localbehaviourofbirthanotterprocesses

An birth rate

Mn deathrate

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P No events happen betweent and tth t Hutten htoch

Tn n Explintun P Tn he Hutten h

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in Ltitth duh och

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Xlt t Xlt Ayu 03h t och

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As h O M Ct kyu Mlt t O 1st order linear ODEa If you havedoneMATH215

DM solve withat AM

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J adM JDS t us the depends on the initialconditionIa enfants to tt K

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Remark If 174 then Mlt grows exponentiallyCsingle birth rate single

death rate

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single birth mate singledeath rate

If pi X M Ct Otto

condition on the value of Tn

P Tn Ch TntTnt hJohppft PCTnt Tnt h Tn t dt

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dt

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Joh pin et HM p Tnt h t dt