Dynamical behaviour of the proposed system.

<p>Dynamical behaviour of the proposed system.</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

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

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

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

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

<p>(A) A <i>SPN</i> consists of a set of places {<i>p</i>₁, <i>p</i>₂, <i>p</i>₃}, set of transitions {<i>t</i>₁, <i>t</i>₂}, rates <i>μ</i>₁, <i>μ</i>₂ and an initial marking <i>M</i>₀ = (2, 2, 0). In case of this example <i>t</i>₁ is 2 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>. (C) The <i>Markov Chain</i> obtained from the reachability graph in (B). Every reachable marking of the <i>SPN</i> is associated with a state of the <i>Markov Chain</i> and a transition between states is labelled with the product of the enabling degree and rate.</p

Dynamic behaviour of infectious class with and without quarantine.

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

Behaviour of susceptible versus recovered compartment.

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