force of infection

{{short description|Rate at which susceptible individuals acquire an infectious disease}}

In epidemiology, force of infection (denoted $\backslash lambda$) is the rate at which susceptible individuals acquire an infectious disease.{{cite journal |pmid= 19765352|year= 2010|last1= Hens|first1= N.|last2= Aerts|first2= M.|last3= Faes|first3= C.|last4= Shkedy|first4= Z.|last5= Lejeune|first5= O.|last6= Van Damme|first6= P.|last7= Beutels|first7= P.|title= Seventy-five years of estimating the force of infection from current status data|journal= Epidemiology and Infection|volume= 138|issue= 6|pages= 802–12|doi= 10.1017/S0950268809990781|hdl= 10067/791410151162165141|hdl-access= free}} Because it takes account of susceptibility it can be used to compare the rate of transmission between different groups of the population for the same infectious disease, or even between different infectious diseases. That is to say, $\backslash lambda$ is directly proportional to $\backslash beta$; the effective transmission rate.

:$$

\lambda = \frac {\mbox{number of new infections}} {\mbox{number of susceptible persons exposed} \times \mbox{average duration of exposure}}

Such a calculation is difficult because not all new infections are reported, and it is often difficult to know how many susceptibles were exposed. However, $\backslash lambda$ can be calculated for an infectious disease in an endemic state if homogeneous mixing of the population and a rectangular population distribution (such as that generally found in developed countries), rather than a pyramid, is assumed. In this case, $\backslash lambda$ is given by:

:$$

\lambda = \frac {1} {A}

where $A$ is the average age of infection. In other words, $A$ is the average time spent in the susceptible group before becoming infected. The rate of becoming infected ($\backslash lambda$) is therefore $1/A$ (since rate is 1/time). The advantage of this method of calculating $\backslash lambda$ is that data on the average age of infection is very easily obtainable, even if not all cases of the disease are reported.{{cn|date=May 2023}}