**7. Insights into conceptual results from mathematical model**

Two approaches can be used to determine the time-scale of disease transmission by utilizing data on individual-to-individual chains of transmission. Estimation of disease generation time (T) is one approach. It may be defined as the expected length of time between infection of an index case and infection of his or her secondary cases. It is the duration of latency plus infectiousness. The generation time of measles is approximately 14 days. A short generation time indicates rapid transmission whereas a longer T suggests slower spread but longer carriage. The duration of carriage of pathogens represents an upper limit on T and it can be concluded that directly transmitted acute infections have T < 1 month and chronic infections have T values in the order of months or years [19]. But, determination of generation time becomes complicated if the disease possesses asymptomatic periods of infection of variable or unknown duration. Another quantity that is estimated is the serial interval. It is the time between clinical onset of symptoms in the index case and the clinical onset of symptoms in the average secondary case [2].

In a system of differential equations, an equilibrium point is a point at which all the equations equal zero. This indicates that the state of the system is not changing. In a mathematical model, a disease-free equilibrium (DFE) and one or more endemic equilibria are present. The DFE indicates that the entire population is susceptible since not a single infective exists in the population. Endemic equilibrium is steady-state equilibrium produced by spread of infection. If the solutions of the equations near the equilibrium points tend toward the points with time, they are said to be locally stable. An equilibrium point is referred to as globally asymptotically stable if the behavior of the system at any point tends toward the equilibrium point as time tends toward infinity.

The stability of DFE and existence of other nontrivial equilibria can be determined from a ratio, known as basic reproduction ratio [20]. A very brief description of the essential conceptual results from mathematical modeling has been given in Table 1.


**Table 1.** Glossary of important parameters associated with mathematical modeling of infectious diseases
