Dynamic behaviour of infectious class with and without quarantine.

<p>Dynamic behaviour of infectious class with and without quarantine.</p

Reachability Graph.

<p>Fig 13 shows the reachability graph consisting of a total of 56 unique markings and 273 transitions with initial marking <i>M</i>₀ = (2, 0, 1, 0, 0, 0).</p

Example of a <i>Standard Petri Net</i>.

<p>(A) A <i>Petri Net</i> consists of a set of places {<i>p</i>₁, <i>p</i>₂}, set of transitions {<i>t</i>₁, <i>t</i>₂} and an initial marking <i>M</i>₀ consisting of one token in place <i>p</i>₁. In this example, the weight of the arcs are not specified so every arc weighs 1. The enabling degree of a transition is determined by number of times a transition can be fired without depositing a token again to the input place of a transition through self-loop. In case of above example <i>t</i>₁ is 1 enabled and <i>t</i>₂ is 0 enabled from the initial marking <i>M</i>₀. (B) The reachability graph obtained from initial marking <i>M</i>₀ of the <i>Petri Net</i>. A reachability graph consist of set of places which can be reached from <i>M</i>₀ and arcs which are labelled with enabled transitions. This graph shows one cycle: (1, 0) → (0, 1) → (1, 0) and contains no deadlock. To reach marking <i>M</i>₁ = (0, 1) from the marking <i>M</i>₀ = (1, 0), a firing sequence <i>S</i> consist of a transition <i>t</i>₁ once and transition <i>t</i>₂ zero time.</p

<i>Model Checking</i> Process.

<p>Model checker takes the system model and property specification as input and generates two types of output: (1) true which means property is satisfied (2) false with counter example which means property is not satisfied.</p

Dynamical behaviour of the proposed system without Quarantine.

<p>Dynamical behaviour of the proposed system without Quarantine.</p

Flow chart of the Proposed Framework.

<p>After reviewing literature, <i>SEIR</i> model is selected and a new <i>SEIDQR(S/I)</i> is proposed by modifying SEIR model. <i>SPN</i> of the proposed model is constructed and analysed in <i>Snoopy</i> and <i>Charlie</i>, after which the system is converted to <i>CTMC</i> and specifications are encoded in CSL for quantitative analysis in <i>PRISM</i> model checker.</p

Behaviour of susceptible versus recovered compartment.

<p>Behaviour of susceptible versus recovered compartment.</p

Behaviour of infectious compartment when infection rate is greater than the recovery rate.

<p>Behaviour of infectious compartment when infection rate is greater than the recovery rate.</p

The states and the transitions of <i>SEIDQR(S/I)</i> model.

<p>The rectangles represent the compartments and the arrows represent the movement of hosts from one compartment to another. The labels on the rectangles indicate the type of compartment i.e. susceptible, exposed, infectious, delayed, quarantined and recovered. The labels on the arrows indicate the rate of transmission of hosts from one compartment to another.</p

The <i>SPN</i> of the Proposed model.

<p>The <i>SPN</i> of the proposed model consists of a set of places <i>P</i> = {<i>S</i>_<i>US</i>, <i>E</i>_<i>XP</i>, <i>I</i>_<i>NF</i>, <i>D</i>_<i>EL</i>, <i>Q</i>_<i>UA</i>, <i>R</i>_<i>EC</i>} and set of transitions <i>T</i> = {<i>t</i>₁, <i>t</i>₂, <i>t</i>₃, <i>t</i>₄, <i>t</i>₅, <i>t</i>₆, <i>t</i>₇, <i>t</i>₈, <i>t</i>₉, <i>t</i>₁₀, <i>t</i>₁₁, <i>t</i>₁₂, <i>t</i>₁₃} and initial marking <i>M</i>₀ = (1000, 0, 1, 0, 0, 0).</p