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

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

Behaviour of susceptible versus recovered compartment.

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

Dynamic behaviour of infectious class with and without quarantine.

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

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

Quarantine effect on different compartments.

<p>Quarantine effect on different compartments.</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

<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