978 [6]. Compartmental models, introduced to study epidemics, are either stochastic or deterministic. Stochastic models include elements of random variation and probability distributions, while deterministic ones give the same result every time they run since they consider average rates with no random deviations [7]. During the 1980s, studies based on network theory were also added to the epidemiology research arena [8]. Stochastic compartmental models and theoretical networks (random, small world, etc.) were combined to facilitate the study of epidemics in disease outbreaks, such as that of HIV. Both stochastic and deterministic models can employ either continuous or discrete formulations. The booming of computational power and software development in the last decades allowed scientists to represent models by systems of Ordinary Dynamical Equations (ODE) which can be solved numerically [9].  
Contemporary policies to eliminate a pandemic can be grouped into two main categories. Quarantine and vaccination policies [10]. Quarantine policies can implement either as prevention or contagion rehabilitation of an infection. It is the movement restriction of persons who are presumed to have been exposed to a contagious disease but are not ill, either because they did not become infected or because they are still in the incubation period. Isolation, containment and social distancing are also some other public health policies to control epidemics [11]. Vaccination policies are the decision to vaccinate individuals and provide immunity to the communities. Decision-makers should take intoaccount factors such as time of vaccination, age groups and vaccine ethics [12]. In this study the vaccines are similar and vaccination effects are the same for all.  
Viral load is the amount of strain in the body of an individual. Its value is connected to the severity of the disease and the shedding volume [13]. Current studiesin the viral load focus on comparing various individual viral loads and their role in the epidemic's evolution [14; 15], as in the COVID-19 epidemic [16]. Researchers try to study the kinetics of the using mostly stochastic models [17]. However, it is also important to take into account the total viral load in the community and its dependence on quarantine and vaccination policies that may be applied.  
In the current work, a scalable compartmental approach based on ODE systems is applied to study viral and/or bacterial load in a pandemic, under the condition that individuals can freely move from one compartment to another. Initially, we examine the viral load in the original SIR system. Secondly, we introduce a model with a cyclic (waving) approach. Then, we add the quarantine and vaccination procedures, separately in combination, to study the beneficial impact of respective policies. The equilibrium states are investigated, as well as their dependence on the different policies. The viral load in each model is determined and is used as a marker for inter-model comparisons and for monitoring the pandemic evolution.